WALSH BUSINESS RITHMETIC JOHN HENRY WALSH GIFT OF WALSH'S BUSINESS ARITHMETIC BY JOHN H. VSfALSH ASSOCIATE SUPERINTENDENT OF SCHOOLS, THE CITY OF NEW YORK THE GREGG PUBLISHING COMPANY NEW YORK BOSTON CHICAGO SAN FRANCISCO ENGLAND: 21 HARRINGTON STREET, LIVERPOOL .^ COPYRIGHT, IQIQ, BY THE GREGG PUBLISHING COMPANY PREFACE IN this work the author has kept in mind the needs of boys and girls that have taken up a commercial course. The latter generally requires the completion of the arithmetical portion by the end of the first year of high school, and care has been taken to keep the problems within the capacity of pupils at this stage. Section I, Recording Business Transactions, presents briefly the clerical tasks likely to confront boys and girls upon their entrance into the business world; the calculations they are expected to make, the simple accounts they may be required to keep, the commoner "forms" they will use, etc. In Section II, Business Calculations, are given com- putations in percentage, trade discount, interest, and bank discount, made in the ways employed by business men. The arrangement that assigns Numbers and Pro- cesses to Section III does not mean that practice in these topics should be deferred until pupils have com- pleted the two previous sections. It is expected that the teacher will take from this portion of the book oral exercises for short daily drills, and abstract written ones weekly, for a longer period, to give facility and accuracy. In this section the pupil is shown the business way of reading numbers, some short cuts used in the several 5I> iv PREFACE processes, methods of combining two operations, and the manner in which results should be tested. In the remaining four sections are presented the arithmetical treatment of conditions arising in the various departments of business, taken in the order of their importance and of their availability for the in- struction of the young student. Every boy and every girl, regardless of his or her subsequent career, will be benefited by the work done in Problems of the Con- sumer, Chapter One of Section IV. In Chapter Two of this section, Problems of the Producer, those of the farmer have been chosen as typical. Later on, the baker is made the typical manufacturer. Broad treatment of conditions readily understandable has been the aim. It is not expected that all of the work here presented will be completed in a year. The teacher should make intelligent selections from the material offered. CONTENTS SECTION I RECORDING BUSINESS TRANSACTIONS CHAPTER ONE. LEARNING BY DOING PAGE PAGE A Boy's Cash Book 1 The Record Strip 11 Single-entry Ledger 3 The Bookkeeper 13 A Better Way 6 The Bank Account 18 CHAPTER Two. A GIRL IN BUSINESS Sales Girl . 24 The Time Clock 36 Bill Clerk 28 Time Sheet 38 Office Assistant 31 Wage Tables 41 CHAPTER THREE. SOME BUSINESS FORMS Invoices and Bills 44 Orders for Goods 52 Bill for Services, etc 49 Bill of Lading 54 Receipts 50 Freight Bill 55 SECTION II BUSINESS CALCULATIONS CHAPTER ONE. PERCENTAGE Finding the Percentage ... 58 Finding the Base 69 Aliquot-part Method .... 62 Rate of Profit 74 Finding the Rate 63 Net Profit 76 CHAPTER Two. COMMERCIAL DISCOUNT Cash Discount 77 Compound Discounts .... 80 List Prices 78 Quantity Discounts 87 CHAPTER THREE. SIMPLE INTEREST Lending Money 89 Aliquot-part Method .... 96 Promissory Notes 90 Sixty-day Method 102 Cancellation Method . 94 Six Per Cent Method . 107 vi CONTENTS CHAPTER FOUR. BANK DISCOUNT Discounting the Note .... 110 Term of Discount 116 Date of Maturity 114 Interest-bearing Note .... 120 SECTION III NUMBERS AND PROCESSES CHAPTER ONE. READING AND WRITING NUMBERS Reading Decimals 126 Roman Numbers 133 The Business Way 127 Graphs 187 Dictating Dollars and Cents . 129 Reading Meters 142 Writing Per Cents 132 Marking Goods 145 CHAPTER Two. PROPERTIES OF NUMBERS Composite Numbers .... 149 Least Common Multiple . . 151 Prime Numbers 149 Divisibility of Numbers . . . 152 CHAPTER THREE. REDUCTIONS Reducing Fractions 155 Denominate Numbers .... 159 Simplifying Complex Fractions 157 Reducing Fractions 166 Changing Decimals to Com- Reducing Decimals 175 mon Fractions 159 CHAPTER FOUR. SIGNS AND OPERATIONS Arithmetical Signs 183 Signs of Aggregations .... 185 Precedence of Signs 184 Indicating Operations .... 186 CHAPTER FIVE. ADDITION Counting Exercises 190 Adding Fractions 200 Adding Integers and Decimals 194 Adding Compound Numbers . 208 CHAPTER Six. SUBTRACTION Making Change 210 Subtracting Compound Num- Subtracting Integers .... 211 bers 226 Adding and Suhtnicting . . . 214 Time between Dates .... 228 Subtracting Fractions .... 222 CHAPTER SEVEN. SPECIAL TESTS Avoiding Mistakes 232 Casting out 9*s 234 Testing Resulta 232 Casting out ll's 237 CONTENTS vii CHAPTER EIGHT. MULTIPLICATION Multiplying and Adding . . . 244 Multiplying Decimals .... 275 Using Factors 251 Multiplying Denominate Num- Multiplying Fractions .... 260 bers 278 Aliquot Parts 265 CHAPTER NINE. DIVISION Dividing by an Integer . . . 279 Dividing by Factors .... 291 Short Division 281 Dividing by Multiples ... 293 Decimal Quotients 285 Decimal Divisors 300 Decimal Dividends 286 Abbreviated Division .... 307 Denominate Dividends . . . 288 Cancellation 311 Fractional Dividends .... 289 Division of Fractions .... 313 SECTION IV PRODUCTION AND CONSUMPTION CHAPTER ONE. PROBLEMS OF THE CONSUMER Family Budgets 318 Household Account 336 ''Balanced" Meals 324 Inventory 340 Efficiency in Home Keeping . 328 Insurance 342 CHAPTER Two. PROBLEMS OF THE PRODUCER Farming as a Business . . . 343 Milk Production 347 Receipts and Expenses . . . 346 Cost of a Crop 349 SECTION V FROM THE PRODUCER TO THE CONSUMER CHAPTER ONE. BUYING AND SELLING AGENCIES Commission 357 Selling Through a Broker . . 361 The Local Buyer 359 Storage 365 CHAPTER Two. TRANSPORTATION PROBLEMS Animal Transportation . . . 368 Express 373 Improved Roads 370 The Mail Matter 375 Railroad Transportation . . 370 Rates of Postage 375 Water Transportation .... 372 Parcel Post 377 CHAPTER THREE. PROBLEMS OF THE MANUFACTURER Making and Selling Bread . . 378 Profit and Loss 386 Factory Costs 383 Overhead Expenses 387 CHAPTER FOUR. THE MERCHANT'S PROBLEMS The Retail Butcher 389 Depreciation 394 Daily Shoe Sales 390 A Wholesale Business .... 396 viii CONTENTS CHAPTER FIVE. PARTNERSHIP Partnership Agreements ... 397 Division of Profits 398 SECTION VI FINANCING BUSINESS CHAPTER ONE. REMITTING MONEY Money Orders 401 Trade Acceptances 409 Telegraphic Transfers .... 402 Bills of Exchange 413 Bank Drafts 404 Documentary Bills 414 CHAPTER Two. BANKS AND BANKING Banks of Deposit and Discount 417 Certificate of Deposit .... 426 Collateral Loans 418 Interest on Balances .... 427 Accurate Interest 424 Savings Accounts 428 CHAPTER THREE. STOCKS AND BONDS Forming a Corporation ... 431 Bonds 438 Par Value of Stock 432 Accrued Interest 440 Stock Prices 433 Rate of Income 442 CHAPTER FOUR. FINANCING THE GOVERNMENT The Taxpayer 443 United States Revenues ... 41!) The Budget 443 Duties 450 State Revenues 443 The Tariff l.io CHAPTER FIVE. PROTECTING THE INDIVIDUAL Fire Insurance . 454 Short-term Rates . 456 SECTION VII BUSINESS MEASUREMENTS CHAPTER ONE. COMMON TABLES Weights and Measures . . . 458 Square Measure 465 Metric System 461 Cubic Measure 466 (MM-TER Two. AREAS AND VOLUMES Lines and Angles 4(W Hoard Mc.isim- 484 Area of Rectangle 470 The Cirrlr isi; Triangles 475 Prism and Cylinder 491 Powers and Roots 476 Pyramid ami Cone 493 WALSH'S BUSINESS AEITHMETIC SECTION I RECORDING BUSINESS TRANSACTIONS CHAPTER ONE LEARNING BY DOING While Edward Kerr was still attending school he obtained employment during his spare time in Hiram Hunt's general store. Being very methodical, Edward kept an account of his receipts and expenditures in a pocket memo- randum book, in the following form: A PAGE OF A BOY'S CASH BOOK 1919 Sep.* 1 2 3 6 7 8 On hand Penknife War Savings Stamps Moving Pictures Tie Wages Hair cut Church Balance On hand School supplies Car fare Lunch Athletic dues 15 3 74 50 10 7 75 10 30 25 25 59 24 45 10 20 25 19 24 19 8 M 7 59 4 The abbreviations for the names of the months are those used by business houses. 1 2 : ,\VAlH'S. Bfi&NESS ARITHMETIC The first entry on this page shows the cash on hand, the amount being written in the first double money column. The next four items are expenditures, the amount of each being placed in the second money column. Then follow a cash receipt and two expenditures. In writing each debit item Edward began close to the date column, and began each credit item one-half inch to the right. BALANCING THE ACCOUNT He closed the account at the end of the week by writing the word "Balance" in red ink as the last item. He then drew a line across the money columns, and below it wrote 19.24, the total of the debits, in the debit (Dr.) money column, and the same amount in the credit (Cr.) column. He inserted the balance, 7.59, in red ink in the Cr. column. This balance he obtained as follows: Adding downward, he thought 10 (5 + 5), 15 (adding 5) and 9 (writing 9) are 24; 9 (carrying 2), 10 (adding 1), 13 (adding 3), 15 (adding 2), 17 (adding 2), and 6 (writing 5), are 22; 12 (carrying 2), and 7 (writing 7), are 19. He tested the correctness of the balance by covering the second total, 19.24, with a strip of paper, on which he wrote the total obtained by adding the second column upward. He then counted his cash on hand, and finding that it amounted to 7.59, he frit sure that he had entered all of the cash transactions for the week. He next drew a double line below the totals and also across the date column, and on the line below he reopened tin- account by the entry "Sep. 8, On hand, 7.59." If he desired to ascertain his available cash, he would add 7.59 to the balance shown by his savings-bank book, his War Savings Stamps, etc. RECORDING BUSINESS TRANSACTIONS WRITTEN EXERCISE Copy the foregoing account, and supply additional items to cover the transactions of the remainder of the second week. Close the account on the morning of September 15, by inserting the balance, and re- open it the same day. Use a sheet of journal paper, or one ruled in the form shown in the foregoing account. On the top line write the word "Cash," but omit the abbreviations "Dr." and "Cr." Do not use the dollar sign ($). PAGE OF A SINGLE-ENTRY LEDGER Mr. Hunt's bookkeeping was limited to the accounts he kept with the few customers to whom he extended credit. To each of these he assigned a page in a ledger. He kept this book by single entry; that is, he entered each transaction but once. The following shows the account of John McKeon, which was kept on page 15 : JOHN McKEON Dr. Cr. 1920 May 1 25 Ib. Sugar .08 2. 5 " Tea .35 1.75 20yd. Muslin .12 2.40 1 bbl. Flour 9.50 15 65 6 8doz. Eggs .35 2.80 Cash 10. 12 80 9 10 Ib. Coffee .29 2 90 27 Cash in full 5 75 18 55 18 55 The foregoing shows that Mr. McKeon on May 1, 1920, received goods to the amount of $15.65, for which he 4 WALSH'S BUSINESS ARITHMETIC did not pay at the time; and that on May 9 he similarly received goods to the amount of $2.90. It shows that on May 6 he paid a total of $12.80 in cash and produce, and that on May 27 he settled in full by a cash payment of $5.75. Only the footing of a day's purchases was carried to the money columns, the separate extensions being written in the space to the left. The first double money column (Dr.) shows the debits of John McKeon to the store, the second shows the credits due by the store to him. When Mr. McKeon called on May 27 to pay the balance he owed, this was determined by deducting his credits of $12.80 from $18.55, the sum of his debits. This difference, $5.75, was then paid, and entered as a credit. In the foregoing account, the items 2. , 1.75, 2.40, 9.50, etc., are called extensions. The total, 15.65, is called a footing. WRITTEN EXERCISE Make out an account similar to the foregoing. Use prices prevailing in the vicinity of the school. Make the total of the Dr. money column agree with that of the Cr. column by the insertion of the necessary amount. Draw a line across the page to show that the account is closed. NOTE: Omit unnecessary words, figures, etc. Do not write Dr. and Cr. above their respective columns. Omit the dollar sign ($). ANTIQUATED METHODS Mr. Hunt made no entries of lii^ tr.-msadtions with the merchants from whom he purchased goods. When he bought on credit, he placed the bill in a tray until it be- came due, and when it was receipted, he filed it away with other receipted bills. RECORDING BUSINESS TRANSACTIONS 5 He kept no cash account. At the close of business each day, he counted the money in the drawer, deducted from the total the amount placed in the drawer in the morning to be used in making change, and added to the balance the total of the cash payments taken from the drawer. If the final result agreed with the total cash sales for the day, as shown on the strip in the cash register, he was satisfied. Not having had experience with anything different, Mr. Hunt felt only vaguely the advantages of a system that would enable him to ascertain his business condition at any time, the expense of selling goods, and the like. CHARGING THE WRONG ACCOUNT It happened once in a while that in the hurry of busi- ness the account of one customer was debited with goods that had been bought by a different one. When the former complained of 'the overcharge shown in the monthly state- ment rendered him, Mr. Hunt was disturbed, not so much at the possible loss of the sum involved as by the feeling that a customer might consider him dishonest rather than unbusinesslike. His annoyance was further increased by being unable at times to determine who was the purchaser. OMITTED ENTRIES One day a customer who wished to settle his account called attention to the omission of a charge for goods bought on credit early in the month. His inability to recall the details of the purchase or its total showed Mr. Hunt once more the need for a better system. A complaint within a day or two from another customer that his monthly statement showed no credit for a cash payment on account made the previous week, confirmed Mr. Hunt's resolution to take up at once the matter of employing business methods. 6 WALSH'S BUSINESS ARITHMETIC A BETTER WAY He called upon Edward's teacher of commercial subjects (Mr. Brown), and asked him if he could suggest a method of keeping accounts that Edward could handle in the short time that he was able daily to devote to the store. Mr. Hunt stated that neither he nor his two regular clerks had had any experience in real bookkeeping, and that his credit transactions were too few in number to warrant the em- ployment of an experienced bookkeeper. He said, too, that he had begun to realize the need of the possession of more information about business conditions than he could get from a ledger that showed merely the store's dealings with a few customers. Mr. Brown explained the advisability of including among the ledger accounts one showing Mr. Hunt's relation to the business, a cash account, a merchandise account, one giving the expense of conducting the business, and one with each individual or firm from whom goods were pur- chased on credit. He showed also that the proper keeping of some of the foregoing accounts would require the employment of the double-entry method, the advantages of which he briefly stated. He recommended the use of a journal daybook, in which transactions are entered in the order of their occurrence. In the case of a complaint that goods had been charged to a person other than the purchaser, a reference to the day- book would supply the name of the latter. The advantages of journali/ing the entries, as a prelim- inary to their transfer to the ledger, were explained. WRITTEN EXERCISE Make out the bill rendered to John McKeon by Hiram Hunt on May 1, 1920 for the six articles purchased by the former on that day. RECORDING BUSINESS TRANSACTIONS A RECORDING REGISTER Mr. Brown stated that the keeping of the books could easily be done by Edward in the time he was then giving the store. The important thing was to put him in posses- sion of all the data required to make the entries. These de- tails, Mr. Brown said, could best be supplied by a register that would record every transaction, giving the sum involved and its character, distinguishing each as either a sale for cash, a sale on credit, a cash payment made at the store for goods previously purchased, or a purchase of goods by the store on credit. He showed Mr. Hunt that the employment of a register in which every transaction was "rung up" would prevent an omission to charge a customer's account with goods sold or a neglect to give him credit for a payment made. THE INVENTORY Mr. Brown stated that the ledger account which should be kept with the proprietor, Mr. Hunt, would require that an inventory should be made to determine the condition of the business on the day the new system was commenced, by ascertaining the amount of cash on hand, the value of the stock and fixtures, and the condition of unsettled accounts. As the new books were to be opened on June 1, an inven- tory was made as of the close of business on May 31. The cash in the safe was found to be $61.14, and that in the bank $2284.75, a total of $2345.89. The value of the mer- 8 WALSH'S BUSINESS ARITHMETIC chandise was taken to be $1836.54, and that of the fixtures $1372.50. There was a balance of $147.85 due by J. H. Richards and one of $137.84 payable to R. A. Black. The total assets (resources) were thus found to be $5702.78, and the liabilities (debts) $137.84, showing a balance of $5564.94, which constituted the net resources. The following is the first entry in the journal daybook, the statement of the assets, of the liabilities, and of the balance, covering the daybook portion. In making this part Edward did not use the money columns, confining all the details to the space to the left. Jun. 1, 1920 (p. 1) Statement of the assets and liabilities at the beginning of business to-day Assets V Mdse. as per inventory 1836.54 V Fixtures, etc. (see list) 1372.50 v/ Cash on hand (and in bank) 2345 . 81) v/ Due from J. H. Richards 147 . 85 5702.78 Liabilities V DueR. A. Black 137.84 V Net Resources 5564.94 5702.78 2 Mdse. 1836 54 5 Fixtures 1372 50 6 Cash 2345 89 10 J. H. Richards 147 85 11 R. A. Black 137 1 Hiram Hunt 5564 JOURNALIZING The form and the details of the first entry were suggested by Mr. Brown, who recommended that the fixtures should be made a separate item in the inventory, and that the lioiild contain a Fixture Account. He showed Edward that in the journal entry the assets should appear as debits and the liahililies as credits, the RECORDING BUSINESS TRANSACTIONS amount of the net resources being credited to an account that should be opened with Mr. Hunt, the proprietor. In writing the journal portion Edward was careful to insert the amount of each debit in the first money column, and that of each credit in the second money column. As he journalized each daybook item, he placed a check mark (V) before the latter. When he completed the journal entry he tested the correctness of his figures by finding the sum of the debits and of the credits, and comparing the two results. The next task was the making of the ledger entries ("post- ing") called for by the inventory. These are shown in the following : FIRST LEDGER ENTRIES HIRAM HUNT (P- 1) 1920 Jun. 1 Investment 1 p564 !)t (p. 2) MERCHANDISE 1920 Jun. 1 Inventory 1 J1836 54 FIXTURES (p. 5) 1920 Jun. (p. 6) 1 Value (See list) 1 |l372 50 !& iSH 1 1920 Jun. 1 On hand i 1*. 89 (P. 10) J. H. RICHARDS 1920 Jun. i Balance > 147 85 [ R. A. BLACK (p. ID I 1920 Jun. 1 Balance '| 187 84 10 WALSH'S BUSINESS ARITHMETIC STARTING THE NEW LEDGER Edward made the account with the proprietor the first one in the new ledger, writing "HIRAM HUNT" at the top of page 1. Since the latter's name appeared in the inven- tory among the credit items, he first wrote 5564.94 in the credit money column. In the first journal column, on a line with this item, he wrote the ledger page. He then wrote "Investment" to specify the character of the item, after which he inserted the date. He completed the posting of this item of the inventory by writing 1, the journal page, in the ledger column to the left of the money one. This he did to facilitate a reference to the journal daybook entry should it become necessary. He opened the ledger accounts called for by the other items of the journal entry, in the order in which they ap- peared in the latter, writing MERCHANDISE at the top of page 2. Noting that the journal specified a debit entry, he made it on the debit side of the page, the left half, pro- ceeding in the manner followed in entering the Hunt item. Because of the likelihood that the number of merchan- dise transactions would be large, he left pages 3 and 4 blank for later uses, and opened the FIXTURES account on page 5. Here he entered the required debit, and then opened the CASH account on page 6. After mak- ing the necessary credit entry, he left three blank pages and opened accounts with J. H. Richards and R. A. Black, respec- tively, on pages 10 and 11, and made the proper entries. This work he completed before school hours on June 1. A DAY'S TRANSACTIONS In accordance with Mr. Hunt's orders, each of the fifty- .-i\ transactions of June 1 was "rung up" on the register. This recorded the number of the transaction, its amount, the date, a letter to denote the person by whom it was handled, and its classification under one of five types, indi- cated as follows: RECORDING BUSINESS TRANSACTIONS 11 * An ordinary sale for cash Pd. A cash payment made by the store Rec. Cash received to be credited to a debtor Ch. A sale made on credit Bt. A credit purchase by the store Transactions registered by Mr. Hunt were denoted by A, those by the two clerks by B and C, respectively. Of the day's transactions, forty-eight were cash sales; the other eight were the following, numbered in the order of their occurrence: 1 Payment of June rent (check) $125. 3 Sale to H. A. Gaynor on a/c 9 . 08 6 Payment of freight bill (check) 19 . 44 9 Check received from J. H. Richards 147.85 11 Purchase of sugar on account 515.20 18 Payment to R. A. Black (check) 137.84 1 Bank deposit 207.85 24 Payment of expressage (cash) 1 . 50 THE RECORD STRIP Each of these was recorded in its appropriate column on the strip. The following portion shows these eight, and includes a few of the cash sales: ft 2- 5.75-B 4- 3.94-B 5-10. 87-C 7- .95-B etc. etc. PD. 1-125. 00-A 6- 19.44-A 18-137 . 84-A 21-207. 85-A 24- 1.50-C REC. 9-147. 85-A CH. 1 3-9.08-B BT. 11-515.20-A THE CARDS Besides making the foregoing records on the strip, the register printed a card in connection with each transaction. On the following, which was issued in connection with the rent payment, the register placed this heading: WALSH'S BUSINESS ARITHMETIC Pd. A 125.00 0001 Jim- 1-20 Mr. Hunt, who made the record, noted on the card, for the information of the book- keeper, that the disbursement was a payment of rent made by check, and placed the card in a drawer. The card for transaction 2, a cash sale, was given to the customer. It contained this heading: * B 5.75 0002 Jun-1-20 In connection with the third transaction, a credit sale, the register printed the heading at the top of a bill and its carbon duplicate in this form: Clerk B filled in the details as shown here- with, gave Mr. Gaynor the bill, and placed the duplicate in a drawer of the register. Transactions 4 and 5, cash sales, were regis- tered in the same way as No. 2, and the cards given to the purchasers. Mr. Richards, transaction 9, not having sent with his check the bill it was intended to settle, Mr. Hunt registered the heading on a blank receipt and its duplicate, which he filled out in the form shown herewith: Ch. B 9.08 0003 Jim -1-20 Hiram Hunt Sold to 24 ib. Butter 5 " Coffee Amount of this purchase .32 .28 Rec. A 147.85 0009 Jun-1-20 He mailed the origi- nal to Mr. Richards, and placed in the drawer the carbon du- plicate, noting on the latter "By check." If Mr. Richards had inclosed the bill, this would have been receipted and returned, and the transaction recorded on a card. Received of J. II. Richards One Hundred Forty-seven 85/100 Dollars in full of account to date. Hiram Hunt RECORDING BUSINESS TRANSACTIONS 13 The bank deposit, transaction 21, while not being one calling for an entry in the daybook, was "rung up" to account for the withdrawal of cash from the drawer and the safe. It appeared thus: Pd A 207.85 0021 Jun-1-20 On the card, which Mr. Hunt placed in the drawer, he noted "Deposit: Cash, $60; Check, $147.85" THE BOOKKEEPER When Edward reached the store, after school, he first counted the cash in the register, which he found to be $37.12. He then examined the register slip to ascertain the number of transactions recorded, and their character. He learned that there were up to that time 44 in all, 36 of which were sales for cash, amounting, according to the register, to $37.48. To this he added $21.14, which had been placed in the drawer in the morning for change, which made a total of $58.62. From this he deducted $1.50, cash paid for expressage, leaving $57.12 to be ac- counted for. The difference between this sum and the $37.12 in the drawer showed that $20 had been taken, presumably for the deposit. An examination of the safe, in which $40 had been left in the morning, showed that this had been used to make up the $60 deposited in cash. Finding the money correct, Edward proceeded to make the entries in the journal daybook. As a preliminary, he collected the necessary data: cards, bills, bank book, check book, etc. Taking up the first transaction recorded on the strip, the payment of $125, he learned from the card that it covered the June rent, and that it had ,^>een made by check. From the check-book stub he found that a check for that amount had been drawn, which had been correctly deducted from the previous balance. 14 WALSH'S BUSINESS ARITHMETIC He then made the following entry of the first transaction, using a ditto mark (") to show that the date was the same as that of the previous entry (June 1) : \/ Paid rent for June Expense Cash 125. 125 125 The first line constitutes the daybook portion. This he "journalized" in the form shown in the next two lines. He first entered 125. , the amount, in each of the two money columns, once as a debit and once as a credit. The transaction, involving an expenditure of cash, requires that the Cash account in the ledger be credited with this sum. The journal entry, therefore, placed "Cash" in the credit place. Inasmuch as expenditures for such items as freight, expressage, postage, taxes, clerk hire, rent, etc., were to be entered in the ledger under the general title of " Expense," Edward debited the Expense account with $125. He began the debit entry item close to the first vertical line and the credit entry about an inch to the right. Finding from the record strip that transaction 2 was a cash sale, Edward went to the next. From the carbon dupli- cate placed in the drawer, he obtained the details, for the daybook portion, which are given in the first three lines of the following entry: V/ Sold H. A. Gaynor on account 24 Ib. Butter .32 7.Q8 5 " Coffee .28 1.40 H. A. Gaynor M.lse. 9.08 In journalizing it, he wrote "9.08" twice, as in the pre- ceding entry. On Jhe first line (the debit one) he wrote "H. A. Gaynor," whose ledger account was to be debited with $9.08 for goods bought. On the credit line, he wrote "Mdse.," the ledger account of which was to be credited. RECORDING BUSINESS TRANSACTIONS 15 Transactions 4 and 5, cash sales, were passed over, and after Edward had verified the extension of the freight bill, examined the check-book stub, etc., he made the following entry of transaction 6: Paid freight Expense Cash 19.44 19 1944 The following are the entries for the remaining transac- tions other than the sales for cash: \/ Received check from J. H. Richards in full of account 147 . 85 Cash J. H. Richards >/ Bought from Franklin Refinery on a/c 25 bbl. Sugar, as per invoice 515.20 Mdse. Franklin Refinery Paid R. A. Black in full of account to date 137.84 R. A. Black Cash \f Paid Cash for expressage Expense Cash 1 . 50 147 85 147 85 515 20 515 20 137 84 137 8-4 1 50 1 50 When business was over for the day, the register showed that the number of cash sales was 48, totaling $63.15. The following was the final entry for Jun. 1 : Received from 48 cash sales, as per register Cash Mdse. 63.15 15 6315 16 WALSH'S BUSINESS ARITHMETIC POSTING THE DAY'S TRANSACTIONS While waiting for remaining sales to enable him to make the final daybook entry, the cash sales for June 1, Edward began to make the ledger entries. Turning to the journal portion of the first transaction he found it to be: 12 Expense II 1251 II 6 Cash 125 which required that the Expense account in the ledger be debited with $125, and that the Cash account be credited with the same sum. Since the ledger did not as yet contain the former account he opened one on page 12, and entered the re- quired debit, inserting in the journal "12," the ledger page of the Expense account. He completed the posting of this transaction by crediting the Cash account with $125, and inserting in the journal "6," the ledger page of the Cash account. He then took up the other journal entries in regular order, opening accounts with H. A. Gay nor and Franklin Refinery on pages 13 and 14, respectively. T. " accounts appeared as follows after the posting of the las. ?tion of the day. A line was drawn under the accour- H. Richards and one under that of R. A. Black to show ti^at each had been settled. THE LEDGER PAGES HIRAM HUNT (p. 1) IIP | 11920 Tun. Investment (p. 2) MERCHANDISE 1920 JlIM. Inventory Frank. Ref. H. A. Gaynor Cash Sales 908 RECORDING BUSINESS TRANSACTIONS 17 FIXTURES (p. 5) 1920 Juu. I Value 1 1372 50 ! 1 (p. 6) 1920 Jun. I 1 1 On hand~ J. H. Richards Sales for day 7 i i CASH 2345 147 63 89 85 15 1920 Jun. 1 1 1 1 Rent Freight R. A. Black Express 1 1 1 1 125 19 137 1 H- 81 50 (p. 10) J. H. RICHARDS 1920 Jun. 1 Balance i 147 85 1920 Jun. 1 Cash HI 147 85 R. A. BLACK (p. 11) 1920 Jun. 1 Cash i 137 84 Jun. 1 Balance 1 137 84 (p. 12) EXPENSE 1920 Jun. 1 1 1 Rent Freight Express i i i 125 19 1 44 50 H. A. GAYNOR (p. 13) 1920 Jun. 1 Mdse. i 908 (p. 14) FRANKLIN REFINERY 11920 Jun. 1 Mdse. 4 515 20 18 WALSH'S BUSINESS ARITHMETIC ORAL EXERCISES 1. State why each item (a) on the debit side of the mer- chandise account is entered therein. (6) On the credit side. 2. What does (a) the debit side of the cash account show? (6) The credit side? 3. How would you journalize (a) the purchase of a plat- form scales from the Fairbanks Company on credit? (6) The purchase of 2000 postage stamps for cash? (c) The payment by check of a bill for electric light? (d) The purchase of 10 tons of coal on credit? 4. (a) What is shown by the difference between the totals of the two sides of the cash account? (6) How can the correctness of this difference be determined? (c) Which side must always have smaller total? Why? THE BANK ACCOUNT Mr. Hunt kept his account with the Newaygo County Bank on the stubs of the check book, as shown on another page. In making a deposit he filled out a slip like the accompany- ing form, which he sent to the bank with the money and the bank book. When the mes- senger returned, Mr. Hunt examined the book to see that the proper entry had been made; then, on the stub he added $207.85, the amount of the deposit, to the previous balance, $2159.75, making a total of $2367.60 to his credit in the bank. Deposited in The Newaygo County Bank, White Cloud, Mich, by Hiram Hunt Address: 4 Court Square. Jun. 1, 1920 Bills Coin Chrck List each check separately 40 20 147 207 RECORDING BUSINESS TRANSACTIONS a 1 s S & > O o o w 19 2 |1 5 * 8 JHIJ i 20 WALSH'S BUSINESS ARITHMETIC When Mr. Hunt made out check No. 458 in payment of the June rent, he detached it, leaving in the book the portion on the left, called the stub. On the latter he wrote the name of the person in whose favor the check was drawn (the payee), the item covered by the payment, its amount, and then deducted this amount from the previous balance, 2284.75. He brought down the remainder, 2159.75, to the stub for check No. 459. WRITTEN EXERCISES 1. On a sheet of paper of the proper size, make a copy of the next two checks with their accompanying stubs. Fill out one check to cover a freight payment, and the other to settle Mr. Hunt's account with R. A. Black. Use the proper number for each, and insert the amounts specified in the entries. Fill out each stub properly, inserting in the last one the deposit of $207.85, made before the check is drawn. 2. (a) How much cash should Mr. Hunt have in the store at the close of business on Jun. 1 ? (6) What should be his bank balance? (c) Compare the sum of (a) and (6) with the difference between the Dr. and the Cr. side of the cash account in the ledger. (p. 16) BALANCING AN ACCOUNT WM. WINKLE 1920 1920 Jun. 2 . To Mdse. 2 27 65 Jun. 20 By Cash 20 50 " 8 u 9 8 43 " 27 41 it 32 u _ it 10 " " 12 19 64 " 30 " Bal. 28 10 n 15 ". " 18 37 53 44 23 44 44 27 9 85 in:; 10 !().{ i<> JuL 1 To Bal. 28 10 RECORDING BUSINESS TRANSACTIONS 21 3. Find (a) the total of the Jun. 1 journal debits, including those of the inventory. (6) The total of the credits, (c) The total of the debits in the ledger entries, (d) The total of the credits. On the first day of July Edward balanced the June ac- counts. The method is shown in the foregoing ledger ac- count with Wm. Winkle. Noting that the Dr. side was the greater, he wrote under the former its total, 103.10, and placed the same total as the footing of the Cr. side, writing it on a line with the other total. He then made the entry "By Balance," writing this in red ink, also the date, "Jun. 30," and the amount of the balance, "28.10." This he ascertained by deducting the sum of $50 and $25 from $103.10. He then drew a line under both totals, closing the account, which he reopened by the entry of Jul. 1, "To Bal., 28.10," which is the amount due from Wm. Winkle. He then mailed to Mr. Winkle the following monthly statement, omitting the details of the purchases, since Mr. Winkle had received a bill with each. Mr. WM. WINKLE MONTHLY STATEMENT WHITE CLOUD, MICH., Jul. 1, 1920 In account with HIRAM HUNT General Merchandise 4 Court Square 1920 Jun. 2 To Mdse. as per bill rendered 27 65 8 " " " " " " 8 43 10 19 64 15 <( 37 53 23 << 9 85 103 10 Cr. Jun. 20 By Cash 50 27 25 75 Due 28 10 (p. 10) WALSH'S BUSINESS ARITHMETIC ANOTHER LEDGER PAGE J. H. RICHARDS 1920 1920 Jun. 8 To Mdse. 9 13 48 Jun. 18 By Mdse. 21 48 66 " 13 " " 15 6 86 " 28 33 87 95 " 16 19 27 95 " 20 23 42 63 27 " " 32 18 04 " 30 " Bal. 27 65 __ 130 6J_ 136 61~ nrn Jul. 1 By Bal. [27 65~ In balancing this account, Edward observed that the credit total was in excess of that of the debits. This re- quired a balance entry in the debit column, for which he left a line. The final debit total, therefore, appeared two lines below the last debit entry; on this line, on the credit side, he entered 136.61, and wrote it on the debit side also. Add- ing the debits and subtracting them from lQ&06~4n one operation, he entered the balance, 27.65, in red ink, and also the date and the word "Bal." He closed it by drawing the necessary lines, and reopened it by entering a credit balance of 27.65. When a bill was received from Mr. Richards, on Jul. 2, Edward compared it with the account, and notified Mr. Hunt to send a check in settlement. WRITTEN PROBLEMS 1. Make a copy of the foregoing account, balance, etc., as it appears in the ledger of J. H. Richards. Write the heading "Hiram Hunt." Credit this account with the items that appear as debits in Mr. Hunt's ledger, and vice versa. Insert journal pages other than those found in Mr. Hunt's ledger. 2. Make out the monthly statement sent to Mr. Hunt by J. H. Richards. 3. Write the check sent by Mr. Hunt in settlement of the account. RECORDING BUSINESS TRANSACTIONS 23 4. (a) Find the total weekly pay of 73 graduates of a boys' technical school who receive weekly compen- sation as follows during the first year of employment: 2 receive $6 16 receive $9 21 7 8 10 20 8 6 11 (6) What is the average weekly pay? 5. Find the average weekly pay of graduates in the second year of employment who received weekly compensation as follows : 8 received $7 11 received $11 19 8 11 12 10 9 9 13 9 10 7 14 6. Find the average weekly pay of graduates in the third year of employment who receive weekly com- pensation as follows : 4 received $10 16 received $15 6 11 6 16 4 12 10 17 9 13 2 18 9 " 14 2 " 20 CHAPTER TWO SALES SLIP No. 1 VII- 1-20 W. S. Julius & Co. Sold to Cash .06 A GIRL IN BUSINESS Miss White began as sales girl in a department store. Her first customer bought, for cash, the goods shown on the accompanying sales slip. In writing this, Miss White made a carbon duplicate. In the space at the bottom of the slip marked "Cash," Miss White wrote 2.31, the total of the trans- action, and in the one marked "Rec'd," she wrote 5., the denomination of the bill handed her by the customer. She then sent both slips, the $5 bill, and the goods to the wrapper. The latter compared the duplicate slip with the original, and the latter with the articles. Finding every- thing correct, she placed her check mark on the original and sent the two slips, with the $5, to the cashier. The latter returned the duplicate to Miss White with the change, and sent the original ta the auditing depart- ment. The wrapper made the goods into a neat parcel 24 3 3 J$iu& ffiovc&z, .36 /6 33 7^ / 06 06 CASH 2.3! REC'D 6. CH'G. ( .0.1). RECORDING BUSINESS TRANSACTIONS 25 and sent it to Miss White, who gave it to the pur- chaser, together with the duplicate slip and the change. To be certain of the correctness of the latter, she counted it out to the purchaser, saying: "2.31 and 4, 2.35; and 5, 2.40; and 10, 2.50; and 50, 3 dollars; and 2, 5 dollars"; handing over, as each item was specified, the 4 cents, the nickel, the dime, the half- dollar, and the $2 bill, supplied by the. cashier. The next sale was a credit one. This is shown by the entry of the total in the space marked "Chg." (charge) at the bottom of the slip. To make sure that the name and residence of the purchaser were correctly written, they were read to the latter by Miss White, from the slip. This, with the duplicate and the goods, was sent to the wrapper. The original slip after being checked went to the charge clerk, and the duplicate with the parcel to the delivery department. SALES SLIP No. 2 VII-1-20 W. S. Julius & Co. Sold to Mrs. J. Carroll Payne 8502 Hamilton Boulevard 2 $0* w&wCa/ .23 Z / // // 5 6 <3oa/ fa .05 30 / 86 CASH REC'D CH'G. 1.86 C.O.D. WALSH'S BUSINESS ARITHMETIC A GIRL'S DAILY SALES On a daily sales card, Miss White entered the amount of each sale, classify- ing it as cash, charge, or C.O.D. At the close of business she entered the total of each type, the grand total, and the number of sales made. This card went to the de- partment of audits. In order to deter- mine how she was suc- ceeding in her work, Miss \Vhite kept a memorandum of the number of her daily sales and their total. She was gratified to perceive that her promptness, cour- tesy, knowledge of the stock, etc., enabled her to make a steady increase in the number of transactions she was able to handle in a day. WRITTEN PROBLEMS 1. From Miss WTiite*s Daily Sales slip for Jul. 1, find the total of the sales (a) made for cash, (6) charged, (c) C.O.D., and (d) the grand total. 2. From the accompanying list of the sales made during the week ended Jul. 6, by the five girls at the DAILY SALES Date VII-1-20 Sold by M. White CASH CH'G. C.O.D. No. Am't. No. Am't. No. Am't. 1 2 31 1 1 86 1 1 35 2 79 2 1 27 2 1 65 3 15 3 3 1 87 4 3 48 4 4 5 2 67 5 5 6 1 10 6 6 7 50 7 7 8 25 8 8 9 3 11 9 9 10 10 10 11 11 11 12 12 12 Tot. (a) (6) (c) No. of Sales U Grand Tot. (d) RECORDING BUSINESS TRANSACTIONS 27 notion counter, find the weekly sales of each, (a) to (e)\ the total sales for each day, (/) to (fc); and the total sales of notions for the week, (/). DAY Miss W. Miss V. Miss U. Miss T. Miss S. TOT. Monday 22 .36 38 .75 32 .63 30 .48 36 .12 (/) Tuesday 11 .17 19 .05 17 .38 15 .72 18 .69 ( ftiz V O/2 g 4 i 5 ra24 Cambric " QY 2 i d % Cambric 3^ " Mohair Sateen " 14}^ h 10 " Cashmere " 85 Cashmere ' 96 ^ j 2^ " ' $& Twill " 8K4 I 16 " Sateen " $% Sateen " 25 (f n 25 o 12X " ;< 24^ p iy 4 " Alpaca q 2 " Padding " 84ff r % " Padding " 84ff s 2# " " 82^ t 4 " Dress Goods ( 11 X " Dress Goods " 42^f o 3% " w?2M " Cambric " 19ff z 64 " Muslin y 36 " Silk " 99^f z 99 " Cashmere ' 2. (a) From 10 times 44, take % of 44; (6) multi- ply 44 by 9& RECORDING BUSINESS TRANSACTIONS 29 3. Give products: a 44 X 19% b 44 X 25 c 44 X 24% d 44 X 24X e 44 X 49% / 44 X 99% g 32 x 19% A 32 x 24% i 32 X 99% MONTHLY BILL OF A DEPARTMENT STORE The following is the heading of the bill rendered monthly by W. S. Julius & Co. to his "Charge" customers : DATE, Jul. 31, 1920 FOLIO 35814 NAME, Mrs. J. Carroll Payne ADDRESS 8502 Hamilton Boulevard, Tucson. AMOUNT OF PAYMENT, $ Tucson, Ariz., Jul. 31, 1920 W. S. Julius & Co. SOLD TO Mrs. J. Carroll Payne 8502 Hamilton Boulevard. TERMS: Settlements required the first part of each month. When the bill is paid, the cashier enters the sum received on the coupon at the top, which he detaches and sends to the department of customers' accounts. He then receipts the bill, which he returns to the customer. The. body of the bill contains three money columns, two for the debits and one for the credits. The second debit column gives the total of the purchases of the day. The credit entries are made in red ink. 30 WALSH'S BUSINESS ARITHMETIC WRITTEN EXERCISES Make out a monthly bill covering the following purchases. Fill in the missing items (a) to (s). Make yourself a purchaser and a local firm the seller. Date Amount Daily Total Credit Jul. 1 2 6 8 10 11 13 15 18 20 27 2 Paste .20 2 Ammonia .23 1 pr. Scissors 1 " " 6 Soap .05 1 yd. Cretonne 4 Towels . 19 VA yd. Padding .82 Kdoz. Plates 2.70 % " " 1.50 1 yd. Cretonne 1 Wrapper 1 Skirt 3% yd. Dress Goods .42 6 Napkins .05 1 pr. Hose 3 doz. Napkins . 35 3% yd. Dress Goods .42 1 Wrapper 4 yd. White Goods .20 3 pr. Hose for 2Ji yd. Cambric .19 6 Handkerchiefs .35 1 Smock S% yd. Embroidery .08 1 Dress 40 46 25 45 30 1 1 1 86 () (/) to C0 35 05 (n) (p) 1 3 38 58 95 38 (a) (b) (d) (e) 3 95 98 (*) W 1 (*) (/) () 1 2 29 (a) 75 Total Less Due % (r) Paid Aug. S, 1920 W. S. JULIUS & Co. by M. E. K. W Do not use the price column when a single article is bought; write the price only in the "amount" column. When but one purchase is made on any day, write the amount only, in the "daily total" column. RECORDING BUSINESS TRANSACTIONS 31 CUSTOMER'S RECEIPT DATE VII-17-20 R 32748 RECEIVED OF Mrs. J. Carroll Payne ADDRESS 8502 Hamilton Blvd. THE CAREFUL CUSTOMER Upon the arrival of each purchase, Mrs. Payne examines the sales slip to be sure that she has received all of the articles charged to her account. She then files away the slips until the arrival of the monthly bill, which she "checks" by means of the slips. She also examines the credit column to ascertain that the proper reduc- tions have been made for the articles re- turned, as shown by her " Customer's Re- ceipts." When she finds that goods received are un- satisfactory or un- necessary, she notifies the store to send for them. The driver gives her a receipt in the accompanying form, which is a carbon copy of the "Call Check" filled out by the driver and brought by him to the store with the articles returned. THE OFFICE ASSISTANT Miss White's desire to become an efficient employee caused her to devote much of her spare time to a review of the commercial branches. Now that she was daily brought face to face with the advantages of RETAIN THIS RECEIPT OF GOODS RETURNED WHYRl CALL DEP'T.- ORDER '. Paid or Charge Check Entry W. S. JULIUS & Co. per T. E. B. WALSH'S BUSINESS ARITHMETIC training, she brought a new interest to her studies, and the latter held for her a new meaning. When, one day, she was offered the position of office assistant to the purchasing agent of The Harrison Company, she accepted it, feeling competent to perform the duties, and glad of the opportunity for more varied work than she would be likely to get in a larger business. THE ORDER BOOK One of her duties is to make stenographic notes of goods to be purchased, and to fill out the necessary order slips. She writes each on a perforated sheet of the order book, a carbon copy being made on a page re- maining in the book. When the bill is re- ceived, she stamps the date on the order. This she also does when the THE HARRISON CO. Office of the Purchasing Agent Happy Valley, Ariz. Nov. 16, 1921 No. 5837 Be sure to place this order number on your bill. CM CM CD O> Messrs. Barrett and Jones 1364 Water Street Cincinnati, Ohio > o O 2 KINDLY SHIP BY Freight 6 2-in. Brass Valves 2 3-in. IBB 2 Victor Gate " F247 F600 P b u w - en d 8 ^ no Purchasing Agent. Mail bills in duplicate when goods are shipped Mail statements the last of every month goods arrive. CARD INDEXES She enters each order on two cards, one headed with the name of the article and the other with the name of the firm. Each set she files alphabetically in the proper file. RECORDING BUSINESS TRANSACTIONS 33 ARTICLE VALVES Date Firm Location Quantity Order No. 1921 Jul. 16 Aug. 4 Nov. 16 Barrett and Jones Delancey Mfg. Co. Barrett and Jones Cincinnati, O. Denver, Colo. Cincinnati, O. 12 6 10 4386 5234 5837 The foregoing card shows all the orders given for valves. The entry of the order number enables a person to turn at once to the proper place in the order book, if details are desired. To the following card Miss White turns to obtain the address of Bar- rett and Jones, from which firm she has been directed to or- der valves. On this card she enters the number NAME Barrett and Jones ADDRESS 1364 Water St., Cincinnati, O. BUSINESS Plumbers' Supplies SALESMAN Aldcroft REMARKS See letter of VI-16-21 ; prices ORDERS 4386, 5837 of the order last sent, then files it away. INCOMING BILLS When the two invoices (original and duplicate) reach the office of the purchasing agent, Miss White stamps on the order sheet and on both invoices the date they are received. On the original invoice she also stamps a form to be initialed by the proper per- sons to certify (a) that the specified number of articles has been received; (b) that each is of the proper quality; (c) that the prices are those agreed upon; and (d) that the extensions, etc., are correctly made. 34 WALSH'S BUSINESS ARITHMETIC When goods arrive, she stamps the date on the order, and on both invoices, and sends the "original" for certification to the persons passing, respectively, upon quality, quantity, and price. When the invoice is returned with the required initials, she adds hers as to the correctness of the extensions, etc., and passes it along to the company's treasurer, retaining the dupli- cate in her files. THE INVOICE CINCINNATI, O., Nov. 21, 1921 BARRETT AND JONES Plumbers' Supplies SOLD TO The Harrison Company Happy Valley, Ariz. Via Freight DATE OF ORDER XI-1 6-1921 YOUR No. 5837 6 2" Brass Valves, F247 7 . 50 45 Plus 5% 2 25 47 25 2 3" IBB Valves, F600 15.00 30 Less 47 % 15 90 2 Victor Gate Valves 22 . 50 45 Less 35% 29 25 92 40 Bill Received, Nov. 24, 1921 Goods Received, Nov. 27, 1921 Quantities Correct. . . ^. IS. Qualities Correct. . / erf. Prices Correct.^, tt,. &. Extensions Correct.???. W. WRITTEN PROBLEMS 1. Copy and complete the following invoice. Try to make all extensions without the use of "side" calculations. RECORDING BUSINESS TRANSACTIONS 35 Folio 649 Terms: Net Cash Your Order 8502 BAILY AND MIDDLESEX Hotel Sundries * Butte, Mont., May 26, 1920 SOLD TO Hotel Burgundy Lorton Valley, Mont. 16 17 18 19 20 100 doz. Tea Cups #4982 1 . 05 100 " Saucers .78 43 " Dishes 6" #4993 1.80 19 Dishes 10" 4.25 5 " 12" 7.09 16 Celery Trays 4.40 80 Tea Cups #4994 1.05 80 Saucers .78 30 Double Egg Cups 1.58 141 Fruits 4" #4995 .72 78 " 5" .90 38 Bakers 3* 1.58 70 Plates 7" #4996 1 . 58 40 Bakers 6" 2.25 105 (a) 5 Crates 2.50 12 50 (b) Write extensions in the first double column, and the footing of the articles at (a) in the second. Write at (6) the total amount due. 2. Make out a bill for the following articles for a hotel: 78 doz. Towels 10 " Unbl. Sheets 54 X 90 12 " Pillow Cases 44 X 36 50 " Red End Towels 25 " Sheets 72 X 108 256 yd. Cheesecloth, P. red 204 Pantry Toweling 200 " Dish P. blue 400 " Glass 200 H 408 " Side F. white 40^ " Sheeting, l % Utica 49 " Fine Glass Toweling @ $4.50 7.92 1.74 1.34 11 .06% .19% .19% .21 36 WALSH'S BUSINESS ARITHMETIC THE TIME CLOCK Miss White ascertains the weekly service of each of the 12 employees by his or her time card. As each arrives in the morning, he takes his card from the "OUT" rack, inserts it in the recording in- strument in the time clock, and pulls a lever. By doing this, he stamps in the first column the time of his arrival. He then places the card in the " IN " rack. When he leaves at noon, he takes his card from the " IN " rack, has the time stamped in the second column, and places it in the "OUT" rack. WTien he returns, he replaces the card in the "IN" rack, after having had the time recorded in the third column. When he leaves for the day, he places the card in the "OUT" RECORDING BUSINESS TRANSACTIONS 37 rack, after the time has been recorded in the fourth column, or in the sixth column in the case of "overtime." THE TIME CARD When the time card is completed by the insertion of the number of hours of daily service, the weekly total, the amount due, and the employee's receipt, it presents the following appearance: Number 4 Name D. Marquard tco* .92 A.M. Noon P.M. Overtime 5 , C i-i Hours ii In Out In Out In Out M. 7.55 12.05 12.55 5.00 8 Tu. 7.57 12.01 1.03 5.02 73 W. 7.56 12.08 12.56 5.00 8 Th. 7.59 12.02 12.57 5.01 8 F. 8.00 12.02 12.58 6.02 9 S. 8.03 1.02 4 3 Total 45 2 TIME 45^ HOURS. RATE $12 Due for week $12. 41 I hereby acknowledge receipt in full, (Signed) DORA MARQUARD These employees are paid a weekly rate based upon 44 hours of service, 4 on Saturday and 8 on each of the other 5 working days. When oppor- tunity offers, Miss White enters in the last column the number of hours of service rendered each day. Miss Marquard, not having been late or absent on Monday, Wednesday, or Thursday, Miss White enters the number of hours for each of these days as 8. She WALSH'S BUSINESS ARITHMETIC enters 7% for Tuesday, owing to the arrival of Miss Marquard after 1. She makes a similar deduction on Saturday after allowing the overtime of an hour. Friday's entry shows 9 hours, which includes the overtime. On Monday, Miss White completes the time cards, entering Saturday's time on each, the total for the week, and the amount due. She also completes the time sheet, shown below, having made as many of the daily entries as possible in her spare time the preceding week. As a check on the accuracy of the total service entered on each time card, and the amount due, she calculates these once more from the time sheet, and compares the results with those shown on the card. TIME SHEET WAREHOUSE Dec. 1, 1921 to Dec. 6, 1921 No. Name Mon. Tues. Wed. Thur. Fri. Sat. Hours Rate Pay 1 Cutshaw, G. 73 8 8 72 8 3 4 44 15. 15. _ 2 Daubert, J. 8 73 8 8 2 8 4 -44 1 12. 12.07 3 Johnson, J. 72 8 8 8 9 4 44 2 12. 12.14 4 Marquard, R. 8 73 8 8 9 43 45 2 12. 12.41 5 Meyers, J. 7 8 8 8 78 5 43 3 12. 11.93 6 Miller, O. 8 8 73 8 8 4 43 3 11 10.94 7 Mowery, H. 9 8 8 73 32 3 10.50 7.82 8 Olsen, I. 8 2 8 8 8 8 2 4 45 10 10.23 Pfeffer, E. 6 8 8 6 43 32 3 9 6.70 10 Rucker, N. 8 8 8 8 4 36 8.50 6.95 11 Stengle, C. 8* 8 8 8 9 5 46 2 8. 8.45 12 Wheat, Z. 8 8 7 2 8 8 3 4 441 6. 6.03 Total 94* 87 s 95 1 87 90 47* 50 3 120.67 The small figures above the others and to the right denote quarters; 94 l meaning 94& 87* meaning 87& and 90 s meaning 90& RECORDING BUSINESS TRANSACTIONS 39 CASH FOR THE PAY ENVELOPES After verifying the correctness of the total, Miss White prepares a check for the amount. This she sends with the time sheet to the purchasing agent. When the latter has affixed his signature to the check, he sends it to the treasurer. THE CHECK H-S 11 S Q & Happy Valley, Arizona, Dec. 8, 1921 No. 8502 THE BATH COUNTY NATIONAL BANK Pay to the Order of Maurice J. Moore $120%o One Hundred Twenty %o Dollars Donald Campbell Treasurer CHANGE SLIP BATH COUNTY NATIONAL BANK When the check is returned to Miss White with the necessary signatures she sends Maurice Moore to the bank to obtain the cash for the pay envelopes, giving him the accompanying "change slip." After Maurice Moore's arrival at the bank, he indorses the check and presents it with the "change slip" to the paying teller. The latter gives him the specified bills and the smaller change, which he counts. Finding the amount correct, Maurice returns with the money to Miss White. She distrib- Kindly send by Maurice Moore the following: 7$10's $70. 6 5's 30. 5 2's 10. 5 1's 5. 5 halves 2.50 6 quarters 1.50 12 dimes 1.20 5 nickels .25 22 pennies Total $120.67 40 WALSH'S BUSINESS ARITHMETIC utes it in the pay envelopes, writing on the back of each the name of the employee and the amount con- tained. Each employee, on receiving his envelope and counting its contents, signs the receipt on the time card. When all the employees have been paid, the cards are sent to the auditor. To determine the denomination of the bills and coins needed for the different envelopes, Miss White makes a memorandum in the following form: CHANGE MEMORANDUM No. Pay $10 $5 $2 $1 50 25^ 10* 5i 1* 1 15. 1 1 _ _ _ _ _ _ _ 2 12.07 - 1 - - _ - 1 2 3 12.14 _ 1 - - 1 - 4 4 12.41 - 1 - - 1 1 1 1 5 11.93 - - 1 I 1 1 1 3 6 10.94 - - - 1 1 1 1 4 7 7.82 _ 1 1 _ 1 1 _ 1 2 8 10.23 1 _ _ _ _ _ 2 _ 3 9 6.70 _ 1 _ 1 1 _ 2 _ _ 10 6.95 _ 1 _ 1 1 1 2 _ _ 11 8.45 _ 1 1 1 _ 1 2 - _ 12 6.03 - 1 - 1 - - - - 3 Tot. 120.67 7 6 5 5 5 6 12 5 22 WRITTEN EXERCISES Writing in a column the amounts due the different employees, she inserts on a line with each the de- nominations required for the envelope. The footings at the bottom give the total number of each denomi- nation. This she verifies when she makes out the change slip. RECORDING BUSINESS TRANSACTIONS 41 WAGE TABLES To insure the correctness of the pay rolls, Miss White obtains the results by two different methods: one by performing the calculations in the common way, and the other by the use of the wage tables. PORTION OF WEEKLY WAGE TABLE Hrs. Rate per 44-hour week Hrs. 44 $15 $12 $11 $10 $9 $8 44 X .0852 .0682 .0625 .0568 .0511 .0455 % % .1704 .1364 .125 .1136 .1023 .0909 % % .2557 .2045 .1875 .1705 .1534 .1364 % 1 .3409 .2727 .25 .2273 .2046 .1818 1 2 .6818 .5455 .50 .4545 .4091 .3636 2 3 1 . 0227 .8182 .75 .6818 .6136 .5455 3 4 1.3636 1.0909 1. .9091 .8182 .7273 4 5 1.7045 1.3636 1.25 1.1364 1.0228 .9091 5 6 2.0455 1.6364 1.50 1.3636 1.2273 1.0909 6 7 2.3864 1.9091 1.75 1.5909 1.4318 1.2727 7 8 2.7273 2.1818 2. 1.8182 1.6364 1.4545 8 9 3.0682 2.4545 2.25 2.0455 1.8410 1.6364 9 10 3.4091 2.7272 2.50 2.2727 2.0454 1.8182 10 20* 6.8182 5.4545 5. 4.5454 4.0909 3.6364 20 30 10.2273 8.1818 7.50 6.8182 6.1364 5.4545 30 40 "18.6364 10.9091 10. 9.0909 8.1818 7.2727 40 50 17.0454 13.6364 12.50 11.3636 10.2272 9.0909 50 WRITTEN EXERCISES 1. From the foregoing table, find the pay at the rate of $15 per 44-hour week for (a) 36 hours, (6) 27 hours, (c) 43% hours, and (d) 39% hours. 42 WALSH'S BUSINESS ARITHMETIC METHOD (a) 30 hr. $10.2273 (b) 20 hr. add_6 " 2.0455 add _7 " 36 hr. 27 hr. (c) 44 hr. $15. - (d) 40 hr. less _%__ less %_ " 43% hr. " 39% hr. To obtain the answer to (a), take from the $15 column of the table the amount payable for 30 hours, and to this add the amount for 6 hours. 2. Find the wages payable on a weekly basis of 44 hours, for (a) 37 hours at $15, for (b) 42 hours at $12, for (c) 37% hours at $10, for (d) 49% hours at $9, for 0) 54 hours at $8. 3. At the rate of $11 per week of 44 hours, find the amount due for (a) 43% hours, for (b) 28% hours, for (c) 39% hours, for (d) 54% hours. METHOD At $11 for 44 hours, the hourly rate is $%. Multiply $X by (a) 43.5, (b) 28.75, etc.; that is, the quotient of these by 4 gives the wages in dollars. 4. At the specified rates for 44 hours, find the wages due for services rendered as follows: a 48 hours at $12 per week d 36 hours at $16 per week b 40 " " $13 " " e 55 " "$21 " " c 52 " " $14 " " / 33 " RECORDING BUSINESS TRANSACTIONS 43 5. From the following time card calculate the pay due Miss Jones for the week, deducting % hour for an absence of each 15 minutes, or less. NUMBER 14 NAME MARY E. JONES A.M. NOON P.M. Overtime Day Hours In Out In Out In Out M. 7.56 12.01 12.55 5.01 Tu. 8.03 12.05 1.02 5.04 W. 7.59 12.03 12.59 5.06 5.30 7.30 Th. 8.31 12.02 1.03 6.01 F. 7.57 12.04 12.56 5.03 5.30 6.30 S. 7.59 12.03 12.58 2.31 6. From the following pay slip determine the hourly rate for each day: NAME Marguerite Carter OPERATION Seaming Coats Day Jan. Hr. Earnings Mon. Tues. Wed. Thurs. Fri. Sat. 4 5 6 7 8 9 m 8% $2.31 2.25 2.80 2.45 2.64 1.36 7. Make a graph 1 showing the fluctuations during the year in the monthly earnings of a girl employed in a "seasonal" occupation: Jan. $48 May $27 Sep. $44 Feb. $48 $50 Mar. $49 Apr. $35 May Jun. Jul. Aug. $27 $36 $42 $47 Sep. Oct. Nov. Dec. 1 For a description of graphs, see Section III, p. 123. CHAPTER THREE SOME BUSINESS FORMS INVOICES AND BILLS WRITTEN EXERCISES 1. Copy and complete the following invoice: Akron, Ohio, Apr. 7, 1920 CLARK, STOWE, & CO. BUILDERS' SUPPLIES SOLD TO Mr. Albert Janson. 2450 Red Brick 30. 85 bags White Sand .30 85 Sand Bags .06 140 bdl. Laths 4.85 73 50 6790 In a bill or an invoice begin with a small letter the word denoting the quantity; lb., bu., etc. Begin with a capital the name of the article. Do not use "of" or "@." Rule your paper as shown above. Write each extension in the first double money column. Write the footing in the second double money column on the line below the last footing. 2. When 2450 bricks cost $73.50, (a) what is the price of one brick? (6) How many can be bought for $30 ? 3. At $4.85 per thousand, (a) how many laths can be bought for $67.90? (b) If this quantity is contained in 140 bundles, how many laths are there to a bundle? 44 RECORDING BUSINESS TRANSACTIONS 45 4. When 52 bags of Portland cement cost $30.55, (a) what is the cost per bag? (6) What is the cost of a barrel of four bags? 6. One item on an invoice is 60 bags of K. W. cement, the rate per unit being $12.50, and the ex- tension $37.50. (a) How many pounds are there in the purchase if a bag contains 100 pounds? (b) How many units are charged for? (c) How many pounds are there in the unit? (d) What is the unit? Invoice clerks do not write "per pound,'* "per gross," "per ton," "per thousand," etc., the assumption being that the buyer knows the quantity represented by the given rate. MADISON, Wis., Apr. 30, 1920 MR. ALBERT JANSON Bought of J. P. Duffy Company Lime, Lath, Brick, Cement, etc. Terms, Net 30 days. Apr. 3 1 cu. yd. Sand 3 _ 5 bags Port. Cement 2.35 2 94 8 4 bbl. Marble Dust 1.75 104 bags Port. Cement 2.30 12 72 " " 2.30 13 3 bbl. N. A. Plaster 1.95 5 85 17 12 bags K. W. Cement 12.50 7 50 24 ' Port. 2.40 1 bbl. Atlas 5 21 4500 Bricks 30.00 150 bdl. Laths 4.80 4 bags Atlas Cem. 5 (a) Or. 27 175 M. T. bags Portland .08 28 72 " " " K. W. .06% 3 " " " R. W. .06 (6) Balance (<0 46 WALSH'S BUSINESS ARITHMETIC In the last invoice the given price of brick is by the M; of laths, by the M, each bundle containing 100 laths; of Portland cement, a barrel of four bags; of K. W. cement, a ton of 2000 pounds, each bag containing 100 pounds. 6. Complete the foregoing invoice, which shows credits for empty (M. T.) bags returned. It differs from a statement by itemizing the purchases made during the month. Write the total debits at (a), the total credits at (6), and the balance at (c). This concern renders invoices (bills) once a month to regular customers. When the goods are delivered, the driver obtains a receipt in the accompanying form, from Mr. Janson's representative, to whom he gives a carbon duplicate. In case there is any question as to articles, quanti- ties, etc., the receipts are referred to. The foregoing invoices are frequently called bills, MEMORANDUM RECEIVED OP J. P. Duffy Company 1 cu. yd. Sand 5 bags Port. Cem Signed . . A. Janson . per M. M. W. Apr. 3, 1920. - T the former name being more particularly applied to the next form, which designates by number the case in which each item is packed. This enables the purchaser to locate a particular article. The goods in the next invoice are contained in two cases; one marked A. S. 53, and the other A. S. 54. Each case contains 6 pieces. 7. Complete the following invoice. Insert at (a) the total number of yards in the second three pieces; at (6) the total in the next six pieces; at (c) the exten- RECORDING BUSINESS TRANSACTIONS 47 sion for the first two lots; at (d) for the next three; etc. Place the footing at (g). SAN FRANCISCO, Aug. 27, 1919 BUSSEY & TAYLOR Wholesale Woolens SOLD TO Albert Shields, Phoenix, Arizona. A. S. 53 54 2 c/s Woolen Mantlings 53/54 48% yd. 46% ' 94^yd. 1.64 C<0 (d) () (/) (a) 47% " 47% " 45% " (a) 1.26 61 " 2.25 47K yd. 62% " 66% " 62^ " 61 " 48% " (&) 1.26 When a monthly invoice contains a great number of items, several are placed on a line to economize space, as in the following. KNOXVILLE, TENN., Oct. 1, 1920. Mr. Henry Schlaefer Bought of Richard H. Wattles GRAIN, HAY, STRAW, MILL FEED Interest charged on overdue accounts Sep. 1 100# Perfection 1.95; 1 bag, .05 2 _ 100# Wh. Bran, 1 .80; 100# Middlings, 2. 3 80 1.09 97^ 2 bu. Corn, 2.18; 2bu. Cr. Corn, 1.95 4 13 .05 .80 2 bags, .10; 2 bags G. A. Salt, 1.60 1 70 NOTE: The character # before a number means "Number"; after a number, it indicates "pounds." 48 WALSH'S BUSINESS ARITHMETIC 8. Complete the foregoing invoice by adding the following: Sep. 4, 2 bags of cracked corn, 1 bag; Sep. 8, 100 pounds Wheat Bran, 600 pounds of corn bran, 2 bushels of corn, 7 bags; Sep. 9, 100 pounds of Perfection feed, 1 bag; Sep. 10, 2 bushels of cracked corn, 1 bag; Sep. 11, 200 pounds of wheat bran, 100 pounds of middlings, 400 pounds of beet pulp, 400 pounds of corn bran, 4 bushels of corn, 2 bushels of middlings, 7 bags; Sep. 16, 100 pounds of Perfection feed, 2 bushels of cracked corn, 2 bags; Sep. 17, 200 pounds of wheat bran, 00 pounds of cotton seed meal, 200 pounds of beet pulp, 200 pounds of gluten, 100 pounds of middlings, 4 bushels of corn, 2 bags; Sep. 22, 500 pounds of gluten, 200 pounds of wheat bran, 200 pounds of beet pulp, 200 pounds of corn bran, 2 bushels of corn, 2 bushels of cracked corn, 1 bag; G. A. salt, 4 bags; Sep. 28, 200 pounds of cotton seed meal, 200 pounds of wheat bran, 200 pounds of gluten, 400 pounds of corn bran, 100 pounds of middlings, 2 bushels of corn, 2 bushels of cracked corn, 6 bags. Use the following prices : Cracked corn, $ .97% per bu. Middlings, $2.00 per 100 Ib. Corn, $1.09 " " Beet pulp, $1.35 " " " \\hoatbran $1.80 " 100 Ib. Cottonseed meal, $1.85 per Corn $1.30 per 100 Ib. 100 Ib. Perfection feed $1.95 " 100" Gluten, $1.85 per 100 Ib. Bags, 5 cents each G. A. salt, $ .80 per bag While every invoice may be called a bill, bills con- taining items for services rendered are not invoices. RECORDING BUSINESS TRANSACTIONS 49 In bills of this kind the heading "Bought of" or "Sold to" is changed to the form given in the following BILL FOR SERVICES AND MATERIALS TOPEKA, KAN., Jun. 11, 1920 Mr. Robert, P. Webb 85th Street and Ridge Boulevard To JOHN TODD, Dr. Plumbing Contractor 1 Range $268 48 _ 2 " Couplings, %" .37# 1 Nippb, %' 10 10# Galv. Fittings . 15 3 Unions .37 19 ft. 2 in. Pipe .12 1 Boiler Coupling 60 2 Couplings, water back . 62) 10 Nipples .13 2 Els, %" . 15 1 Tee, 1" 15 2 Elbows, 45 degrees . 15 3 lengths Pipe . 10 1 Damper, 6* 30 2 Black Elbows, 6" .20 1 Brass Ring 9 1 Galv. Cross 20 2 " Ells .15 4 " Elbows .10 2 Black Ells .15 1 Plate Rack 3 Time, 2M days 4. Received Payment June 15, 1920 JOHN TODD per W. H. M. 9. Copy and complete the foregoing bill. 10. Make out a check on the School Bank in settle- ment of the foregoing bill. 50 WALSH'S BUSINESS ARITHMETIC RECEIPTS A person to whom an express package is delivered, a telegram, a special delivery letter, etc., acknowl- edges the delivery by writing his name in the proper place in the receipt book carried by the messenger, driver, carrier, etc. The receipt of Mr. Brown's money by a bank, on deposit, is shown by the teller's entry in the passbook. When Mr. Webb settled Mr. Todd's bill, the latter indicated the fact by "receipting" the bill. If Mr. Webb did not have the bill with him, Mr. Todd's clerk would give him the following RECEIPT IN FULL TOPEKA, KAN., Jun. 15, 1920. RECEIVED OF MR Robert P. Webb Too DOLLARS in full of account to date. JOHN TODD $ per 11. Copy and complete the foregoing receipt, in- serting the dollars in words on the third line, and in figures on the last line, expressing the cents as a frac- tion of a dollar in each place. Use your own initials as the clerk who receives the money for Mr. Todd. 12. Write John Whalen's receipt for $125, sent him by Hiram Hunt for the rent of his store for Jun., 1920. Insert on the third line "For rent of premises No. 4 Court Square for June, 1920." RECORDING BUSINESS TRANSACTIONS 51 CHECKS AS RECEIPTS To save the time and expense of mailing receipted bills to thousands of customers making monthly settlements by check, many business concerns print at one end of the bill a coupon to be detached therefrom and inclosed with the check sent in payment, unless the customer prefers to send the bill, and to have it returned to him receipted. If no further receipt is desired, detach this coupon and mail with your check. The canceled check is your receipt. Date, Jul, 31, 1920 W. S. Julius & Co. Mrs. J. Carroll Payne, Folio 35814 8502 Hamilton Boulevard. Amt. $114 . 42 Some bills contain a form similar to the one on the right in which the customer CUSTOMER'S RECORD makes the necessary entries. Paid by Check No. V- 7 6 If a second bill for the same Bank ^^^ i/tA*ol purchases should be pre- Date > ^' *' f ^ sented, the record on the original bill will furnish the number of the check. The presentation of the can- celed check with its indorsement showing that it was collected by the merchant will be satisfactory evidence that the bill was paid, and that he made an error in rendering the second bill. It is unnecessary to state that receipts, receipted bills, and canceled checks should be carefully preserved. 13. Copy and complete the following check by which Mrs. Payne pays the bill of A. D. Winkle for $84.75. She notes in the left the purpose of the check and WALSH'S BUSINESS ARITHMETIC signs the check with her own name. She also notes upon her check-book stub the purpose of the check, and mails it, with the coupon. She fills out the " Customer's Record" on the bill and files away the latter. 1 TUCSON, ARIZ., Aug. 3, 1920 No. 476 o ARIZONA SCHOOL BANK g S>1 Pay to the U - $ ~ >- Dollars. c 3s Elizabeth Payne.. ORDERS FOR GOODS When a merchant orders goods by ORDER SLIP Fairfax Furniture Co. Brockton, N. Y. Dressers and Chiffoniers VI-9-1920 Salesman Yates. Order No. 231 Ship to Jervis Johnson & Co. Address 255 Columbia Ave., Passaic, N J. Ship via Penn. R. R. Terms 60; 5/30 F. o. b. Brockton. Quantity No. Finish Price 3 2784 Mah. Dress 11 75 3 2658 " Chiff. 12 50 3 3062 Oak Dress. 12 25 S 3817 " Chiff. 12 75 J. JOHNSON & Co. mail he retains a carbon copy of the order slip in the order book (see p. 32). When he gives a verbal order to a seller's agent, the latter makes out a slip. In the accom- panying one Mr. Yates, a sales- man . for the Fairfax Furni- ture Company, sells Jervis John- son & Co. the specified articles at the prices RECORDING BUSINESS TRANSACTIONS 53 given. The slip shows the terms of credit and that the goods are to be delivered to the railroad company. Mr. Yates obtains the signature of J. Johnson & Co. to the original, which he sends to the Fairfax Furniture Co. He gives a carbon duplicate to J. Johnson & Co. for their files. The following is the invoice: No. 647 Fairfax Furniture Company Manufacturers of Dressers & Chiffoniers Order No. 231. Dated VI-9-1920. Sold to Jervis Johnson & Co. 255 Columbia Ave., Passaic, N. J. Shipped by Penn. R. R. Car P. R. R. 85026 F. o. b. R. R. Terms: 60 da. net; 5 %, 30 da. Brockton, N. Y., June 11, 1920 Salesman Yates. 3 Mah. Dress. 11.75 3 " Chiff. 12.50 3 Oak Dress. 12.25 3 " Chiff. 12.75 NOTE; F.o.b. R. R. means that the goods are delivered to the rail- road company without charge for cartage "Free on Board." WRITTEN EXERCISES 1. Copy and complete the foregoing invoice. 2. Make out a check on the Passaic National Bank for the amount of the bill, dating the check about 40 days after Jun. 11. 3. Make out a check to the order of the Pennsyl- vania Railroad Company for the freight on 2700 pounds at 45 cents per 100 pounds. 54 WALSH'S BUSINESS ARITHMETIC BILL OF LADING When the goods are delivered to the railroad, the freight agent gives the shippers a Bill of Lading, which is a form of receipt, acknowledging that the goods have been delivered to the railroad. The Fairfax Company mails this bill of lading to Jervis Johnson & Co., who present it to the freight agent at Passaic as evidence that they are the owners. The following is an abbreviated form of a BILL OF LADING Pennsylvania Railroad Company Date Jun. 11, 1920 Received at Brockton, N. Y., from Fairfax Furniture Co. the property described below, in apparent good order except as noted, contents and condition of contents of package unknown. The rate on freight from Brockton, N. Y., to Passaic, N. J. is in cents per 100 pounds 1st class 2d class 3d class 4th class 5th class 6th class Special 45 Consigned to Jervis Johnson & Co., 255 Columbia Av. Destination, Passaic, State of New Jersey Route N. Y. C., Penn. Car Initial P. R. R. Car No. 85026 Number of Package Description Weight 6 6 Crates Dressers Chiffoniers 750 # 600 # ANDREW JAV1NS, Agent per M. E. K. RECORDING BUSINESS TRANSACTIONS 55 Upon presentation of the bill of lading and the payment of the freight the twelve crates are delivered to the consignees. FREIGHT BILL Consignees: Jervis Johnson & Co. No. 1669 255 Columbia Av. Date VI-16-1920 To Pennsylvania Railroad Company, Dr. Passaic Station, from Brockton, N. Y. Waybill No. 92 Date VI-1 1-1919 Via N. Y. C., Penn. Car P. R. R. 85206 FREIGHT BILL Shipper Fairfax Furniture Co. Original Point of Shipment Brockton, N. Y. Description of Articles Weight Rate Charges Total 6 crt. Dressers 6 " Chiffoniers 1500 1200 45 2700 Claims for loss or damage must be promptly made in writing to Freight Agent accompanied by this bill. Make check payable to Pennsylvania Railroad Company Received Payment for the Company Jun. 16, 1920 John Carrol Freight Agent WRITTEN EXERCISES 1. Find the amount of the foregoing freight bill. 2. Make out a bill for the following articles bought of the Wolverine Manufacturing Company of Detroit, Mich.: 4 mahogany library tables, at $9.65; 4 at $7.75, 4 at $8.75; 8 golden oak parlor tables at $1.50; and 8 mahogany parlor tables at $1.55. 56 WALSH'S BUSINESS ARITHMETIC Insert catalogue numbers to denote the styles. Use Mah. for mahogany, G. O. for golden oak, Lib. for library, Par. for parlor, Tab. for table. 3. Make out a freight bill for the delivery of the foregoing goods in the home town. Obtain from the local freight agent the rate on furniture from Detroit, also a copy of a bill of lading and a blank freight bill. Assume that the articles are shipped hi 28 boxes; the legs in 8 boxes weighing, with the contents, 15 pounds each; each library table top in a box, weighing with its contents 70 pounds; the 16 parlor table tops in 8 boxes, each weighing with its contents 85 pounds. 4. Make out an order slip for the forgoing articles, using the form shown on p. 52. Insert the catalogue numbers, but not the prices. 5. Make out a check on the School Bank for the amount of the bill. Be careful in your selection of dates to allow a proper interval to elapse between the date of the order, that of the bill, and that of the freight bill. For other business forms see Statements, Notes, Drafts, Bills of Ex- change, Trade Acceptances, etc. SECTION II BUSINESS CALCULATIONS CHAPTER ONE PERCENTAGE PREPARATORY EXERCISES 1. A sales girl received, as part of her pay $6 on sales of $120. (a) What fraction of the amount of her sales did she receive in this way? How much should she receive, at the same rate, on sales (6) of $150? (c) Of $100? 2. A man received $9 on sales of $150. (a) What fraction of the amount of his sales did he receive? How much should he receive on sales (6) of $200? (c) Of $100? 3. (a) How many problems out of 20 should a boy solve who solves 95 out of 100? (b) How many out of 25 should a girl solve who solves 96 hundredths of her problems? A rate of $6 on $100 is stated in business as 6 per cent, which means 6 hundredths, or .06. It is written 6%. Any decimal may be written as a per cent by express- ing it in hundredths, omitting the decimal point, and placing after it the per cent sign. Thus 5 tenths, which is equal to 50 hundredths, is written 50%; 125 thousandths, which is equal to 12% hundredths, 57 58 WALSH'S BUSINESS ARITHMETIC is written 12%%; 36 thousandths, which is equal to 3.6 hundredths, is written 3.6 %. FINDING THE PERCENTAGE WRITTEN EXERCISES 1. (a) How much does a man receive who is given 6% of $347.50? (6) How much weight is lost during the whiter by 256 tons of hay, if the loss in weight is 3%? (c) What is the cost of insuring a store for $7500 when the rate is % of 1 %? (d) How many pounds of butter fat are there in 231 pounds of milk, when it contains 3.6 % of butter fat? METHOD Base (a) $347.50 Rate X .06 (6) 256 T. X.03 (c) $7500 X .00% Percentage $20.8500 Ans. 7.68 T. $37.50 To find the percentage, multiply the base by the rate expressed as a decimal. 2. A salesman receives a commission of 3% on the amount of his sales. How much does he receive on sales of $1575? 3. A man bought a house for $3500 and sold it at a profit of 35 %. (a) What was his profit? (b) How much did he receive for the house? 4. In a school of 425 pupils 96 % of them are present, (a) How many are present? (6) What per cent are absent? (c) How many are absent? BUSINESS CALCULATIONS 59 5. In this school 48 % of the pupils are boys, (a) How many boys are in the school? (6) how many girls? 6. How many hits does a player make in 480 at- tempts, when 35% of his attempts are successful? 7. How much tax does an owner pay when he pays %% of $7800 which is the valuation of his farm for purposes of taxation? 8. A contractor agrees to do a piece of work in 140 days. How many days should he require to do 65 % of the work? 9. A dealer bought a suit of clothes for $15 and sold it at an advance of 66%%. (a) How much was the advance? (b) The selling price? It takes 30% of the selling price to do business. (c) What did it cost him to sell the suit? (d) What was his net profit? 10. A man whose income is $1500 a year, spends 24 % of it for rent. How much is his rent (a) for a year? (b) For a month? SIGHT EXERCISES 1. Change to common fractions, lowest terms: a .4 b .14 c .124 d .3125 e .8 / .32 g .328 h .5625 2. Express as per cents : ay, by, c y 4 dy, e % f % g % ky lQ i % j % k% l % m % n%5 o%) P% 9 % r % s t % u s / lQ v %o w V* x% Q 60 WALSH'S BUSINESS ARITHMETIC 3. Express as common fractions, lowest terms a 25% 650% c 33%% d87%% i 37% % j 83% % k 62% % / 8% % 4. Find (a) 25 % of 36, (b) 6% % of 75 METHOD (a) 25 % of 36 = % of 36 = 9, Ans. (&) 6%% of 75 = % 5 of 75 = 5, Ans. Change per cents to fractions. 5. Give answers: a 25 % of 96 d 6% % of 176 g 37%% of 480 j 87%% of 88 b 33%% of 69 e 75 % of 72 * 8% % of 252 A; 62%% of 840 c 12%% of 248 f 66%% of 99 i 50 % of 83 1 6% % of 165. 6. Find (a) 4% of 375; (b) 6% of 450. ONE WAY (a) 4% of 375 = .04X375 =4X3.75 =4X3% = 15, Ans. (6) 6% of 450 = .06X450 = 6X4.5 = 6x4%=27, Ans. Instead of taking the rate in hundredths, divide the base by 100, changing the quotient to a mixed number. 7. Give answers: a 4 % of 975 b 12 % of 633% c 8 % of 937% d 6 % of 850 e 16 % of 412% / 6 % of 566% g 8 % of 725 h 24 % of 216% i 9 % of 833% BUSINESS CALCULATIONS 61 8. Find (a) 69% of 33%; (6) 88% of 37%. METHOD (a) 69 % of 33% = 33% % of 69 = % of 69 = 23, Ans. (6) 88 % of 37% = 37% % of 88 = % of 88 = 33, Ans. 9. Give answers: a 99 % of 33% b 88 % of 25 c 72 % of 16% d 48 % of 12% 84 % of 75 / 66 % of 66% 32 % of 37% A 92 % of 50 i 56 % of 62% WRITTEN EXERCISES 1. A merchant's sales were $14,880 last month. How much will be this month's increase at the rate (a) Of 25%? (b) Of 33%%? (c) Of METHOD (a) $14,880 (b) $14,880 (c) $14,880 X25 .33% .06% $3,720 Ans. $4,960 Ans. $930 Ans. Write the given per cents as shown above, but obtain the result by dividing $14,880, the base, by 4 in (a), by 3 in (6), by 16 in (c): that is, multiply the base by %, %, and % 6 , the fractional equivalents of the respective rates. 2. Write answers from the book: a 25 % of 24,672 6 33% % of 34,569 c 6% % of 17,632 d 50 % of 17,976 e 11% % of 96,543 / 8% % of 12,396 62 WALSH'S BUSINESS ARITHMETIC METHOD BY ALIQUOT PARTS While at school a pupil should accustom himself to the employment of methods used in the business world, specimens of which are given in the following examples : 3. Find (a) 37%% of 872, (b) 62%% of 984, (c) 27%% of 548, (d) 36%% of 936. METHOD (a) 37%% of 872 (b) 62%% of 984 25% = 218 50% = 492 + 12%% = 109 + 12%% = 123 37%% = 327 Ans. 62%% = 615 Ans. (c) 27%% of 548 (d) 36% % of 936 25% = 137 33%% = 312 + 2%% = 13.7 + 3%% = 31.2 27%% = 150.7 Ans. 36^% = 343.2 Ans. In (a) find 25 % of 872 by taking }{ of it; find 12% % of 872 by taking % of the one-fourth. Test (a) by multiplying 109 by 3; (6) by multiplying 123 by 5; (c) by multiplying 13.7 by 11; (d) by multi- plying 31.2 by 11. Why? 4. Find answers: a 37^ % of 392 b 62% % of 664 c 27% % of 680 d 36% % of 780 e 31^ % of 384 / 56# % of 7G8 g 5&A % of 760 // :*6% % of 690 i 18% % of 5*4 6. Find (a) 17X%, (6) 68%, (c) 81H%, ( .35 WRITTEN EXERCISES 1. Copy and complete the foregoing invoice. 2. (a) How much discount will be allowed if the invoice is paid in January, 1920? (6) What sum will settle the invoice on this date? The terms are sometimes expressed in a shortened form; 60-2/30, meaning that a credit of 60 days is granted, with discount of 2 % for pay- ment within 30 days. . 77 78 WALSH'S BUSINESS ARITHMETIC 3. Find the sum that will settle each of the follow- ing bills (invoices) on the date specified: a Bought Nov. 16, 1920 b Bought Mar. 23, 1921 2 library tables at $9.65 7 cases milk $3.50 4 parlor tables at $2.50 3 " " 4.20 Terms 60-2/30 Terms 30-1^/10 Paid Dec. 4, 1920 Paid_Apr. 4, 1921 The terms of the following in voice, 60 - 2/10 - 1/30 indicate a credit of 60 days, a discount of 2 % for pay- ment within 10 da,ys, or 1 % for payment within 30 days. 4. W. S. Goodnough buys of John Ziegler & Co., on January 7, 1920, 1% doz. milk kettles @ $18 per dozen, and 2%doz. dippers @ $2.10 per dozen. What sum will settle the bill (a) on February 14, 1920? (b) On January 12, 1920? (c) On March 12, 1920? 5. A grocer bought on March 1, 1921, 1500 pounds of coffee at 18.75^ per pound. Find (a) the net amount of the bill ; that is, the sum due at the expi- ration of the credit period, (b) The sum required to pay the bill on March 10 with 1% discount, (c) The sum payable on March 13, if the seller allows a dis- count for 48 days at the rate of 6 % per year. TRADE DISCOUNTS "List Prices" Many manufacturers issue catalogues describing their products. The prices given in these catalogues (list prices) are much higher than those actually charged to dealers, being subject to a trade discount. BUSINESS CALCULATIONS 79 which is not specified in the catalogue, but is contained in a discount sheet supplied only to customers. When rates are changed, a new discount sheet is sent out. The following bill (invoice) for sewer pipes provides for specified trade discounts. A cash discount of 2% of the net amount is offered for payment within 15 days. The net amount of a bill is generally taken as the sum required to settle the bill at the end of the credit period, viz., $188.24 in the one given below; that is, the sum remaining after the deduction of the trade discounts. Denver, Colo., April 26, 1920 Messrs. Tully & Larkin Manitou, Colo. Order #53516 Bought of AMERICAN SEWER PIPE COMPANY Terms: 30 da.; 15 da. less 2% Buyer's Order Pieces Size Kind List Price Gross Amt. Net Total No. 1149 400 6" Pipe #2 80 320 _ 15 15" " " 2 70 (a) 15 24* 6 50 (b) 458 Dis ct. 72% () 128 24 250 8" Pipe #3 80 (d) Dis ct. 70 % 140 60 188 24 WRITTEN EXERCISES 1. Copy the foregoing bill, filling out the missing extensions; (a), (6) and (d), also (c) the missing dis- count. 2. What sum will pay this bill on May 25? 80 WALSH'S BUSINESS ARITHMETIC 3. Find the net amount of a bill for 300 pieces of 8" pipe at $1.10, and 50 pieces of 12" pipe at $2, less 74%. SIGHT EXERCISES 1. What is (a) the discount on a purchase of pipe listed at $250 when the rate is 72 %? (6) The net price? (c) What per cent of the list price is the net price? 2. When the discount is 70% (a) what per cent of the list price is the net price? (6) What is the net price of an article listed at $333? 3. When the discount is 90 %, what is the net price of an article listed at $475? 4. Give answers : a List price, $150; discount rate, 15 % Discount? b " " 203; " 30% Net price? c " " 320; " 20% Discount? d " " 110; " 40% Net price? e " " 284; " 50% Discount? / " " 560; " 25% Net price? g " " 675; " 10% Discount? h " " 222; " 60% Net price? i " " 102; " 18% Discount? j 313; 90% Net price? COMPOUND DISCOUNTS Some discount sheets offer two, three, or more, successive discounts on a given article: 25 and 5%, for example; SS 15, and 10%; 35, 10, 5, and 2^%; etc. In expressing these, the per cent sign (%) is written only after the last rate of a series. On bills, these compound discounts are frequently written thus: 25/5, 331/15/10, 35/10/5/2, without the per cent sign. The general method of determining the net price of an article subject to a compound discount is shown in the following example. The first discount is taken BUSINESS CALCULATIONS 81 on the list price, the next is taken on the remainder left after the deduction of the first discount, the next is taken on the remainder left after the deduction of the second discount, etc. WRITTEN EXERCISES 1. Find the net price of an article "listed" at $102, and subject to discounts (a) of 25 and 5%; (6) of 33%, 15, and 10%; (c) of 35, 10, 5, and 2%%. METHOD (a) List price $102. (b) List price Less 25% 25.50 Less 33%% 34. Remainder $76.50 1st Remainder $68.00 Less 5% 3.825 Less 15 % 10.20 Net price $72.68 2d Remainder $57.80 Less 5% 2.89 Net price $54.91 (c) List price $102. Less 35 % 35.70 1st Remainder $66.30 Less 10% 6.63 2d Remainder $59.67 Less 5 % 2.983 3d Remainder $56.687 Less 2%% 1.417 Net price $55.27 Test each result by taking the separate discounts in a different order; in (a) 5 and 25%; in (b) 5, 15, and 33%%; and in (c) 2%, 5, 10, and 35%. 82 WALSH'S BUSINESS ARITHMETIC 2. Find the net price of each: List price Discount Rate List price Discount rate a $104 33% and 15 % b $200 35, 10, and 5 % c 220 25 and 10 % d 300 33%, 15, and 10 % e 310 45 and 5 % / 100 45, 10, and 2%% g 201 15 and 10 % /i 150 15, 5, and 3 % i 142 35 and 5 % j 400 25, 10, and 10 % 3. What is the net price of an article listed at $275 and subject to a discount of 60 and 20 %? METHOD r\nr*f>, Z15. complements of the per cents con- 40% of (a) 110. (b) stituting the discount rate 80% of (6) $ 88. Net price To obtain the complement of a per cent, deduct it from 100%. Thus: 25 % is the complement of 75 %, 95 % is the complement of 5 %, etc. 4. Write from the book the net price of each of the following: List price Discount List price Discount List price Discount a $123.40 20% b $312.20 40% c $369.36 66%% d 211.15 30% e 156.84 50% / 248.24 87%% g 486.40 75% h 215.25 60% i 486.12 83%% 5. Using the complements of the given rates, find the net price of each of the following: a $420; 60 and 20 % 6 $465; 50 and 30 % c $450; 66% and 20 % d 352 ; 50 and 30 % e 352; 75 and 30% / 864; 87% and 30% g 275; 40 and 40 % h 576; 60 and 30% i 648; 83% and 20% BUSINESS CALCULATIONS 83 6. Copy and complete the following bill for iron pipes. Take the quantity given in feet and inches at the list price per foot. Use the "gross" column only when more than one item is subject to the same discount. INTERNATIONAL TUBE COMPANY Birmingham, Ala. SOLD TO Thomas N. DeLaney, Wilmington, N. C. Terms 60-2/10. Route S. A. L. March 29, 1921 Agency Order 5188 Customer's Order 3716 Car S. A. L. 75190 F.o.b. Wilmington Bdls. Size Description Feet In. List Price Gross Total Dis. Net 15 3 '/ Wro't Pipe 5322 6 .10 532 25 60-20 to 15 3 " (C 2093 3 .20 418 65 25 r ( 2 82 4 .30 804 70 1223 35 70-20 (/) 15 3652 9 .16 (a) 75-20 (9) 25 if " 1562 .40 (&) 25 ir 1534 8 .50 JL (d) 70-30 (h) K4 NOTE: F. o. b. Wilmington means that the goods are delivered at the R. R. station at Wilmington without charge for cartage at Birmingham or freight charges to Wilmington. The buyer is expected to remove them promptly from the freight car upon notification of the arrival of the latter. The invoice gives the designation of the car S. A. L. (Seaboard Air Line) and its number. SIGHT EXERCISES 1. Give the per cent of the list price equal to: a 40 % of 80 % of it. c 50 % of 70 % of it. e 25 % of 70 % of it. 6 33%% of 80% of it. d 12K%of 70% of it. / 16%% of 80% of it. 84 WALSH'S BUSINESS ARITHMETIC 2. What per cent of the list price is the net price when the discount rate is: a 20 and 10 %? b 30 and 20 %? c 75 and 20 %? d 40 and 20 %? e 50 and 10 %? / 66% and 10 %? 30 and 10 %? A 40 and 30 %? i 87^ and 20 %? j 60 and 20 %? fc 70 and 10 %? / 83# and 40 %? 3. Give the net price of each of the following: List price Discount List price Discount a $444 75 and 20 % b $312 66% and 10 % c $695 87/ 2 and 20 % d $547 83% and 40 % 4. What single discount equals a double discount of 40 and 20%? When the discount is 40 and 20%, the net price is 60% of 80% of the list price; that is, it is 48% of the list price. The discount is, therefore, 52% of the list price (100% T 48%). A shorter method to obtain the latter is to deduct from the sum of the successive discounts their product. (40% + 20%) - (40% of 20%) = 60% - 8% = 52% 6. Give the single discount equal to each of the following : a 60 and 10% b 50 and 40% c 90 and 10% d 33% and 10% e 80 and 20 % / 60 and 30 % g 70 and 20 % h 66% and 10 % 1 70 and 10 % j 80 and 10 % k 60 and 40 % I 83% and 10 % 6. Which is the better discount for the buyer? a 60 and 10 % or 50 and 20 % b 40 and 20 % or 30 and 30 % c 80 and 20 % or 70 and 30 % d 50 and 40 % or 60 and 30 % e 50 and 30 % or 40 and 40 % / 30 and 20 % or 40 and 10 % WRITTEN EXERCISES 1. Two manufacturers list a certain grade of piano at $975. One offers a discount of 60 and 20%; the other offers 50 and 30%. (a) What per cent of the list price does the purchaser save by taking the better BUSINESS CALCULATIONS 85 offer? (6) How much money does he save on each piano purchased at the lower rate? 2. What single discount is equal to a discount of 45, 10, and 5 %? METHOD A discount of 45 and 10% = 45% + 10% - (10% of 45%) = 55% - 4.5% = 50.5%; a discount of 50.5 and 5 % = (50.5 % + 5 %) -- (5% of 50.5%) = ? First combine two of the successive discounts into an equivalent single discount; then combine the latter and the third successive discount into an equivalent single discount. 3. Find the single discount equivalent to each of the following: a 40, 10, and 10% 6 50, 20, 10, and 5% c 30, 20, and 10% d 60, 30, 10, and 5% 4. What per cent of the list price is the net price when the discount rate is 50, 30, and 20%? METHOD Using the complements, take 50 % of 70 % of 80 %, which can be simplified by taking 50% of 80% of 70%. 5. What per cent of the list price is the net price when the discount rates are, respectively? a 75, 20, and 10 % 6 87& 20, and 10 % c 66%, 10, and 5 % d 8S& 40, and 5 % e 45, 10, and 5 % / 60, 30, and 10 86 WALSH'S BUSINESS ARITHMETIC 55% lessKo 5.5 49.5 % less Ko 2.475 47.025 % METHOD Many accountants prefer the de- duction of Xo to the multiplication, by 90%. All prefer the deduc- tion of Ko to the multiplication by 95%. Begin with 55 %, the complement of 45%. 6. What per cent of the list price is the net price when the discount rates are, respectively? a 55, 15, and 5% b 45, 15, 10, and 5% To be enabled to make calculations more rapidly, bill clerks use tables showing the per cent of the list price to be taken in determining the net price of articles subject to a compound discount. The table also gives the equivalent single discount. The following shows a portion of one of the pages: COMPOUND DISCOUNT TABLE 30 40 50 60 Supplementary Discounts Dis. Net Dis. Net Dis. Net Dis. Net .30 .70 .40 .60 .50 .50 .60 .40 5 .335 .665 .43 .57 .525 .475 .at .38 10 .37 .63 .46 .54 .55 .45 .64 .36 10 5 .4015 .5985 .487 .513 .5725 .4275 .658 .342 15 .405 .595 .49 .51 .575 .425 15 5 .43475 . -5i;.>*5 .5155 .4845 .59625 . 40375 15 10 .4645 .535 .541 .459 .6175 .3825 15 10 5 .491275 .508725 .56395 .43605 .636625 .363375 20 .44 .56 .52 .48 20 5 .468 ,m .544 .456 20 10 ,4M .504 .568 .432 20 10 .5212 .4788 .5896 .4104 BUSINESS CALCULATIONS 87 7. Calculate (a) the missing net rates; (b) the missing equivalent single discounts. Check results by finding the total of (a) and (6) in each case. 8. Find 'the net price of goods subject to a discount of 30, 15, 10, and 5% and listed (a) at $4812; (6) at $481.20. 9. Find the net price of each of the following: List price Discount List price Discount a $568 30, 15, 10, and 5 % b $4812 40, 15, and 5 % c $328 50, 15, 10, and 5 % d $6408 50, 15, and 5 % 10. Find the net price of goods subject to a discount of 30, 15, 10, and 5 % and listed (a) at $3876; (b) at $387.60. 11. Find the net price of each of the following: List price Discount List price Discount a $678 30, 15, 10, and 5 % b $4929 40, 15, and 5 % c $547 50, 15, 10, and 5 % d $6457 50, 15, and 5 % QUANTITY DISCOUNTS Manufacturers of certain staples frequently offer discounts dependent upon the quantity purchased. The following bill shows a deduction of 20 cents per 100 pounds from the rate charged to smaller buyers. To withhold from other customers information as to the jobber's discount, it is inserted by means of a rubber stamp only upon the bills of such purchasers as are entitled to receive it. 88 WALSH'S BUSINESS ARITHMETIC SAN FRANCISCO, CAL., Jan. 8, 1921 Messrs. Jno. Ziegler & Co. Bought of THE PACIFIC SUGAR REFINING COMPANY Terms 10 days; cash less 1 % 7 days Bbl. Cases Bags Fine #5 #2 Less 5i and 10^ per 100 Ib. special 5 " " Net 12790 3200 (d) Price 7.34 7.44 (b) (3} WRITTEN EXERCISES 1. Copy the foregoing bill, filling in the omitted items. 2. Give the sum that will settle it if payment is made on Jan. 12. Sometimes the discount is conditioned upon payment within a specified time. INDIAN ROCK, VA.. Aug. 2, 1919 Messrs. Popkins & Appich Meadow Springs, Ohio Bought of SWIFT & STEVENSON Manufacturers of Building and Agricultural Lime 130 bbl. Lime 1.35 $ Terms: 5t per bbl. discount if paid in 10 days from date of bill, 60 days net. When the allowance of a discount, or its amount, depends upon the time of payment, the seller does not enter the dis- count upon the bill. The buyer makes the proper deduc- tion, if any, and sends his check for the remainder. CHAPTER THREE SIMPLE INTEREST LENDING MONEY Banks, life insurance companies, individuals, etc.,, are always ready to loan their spare funds to reputable borrowers that furnish satisfactory security to pay a fair rate for the use of the money and to return the latter at a specified time. The sum loaned is called the PRINCIPAL. The sum paid for the use of the principal, is called the INTEREST. The per cent of the principal to be paid for its use for a year, is called the RATE. BONDS Among the borrowers are the United States, in- dividual states, counties, cities, railroads, etc. As evidence of the loan the lenders receive bonds. These documents specify the sum loaned, the rate of interest, the time of successive interest payments (which are generally made half yearly or quarterly), and the date for the repayment of the principal. MORTGAGES, DEEDS OF TRUST The owner of a house or a farm can borrow money by giving, as security, a mortgage or a deed of trust. 89 90 WALSH'S BUSINESS ARITHMETIC Either document provides that if the borrower defaults in making payments of interest or principal, the lender may cause the property to be sold, and the amount due to be paid him from the proceeds. BANK BOOK The evidence of the loan to a savings bank by a depositor is given by the entry made in the latter 's pass book. PROMISSORY NOTES A common evidence of indebtedness is a promissory note, which every lender should require in the absence of other security. This should show the sum loaned, the date of the loan, the time for its repayment, the rate of interest, etc. PREPARATORY EXERCISES 1. A man borrows $1000 on a mortgage, agreeing to pay annually for the use of the money 6% of the sum borrowed, (a) How much does he pay each year? (b) If he makes these payments every six months, how much is each semi-annual payment? 2. At 6 % per year, how much should a person pay (a) for 1 month's use of $1000? (b) For 2 months' use? (c) For 5 months' use? 3. A woman has $400 on deposit in a savings bank. If the bank allows her 4% per year, how much will her money earn in 6 months? 4. How much interest does a girl receive every 3 months on a $50 Liberty Bond that pays 4 per cent interest each year? BUSINESS CALCULATIONS 91 SIGHT EXERCISES 1. Give the interest on $1200 for 1 year at: a 6% b 5% c 7% d 4^% e 5%% f g 8% h 4% i 3% j 6^% k 3%% I 2. Give the interest at 6% for 1 year on: a $100 6 $150 c $200 d $250 e $1200 / $1250 g $125 h $225 i $325 j $425 & $1500 / $2100 3. Give the interest for 1 year on: a $150 at 5 % b $225 at 4 % c $1230 at 3 % d $310 at 6 % e $510 at 8 % / $2010 at 7 % 4. Give the interest at 6% on: a $150 for 2 yr. 6 $300 for % yr. c $400 for 6 mo. for 3 yr. e $400 for % yr. / $600 for 4 mo. 5. Give the interest on: a $200 at &% % for 3 yr. b $300 at 5 % for 6 mo. c $120 at 4^ % for 2 yr. d $500 at 4 % for 3 mo. e $400 at 3%% for 4 yr. / $100 at 6 % for 8 mo. 6. Assuming the year to consist of 360 days, give the interest at 6% on $300 for: a 120 da. 6 180 da. c 90 da. d 60 da. e 40 da. / 20 da. WRITTEN EXERCISES 1. (a) In 3 years at 5%%, how much interest does a man pay on a mortgage of $1580? (5) How much interest is paid on a loan of $875 in 4K years at 6%? 92 WALSH'S BUSINESS ARITHMETIC METHOD (a) Principal $1580 (6) Principal 875 Rate X .05# Rate X .06 790 Interest for 1 yr. $52.50 7900 Time in years X 4^ Interest for 1 yr. $86.90 2625 Time in years X 3 21000 Int. for 3 yr. $260.70 Int. for 4^ yr. $236.25 Reverse the order of the factors, in (a) multiplying $1580 by 3 and this product by 5%; or, combine the factors into a single one, multiplying $1580 by 16& In (6) multiply $875 by 27. To find the interest multiply the PRINCIPAL by the RATE (expressed as hundredths) by the TIME (in years) . 2. Find the interest on: a $756 at 6 % for 4 yr. 6 $968 at 5 % for 1% yr. c 359 at 4 % for 1 yr. 6 mo. d 642 at 5 % for 3 yr. e 495 at 7 % for 2M yr. / 825 at 6 % for 2 yr. 3 mo, g 508 at 7 % for 2 yr. h 287 at 6 % for 3^ yr. i 163 at 9 % for 3 yr. 4 mo. j 753 at 4 % for 1 yr. 4 mo. 3. Find the interest at 6% on: a $120 for 5 mo, 6 $480 for 12 da. c $840 for 5 mo. 12 da. d 240 for 7 mo. e 600 for 18 da. / 960 for 7 mo. 18 da. g 360 for 9 mo. h 720 for 24 da. i 180 for 9 mo. 24 da. BUSINESS CALCULATIONS 93 4. Find the interest on $180 at 6% for (a) 24 da. (b) 8 mo. 24 da. a METHOD .03 12 .03 X .00 X ft* , $WP X .00 X 264 Indicate the time in years by writing it in (a) as %o, and in (6) as 2 % , changing 8 mo. 24 da. to 264 da. 5. Find the interest on $720 at 6 % for (a) 25 da. (6) 68 da. (c) 2 mo. 8 da. (d) 6 mo. 26 da. 6. On March 1, 1917, Charles Wilcox borrowed $475 of Arthur Washburn, which he agreed to repay on demand with interest at 6%. As evidence of the indebtedness he gave Mr. Washburn the following note: Harvey, Neb., March 1, 1917 On demand after date, I promise to pay to the order of Four Hundred Seventy-five %o ..................... Dollars Value received, with interest at 6%. 94 WALSH'S BUSINESS ARITHMETIC Every six months Mr. Wilcox paid % year's interest. (a) How much was each payment? (6) How much had he paid in interest up to and including the pay- ment on March 1, 1920? (c) If he settled the indebtedness on Aug. 18, 1920, how much would be the sum of his interest payments? (d) Find the interest on $475 at 6 % for 5 mo. 17 da. CANCELLATION METHOD (c) Find by compound subtraction the time 1920-vin-18 for which interest is paid. 1917- in- 1 3- v-17 Syr. = 1080 da 5 mo. = 150 " 17 da. = 17 1247 360 Change the compound number 3 yr. 5 mo. 17 da. to days (1247). Write 360 as a denominator, thus expressing it in years (in the form of an improper fraction.) Indicate the product of the principal, by the rate (in hundredths), by the time in years; cancel. 95 .01 12 (d) The interest for 167 days is indicated thus $475 X . 06 x 167 360 Test Test both results by deducting (d) from (c). The difference should be the interest for 3 years. When the time is given in years, months, and days, take each year as 360 days and each month as 30 days. BUSINESS CALCULATIONS 95 7. Find the interest at 6%: a $378 for 3 mo. 18 da. b $840 for 2 mo .9 da. c 156 " 4 " 20 tt d 252 " 6 n 8 " e 618 " 8 " 17 n f 507 " 5 a 3 " 9 405 " 9 " 28 ft h 936 " 7 a 6 " i 864 " 1 tt 25 tt 3 738 " 2 tt 5 " k 534 " 2 20 I 351 " 1 tt 7 " 8. Find the interest on: a $426, ,60 for i yr. 3 mo. 18 da. at 4% b 318.75 tt 2 " 7 tt 15 " a 6% c 563, ,10 " 3 " 4 n 24 " " 5' % d 911 25 2 " 8 tt 13 " a 3% e 123, 45 tt 1 " 5 n 16 " " 8' f 708, ,36 tt 2 " 9 a 17 " a 7% 9 245 .70 a 3 " 6 tt 11 " st 9' h 636 ,30 a 2 " 2 if 23 " ** 8.' % i 824, ,40 " 1 " 7 it 14 " ' 5' % j 135.66 tt 2 " 1 tt 12 " tt 6% 9. Find the interest on : a * 378 at 6 % for 140 da. b $156 at 3 % for 57 da. c 405 "5% tt 105 " d 804 " 6% " 69 e 980 "6% 126 tt f 252 " 5% " 87 " g 536 "4% tt 144 a h 438 m 25% n 31% o 20% p q 22K r 24% * 26% t u 11% v 18% EXPRESSING A FRACTION IN LOWEST TERMS 5. What fraction of a yard is (a) 27 inches? (6) 24 inches? (c) 32 inches? PROCESS (a) 27 in. = % yd. = % yd. Ans. (6) 24 in. = % yd. = % yd. Ans. (c) 32 in. = % yd. = % yd. Ans. (a) Reduce % by dividing both terms by 9. (b) Reduce % by dividing both terms by 12. (c) Reduce % by dividing both terms by 4. A pupil who does not see at once that 9 is the greatest common divisor of 27 and 36 may first reduce % to & by dividing each term by the com- mon factor, 3. Before announcing % as the answer, he should be expected to note that it is further reducible to %, 9 and 12 having 3 as a common factor. NUMBERS AND PROCESSES 157 6. Express in lowest terms : a % b % c % d % / % 9% h % i % j % k % / % m % n % o % p % g % r % ^ % t %o t* % ^ % w 3 %4 a; % y % 7. Give the greatest common factor of: a 18 and 27 6 25 and 60 c 16 and 36 d 36 and 48 e 40 and 72 / 20 and 75 g 48 and 72 h 36 and 54 i 15 and 50 j 75 and 90 fc 36 and 60 I 20 and 75 8. What is the greatest common factor of 57 and 95 ? PROCESS A pupil that does not see at once that 19 is a common factor of 57 and 95, should note that both 57 and 95 are composite numbers. Obtaining 3 and 19 as the factors of 57, he tests 19 as the divisor of 95. 9. Express in lowest terms: a % b % c % d % e % / % g % h % i % j % SIMPLIFYING A COMPLEX FRACTION 10. What fraction of a rod (16# feet) is (a) 12# ft.? 9% ft.? 158 WALSH'S BUSINESS ARITHMETIC PROCESS Express each as a complex fraction of a rod by writing 16% as the denominator. Simplify the com- plex fractions. 12% 25 W E * M rf (a) Multiply both terms of the complex fraction by 2. (6) Multiply both terms by 6, the least com- mon denominator of % and %. 11. Express as a simple fraction: 1% , 2% 3% , 4K 5% ct o c a 6 4 3 7 8,9 A & A _! 8 ^l/ " r "t\/ Q3/ G2/ 1 HI/ ,2% . 8M 1% 5% 4% fc_f /-^ 771-^ n Ql/ 1 2/ 1 1/ 017 Ql/ 0/2 1/5 1/4 ^73 "72 7} O 7" S * Y VA * 2/io 2^ 3^ 4% ^3^ ^2K ^tt ^.3^ 7 W EXPRESSING A COMMON FRACTION AS A DECIMAL 12. \Vhat decimal of a pound is an ounce? PROCESS 1 oz. = KG lb. = .0625 Ib. Think of & as % of & which is % of .25. This is or .0625. NUMBERS AND PROCESSES 159 13. Express as a decimal: a 1 A b^ c % d% e % f % 9% h fa i % j % k YB I % m Ko n fa o %> P r& Q /oO f 720 ^ /80 ' 725 u fa v fa . w %o x %o y fa CHANGING A DECIMAL TO A COMMON FRACTION 14. Change to a common fraction, lowest terms: (a) .87. (6) .124. (c) .0275. PROCESS (a) .87 = % , Ans. (6) .124 = "ft = %o, Ans. (c) -.0275 = 27 Koooo = 5 ^ooo = %o, Ans. (a) The common fraction %o is expressed in lowest terms since 87 is divisible by neither 2 nor 5. (6) Express as a common fraction and reduce to lowest terms by dividing both terms by 4. (c) If you do not observe that both terms are divis- ible by 25, divide twice by 5. 15. Express as a common fraction lowest terms : a .5 b .25 c .33 (2 .125 c .008 / -8 k .6 g .45 I .06 /* .05 m .08 i .025 n .375 j .012 o .037 P - 7 u A q .32 v .09 r .44 w .56 5 .625 x .875 * .045 y .168 DENOMINATE NUMBERS LOWER TERMS 16. A vessel made a trip from Liverpool to New York in 5 days 12 hours. How many hours were consumed in making the trip ? 160 WALSH'S BUSINESS ARITHMETIC PROCESS 5 da. 12 hr. = 132 hr., Ans. Think 120 hr. (5 times 24 hr.) 132 hr. (adding 12 hr.) 17. Change to hours: a 2 da. 13 hr. b 3 da. 20 hr. c 4 da. 16 hr. d 5 da. 18 hr. e 6 da. 11 hr. / 7 da. 10 hr. g 8 da. 12 hr. h 9 da. 15 hr. i 8 da. 16 hr. 18. Change to ounces: a 4 Ib. 15 oz. 6 5 Ib. 14 oz. c 10 Ib. 8 oz. d 6 Ib. 13 oz. e 7 Ib. 12 oz. / 20 Ib. 5 oz. g 8 Ib. 11 oz. h 9 Ib. 10 oz. i 30 Ib. 7 oz. 19. Change to quarts: a 13 gal. 1 qt. b 15 gal. 2 qt. c 17 gal. 3 qt. d 19 gal. 3 qt. e 21 gal. 2 qt. / 23 gal. 1 qt. g 25 gal. 1 qt. h 31 gal. 2 qt. i 42 gal. 3 qt. 20. Change to months: a 7 yr. 10 mo. 611 yr. 8 mo. c 20 yr. 9 mo. d 8 yr. 11 mo. e 12 yr. 7 mo. / 25 yr. 7 mo. g 9 yr. 10 mo. h 13 yr. 6 mo. i 30 yr. 3 mo. 21. Change to pecks: a 12 bu. 3 pk. b 32 bu. 1 pk. c 24 bu. 3 pk. d 22 bu. 1 pk. e 41 bu. 2 pk. / 52 bu. 2 pk. g 15 bu. 2 pk. h 18 bu. 3 pk. i 61 bu. 1 pk. 22. Change to quarts: a 13 pk. 7 qt. b 21 pk. 4 qt. c 41 pk. 1 qt. d 14 pk. 6 qt. e 22 pk. 3 qt. / 51 pk. 2 qt. g 15 pk. 5 qt. h 31 pk. 2 qt. i 61 pk. 3 qt. NUMBERS AND PROCESSES 161 23. Change to inches: a 11 ft. 6 in. b 21 ft. 3 in. c 13 ft. 5 in. d 25 ft. 9 in. e 15 ft. 8 in. / 22 ft. 7 in. g 31 ft. 2 in. h 33 ft. 1 in. i 12 ft. 4 in. 24. Change to feet: a 33 yd. 1 ft. b 25 yd. 1 ft. c 43 yd. 2 ft. d 22 yd. 2 ft. e 53 yd. 2 ft. / 23 yd. 1 ft. g 42 yd. 1 ft. h 24 yd. 1 ft. i 32 yd. 2 ft. 25. Change to yards (1 rd. = 5% yd.) : a 4 rd. 1 yd. b 12 rd. 4 yd. c 14 rd. 3 yd. d 6 rd. 2 yd. e 10 rd. 5 yd. / 22 rd. 2 yd. g 8 rd. 3 yd. & 20 rd. 4 yd. i 30 rd. 1 yd. 26. A strip of embroidery measured % yd. What was its length in feet and inches? PROCESS % yd. = % times 3 ft. = % ft. = 2K ft. = 2 ft. 6 in. Ans. Change % yd. to feet by multiplying by 3. Change % ft. to inches by multiplying by 12. 27. Change to compound denominate numbers of lower denominations: a % 2 yd. 6 % 2 yd. c % yd. d % yd. e % wk. / }i wk. g % wk. h % wk. i % yr. j % yr. fc % yr. / Ko yr. ?7i % da. n % da. o % da. p % da. 162 WALSH'S BUSINESS ARITHMETIC EXPRESSING A FRACTION OF A DOLLAR AS CENTS 28. When silk is sold at $% a yard, what is the price in cents? PROCESS $j/ = 700^ -=- 8 = 87K cents, Ans. Do not perform this division unnecessarily. The pupil should know 12% cents as $%, and multiply by 7. 29. Change to cents: a $) b $X c $X 6 d $ $X / $% <7 $& /? $ * $Y* j $X A: $Ko / $ m $K n $}^ o $Ko p $ 9 $^ r $% s $/5o ^ $ W ^/ 8 V $% ^ $^5 $ HIGHER TERMS 30. What fraction of a dollar is 6% cents? PROCESS $6% $20 If you do not surely recall the fraction, express 6% cents as a complex fraction of a dollar. Re- duce this to a simple fraction by multiplying both terms by 3. Express this fraction in lowest terms. NUMBERS AND PROCESSES 163 31. Express as a fraction of a dollar: a 1%^ b \%%i c 37%t d f 2% g W%t h 83}^ i k m I 18% m SlYd n 951 o p 6%t q 33% r 62% s 60^ t 22% u 8% v 43% w 68% x 65 j y 28% 32. Interest for 144 days is due on a loan. What part of a year's interest is due? PROCESS 144 da. = 14 % 6 o yr. = % yr. Ans. Express the time as the fraction of a year of 360 days. Reduce this fraction to lowest terms. 33. Express as a fraction of a year: a 80 da. b 108 da. c 120 da. d 180 da. e 72 da. / 144 da. g 135 da. h 216 da. i 60 da. j 225 da. k 285 da. I 215 da. m 45 da. n 200 da. o 160 da. p 252 da. g 40 da. r 320 da. s 324 da. < 280 da. 34. What fraction of a year is 10 months 15 days? PROCESS 10 mo., 15 da. = 10% mos. = - yr. = % yr. % yr.; or change 10 mo., 15 da. to 315 da., or 31 % 60 3 Reduce this fraction to %, then to %. 164 WALSH'S BUSINESS ARITHMETIC 35. Express as a fraction of a year: a 1 mo. 10 da. d 4 mo. 20 da. g 1 mo. 15 da. j 4 mo. 24 da. ra 9 mo. 18 da. b 9 mo. 10 da. e 2 mo. 12 da. h 3 mo. 18 da. k 7 mo. 15 da. n 1 mo. 20 da. c 6 mo. 20 da. / 4 mo. 15 da. i 3 mo. 20 da. 1 9 mo. 45 da. o 4 mo. 12 da. 36. A plot of ground contains 600 square rods. How many acres and square rods does it contain? PROCESS 600 sq. rd. = 3 A. 120 sq. rd. Ans. Divide 600 sq. rd. by 160 sq. rd., which gives a quotient of 3 and a remainder of 120 sq. rd. 37. Change to acres and square rods: a 197 sq. rd. b 325 sq. rd. c 1681 sq. rd. d 968 sq. rd. e 487 sq. rd. / 3207 sq. rd. g 360 sq. rd. h 645 sq. rd. i 4809 sq. rd. 38. Change to pounds and ounces: a 57 oz. b 73 oz. c 100 oz. d 164 oz. e 68 oz. / 84 oz. g 120 oz. h 329 oz. i 97 oz. j 45 oz. & 110 oz. I 485 oz. 39. Change to feet and inches: a 99 in. b 35 in. c 79 in. d 110 in. e 88 in. / 57 in. g 93 in. h 137 in. i 46 in. j 90 in. k 63 in. J 150 in. 40. Change to days and hours: a 35 hr. 6 42 hr. c 53 hr. d 100 hr. e 60 hr. / 75 hr. g 80 hr. h 121 hr. i 95 hr. j 90 hr. k 97 hr. I 250 hr. NUMBERS AND PROCESSES 165 41. Change to years and months : a 98 mo. b 87 mo. c 45 mo. d 109 mo. e 38 mo. / 56 mo. g 90 mo. h 123 mo. i 77 mo. j 92 mo. k 66 mo. I 100 mo. 42. Change to months and days: a 72 da. b 87 da. c 196 da. d 164 da. e 45 da. / 96 da. g 215 da. A 265 da. i 58 da. j 69 da. A; 257 da. / 338 da. 43. Change to pecks and quarts: a 100 qt. b 121 qt. c 169 qt. d 180 qt. e 201 qt. / 150 qt. g 243 qt. h 325 qt. z 165 qt. j 281 qt. k 401 qt. / 487 qt. 44. Change to bushels and pecks: a 245 pk. b 50 pk. c 63 pk. d 89 pk. e 127 pk. / 97 pk. g 75 pk. h 91 pk. i 169 pk. j 85 pk. k 59 pk. I 77 pk. 46. Change to gallons and quarts: a 317 qt. b 89 qt. c 98 qt. d 51 qt. e 285 qt. / 57 qt. g 77 qt. h 66 qt. i 174 qt. j 94 qt. fc 83 qt. / 71 qt. 46. Change to yards and feet: a 50 yd. b 97 yd. c 29 yd. d 154 yd. e 88yd. / 70yd. g 46yd. /* 218yd. i 82 yd. j 52 yd. k 80 yd. / 163 yd. w 40 yd. n 49 yd. o 95 yd. p 241 yd. OMITTING "SIDE" CALCULATIONS To show the pupil that he can dispense with many figures he has been accustomed to use, a feature should 166 WALSH'S BUSINESS ARITHMETIC be made of exercises in which the pupil writes only the answers to examples from the blackboard or the textbook. These exercises should be more difficult than the regular "sight" exercises. REDUCING FRACTIONS Only answers to be written Write answers directly from the book: 1. How many twenty-fourths are there in PROCESS 223% = 53 % Ans. Multiply 223 by 24 and "add in" 17. Say 72 (24 times 3), 89 (adding 17); write 9. Say 48 (24 times 2), 56 (carrying 8); write 6. Say 48 (24 times 2), 53 (carrying 5); write 53, 2. Change to an improper fraction: a 27% b 32% c 36% d e 45% / 21& g 33% h i 36% j 11% k 1% / m 54% n 22%, o 39%o p 3. How many ISth's are there in 9%? PROCESS 9% = '% Ans. Multiply 18 by 9, and "add in" 13. Think 72 (9 times 8), 85 (adding 13); write 5, Think 9 (9 times 1), 17 (carrying 8); write 17. NUMBERS AND PROCESSES 167 4. Change to an improper fraction: a S 7 / b 9% c 1%, d 8fc e % / 8% g 9% h 6% i 9% j 8% k 4% 9 I 3% m 7%3 n 8% o 9& p 6% 5. How many 84ths are there in 7%? PROCESS 7% = 65 %4 Ans. Instead of adding 65 to 7 times 4, add only 5, adding 6 (tens), the next partial product, to 8. Think 28 (7 times 4), 33 (adding 5); write 3. Think 56 (7 times 8), 59 (carrying 3), 65 (adding 6); write 65. 6. Change to an improper fraction: a 3% 6 4% c 7% d 5% e 6% / 8% g 9% * 8% i 4% j 5% fc 6% / 7% m 5% n 6% o 7% p 8% 7. Change 65 %4 to a mixed number. PROCESS p DENOMINATE NUMBERS 9. How many ounces are there in a package weighing 23 pounds 11 ounces? PROCESS Change 23 Ib. to oz. by multiplying 16 oz. by 23, and "adding in" 11 oz. Use 16 as the multiplier. Think 48 (16 times 3), 59 (adding in ll); write 9. Think 32 (16 times 2), 37 (carrying 5); write 37. Ans. 379 oz. 10. Change to numbers of the lower denomination : a 27 bu. 5 pk. d 48 yr. 5 mo. g 29 gal. 2 qt. j 16 wk. 6 da. m 38 ft. 7 in. b 32 Ib. 13 oz. e 38 ft. 11 in. h 11 mo. 27 da. k 15 yr. 11 mo. n 22 Ib. 11 oz. c 21 da. 5 hr. / 43 yd. 2 ft. i 25 pk. 6 qt. I 16 rd. 2 yd. o 36 yr. 7 mo. 11. A certain journey requires 179 hours. How many days and hours does it require? NUMBERS AND PROCESSES 169 PROCESS 179 hr. = 7 da. 11 hr. Ans. The integral part of the quotient of 179 hr. divided by 24 hr. is 7; write 7 (da.j. To obtain the number of hours remaining, deduct 7 times 24 from 179. Think 28 (7 times 4), and 1 (writing 1) are 29. Think 14 (7 times 2), 16 (carrying 1), and 1 (writ- ing 1) are 11. 12. Change to compound numbers two denomi- nations : a 191 hr. 6 157 oz. c 257 in. d 223 pk. e 354 da. / 235 mo. g 389 in. h 197ft. i 200 hr. j 180 oz. k 225 pk. I 205 oz. m 475 da. n 195 mo. o 157 hr. p 365 da. q 365 s. r 364 far. WRITTEN EXERCISES REDUCING FRACTIONS 1. When steel bars are worth $43.20 pen ton, how much can be bought for $16.20? PROCESS $16.20 -^ 43.20 = 16 % 32 = % 6 = & = X (T.) Ans. Change the original fraction to *%2 by rejecting the dollar signs, the decimal points, and the ter- minal ciphers of both terms. Divide both terms of l %2 by 2, since they are even numbers. Divide both terms of % 6 by 9, since the sum of the digits in each is 9. Divide both terms of % 4 by 3. To complete the answer, write T. in a parenthesis. 170 WALSH'S BUSINESS ARITHMETIC 2. Reduce to lowest terms: a 19 %88 b %, c 2 % 6 d A; 1( %4 Z 1( %o m *%o n 2 % o 18 % 6 p x % 2 s 2 < "os 3. A woman paid $3.22 for a piece of velvet, at the rate of $5.22 per yard. What fraction of a yard did she buy? After 322/552 is reduced to 161/276, a common divisor of 161 and 276 is not readily determinable by inspection, 161 not being divisible by 2 or by 3, which are factors of 276. Employ the following method: PROCESS 32 %52 = 1( %6 = 7 / 2 (yd.), Ans. 161 Divide, 276 by 161. Omit the quo- 46 276 115 23 tient, 1; write only the remainder, 115. Divide 161 by 115, writing only the remainder, 46. Divide 115 by 46; omitting the quotient, 2. Obtain the remainder, 23, by thinking 12 (twice 6), and 3 (writing 3), are 15; 8 (twice 4), 9 (carry- ing 1) and 2 (writing 2) are 11. Divide 46 by 23. Since there is no remainder, 23 is a factor of 46; it is, therefore, a common factor of 161 and 276. Divide both terms of the fraction by 23, the G. C. D. NUMBERS AND PROCESSES 171 4. Express in lowest terms: Reduce as far as possible by dividing both terms by 2, 3, 5, etc., before using the foregoing method of obtaining the greatest common divisor. a 3 % 2 6 2 % 4 c 3 % d 3 % 2 e 4 % 5 / m /m 9 5 %6 h *% 5 i 4 %4 j *%4 k 3 % 4 I 3 %o m 4 %2 n %2 o / m p *% 7 5. A farmer has 231 acres of land under cultivation. There are 112 acres of corn, 78 of wheat, 22 of rye, and 19 of oats. Find for each of the foregoing (a) the fraction it constitutes of the total, and (b) the decimal (4 places). PROCESS (a) (&) Corn 112 acres, *%i = % = -4848 + Wheat 78 " %i = % = .3377 - Rye 22 " %i = & = .0952 + Oats 19 " % 1 = %i= .0823- Total 231 " 2 %3i 1 1.0000 Express each item as a fraction, making its number of acres the numerator, and 231 its denominator. For (a), reduce each fraction to its lowest terms. For (6), change each fraction to a decimal by dividing its numerator by its denominator. 4848 4- Pl ace a decimal point after 16 and annex a cipher. Place a decimal point in the quotient immediately over the one in the dividend. When the second remainder is found to be 16, the same as the original dividend, 172 WALSH'S BUSINESS ARITHMETIC discontinue the division, as the quotient will be 48484848 ad infinitum. Write a plus sign after the fourth decimal to show that the next figure is less than 5. 33766 In this division the fifth figure is - greater than 5. Write the answer, ' therefore, as .3377 , the minus sign indicating that the result is greater than .33765. 48 Place two ciphers after the decimal .09523 point in this dividend. Follow the 21)2.00 decimal point in the quotient with 110 a cipher preceding 9, the first sig- 50 nificant figure. Write a plus sign 8 after 2 to show that the next figure is less than 5. Since the fifth .08225 figure is more 231)19.00 than 5, write 520 the answer as 580 .0823- 118 6. Express as 4 place decimals: a fa 6 % cfa d %! e % / % g % h % 7 Since the denominator of a decimal is a power of 10, the prime factors of which are 2 and 5, a fraction expressed in lowest terms is not reducible to a pure NUMBERS AND PROCESSES 173 decimal, unless its denominator is a power of 2 (2, 4, 8, 16, etc.); a power of 5 (5, 25, 125, 625, etc.); or a product of a power of 2 and a power of 5 (10, 20, 40, etc.); when the fraction is expressed in lowest terms. 7. There are 128 cubic feet in a cord of wood. What decimal of a cord is 5 cubic feet? PROCESS .625 .078125 = .0390625 (cord) Ans. 128 16 2 Divide both terms of the fraction %28 by 8, remem- bering that 5^8= .625. Divide both terms of the new fraction . 62 %> by 8. The new numerator becomes .078%. At this point substitute 125 for % without completing the division. 8. Change to decimals (carrying out as many places as may be necessary to give the exact value): a KG b & c % d g %2 hy M i 9. Change to decimals: (a) % 5 (b) % PROCESS (a) %5 = 2 %oo = .296, Ans. (b) % 25 = 4 %ooo = 13 %oooo = .01328, Ans. In (a) change the denominator to 1000 by multi- plying it by 8. Multiply the numerator by 8. Write the resulting fraction in decimal form. In (6) multiply both terms of the fraction by 8, and of the resulting fraction by 4. 174 WALSH'S BUSINESS ARITHMETIC 10. Change to decimals: a %B b 37 /625 C *%25 11. What decimal of a ton of 2000 pounds is 163 pounds? PROCESS = .0815 (T.) Ans. Divide the denominator by 1000 by canceling the three ciphers; divide the numerator by 1000 by pointing off three decimal places. Then divide .163 by 2. Be careful to point off the quotient properly. Write the decimal point. Think 2 into 1 does not go; write a cipher. Think 2 into 16 goes 8 times; write 8, etc. 12. Change to decimals: a %o b % c %o d e '%<> / % g 117 /x> h %o i 7 /&>o j fc k **% I %> 13. The distance between two houses is 281 rods. What fraction of a mile (320 rods) are they apart? NUMBERS AND PROCESSES 175 PROCESS Cancel the cipher in the denominator, thus divid- ing it by 10. Divide the numerator by 10 by point- ing off one decimal place. Reduce further by dividing both terms by 4; then by 8. CHECK Multiply .878% by 320, by first multiplying it by 8, then by 4, then by 10. 14. Change to decimals: a %o b *%o c % d 1( %o e %o / *%> <7 14 Keo . A 2 %o 15, Change to four-place decimals. First multiply both terms by 2: a % & % c % d % 5 P IV. f 9 /r fl 29 / C / 31 /r ^ 745 J 755 W 736 "' 745 REDUCING DECIMALS WRITTEN EXERCISES 1. Of the 400 employees in a store, .3125 are men, .3 are women, .29 are boys, and the remainder are girls. Find (a) the corresponding fraction for each, and (6) the number of each class of employees. 176 WALSH'S BUSINESS ARITHMETIC PROCESS (a) (6) Men .3125 = 31 % 00 o = & = 125 Women .3 = Xo = 120 Boys .29 = = %o = 116 Girls .0975 = 9 %oo = % = 39 1.0000 4 % 400 First find the decimal of the girl employees. Express each as a common fraction, and reduce the latter to lowest terms. TEST Test results (a) by employing the fractions to ascertain the items of (6). If these total 400, the answers to both questions are correct. NOTE: A common fraction, with its denominator a power of 10, cannot be reduced unless its numerator is an even number, or ends in 5 . 2. Express as common fractions or mixed numbers. Write answers directly from the book. a .008 6 .075 c 6.0125 d 84.0075 e .179 / .004 g 3.0044 h 63.0648 i .084 j .175 k 8.0C25 / 57.0005 m .165 n .005 o 7.0365 p 70.0125 q .006 r .395 s 9.3284 t 25.3125 u .316 v .002 w 5.3248 x 40.0375 3. Change the following complex decimals to com- mon fractions, lowest terms: a .03% b &X c .006% NUMBERS AND PROCESSES 177 PROCESS a .03^ = 3^/100 = % = Mo Ans. b .8# = 8^/10 = % = K Ans. c .006% = 6%/1000 = 2 %ooo = K5o Ans. Write each as a complex fraction. Change to a simple fraction by multiplying both terms by the denominator of the fraction in the numerator. Re- duce the simple fraction to lowest terms. 4. Express as common fractions or mixed numbers : a 1.83X b .85^ c 13.42% d .742% e S.51X? / .08% g 54.23X 3 h .384% i 5.06% j -54%i 77.06% I .210% DENOMINATE NUMBERS WEIGHING AND MEASURING There is a growing tendency in the business world to substitute weighing for measuring. The farmer dis- poses of cabbages in large quantities by the ton; olive oil and milk are sold by the pound; the number of bushels in a given quantity of grain is determined by its weight. All kinds of vegetables are retailed by the pound. (For Tables see pp. 459.) REDUCING DENOMINATE NUMBERS CHANGING TO LOWER DENOMINATIONS WRITTEN EXERCISES 1. A vessel took 14 weeks, 6 days, 18 hours to make a trip to the East Indies. How many hours were required to make the trip? 178 WALSH'S BUSINESS ARITHMETIC PROCESS Change 14 wk. 6 da. to days by multiplying 7 da. by 14 wk. 6 da. 18 hr. 14, and "adding in" 6 da. 104 da. However, use 7 as a multi- Ans. 2514 hr. plier, but do not write it. Think 28 (7 times 4), 34 ("adding in" 6); write 4 da. under 6 da. Think 7 (7 times 1), 10 (carrying 3); write 10. Change 104 da. 18 hr. by multiplying 24 hr. by 104, and "adding in" 18 hr. However, use 24 as a multiplier, but do not write it. Think 96 (24 times 4), 104 (carrying 8); write 4 hr. under 8 hr., dropping a line. Think (24 times 0), 10 (carrying 10), 11 ("add- ing in" 1); write 1. Think 24 (24 times 1), 25 (carrying 1); write 25. CHECK See the reduction of 2514 hr. to days, weeks, and hours, p. 205. 2. Change to hours: a 15 wk. b 12 wk. 6 da. c 15 wk. 5 da. 15 hr. d 35 da. e 21 da. 5 hr. / 11 wk. 3 da. 21 hr. g 22 wk h 33 wk. 9 hr. i 13 wk. 9 da. 18 hr. 3. Change to ounces: a 24 Ib. 15 oz. b 35 Ib. 14 oz. c 20 Ib. 8 oz. d 34 Ib. 13 oz. e 53 Ib. 12 oz. / 55 Ib. 5 oz. g 42 Ib. 11 oz. h 45 Ib. 10 oz. i 43 Ib. 7 oz. NUMBERS AND PROCESSES 179 4. Change to quarts: a 19 bu. 3 pk. 7 qt. b 37 bu. 1 pk. 4 qt. c 28 bu. 2 pk. 5 qt. d 26 bu. 3 pk. 3 qt. e 35 bu. 1 pk. 6 qt. / 18 bu. 2 pk. 2 qt. 6. Change to hours (a) 38 wk. (b) 29 wk. 9 hr. PROCESS Either change to hours (a) 35 wk. directly by multiplying 245 da. 168 hr. by 35, or employ Ans. 5880 hr. the factors 7 (da.) and 24 (hr.) as shown above. (b) 29 wk. da. 9 hr. Insert da. (the miss- onQ , , . . x A\)5 ola. ing denomination). Ans. 4881 hr. CHECK If the result in (a) is obtained in the manner shown above, check it by multiplying 168 hr. by 35. Check (b) by multiplying 168 hr. by 29, "adding in" 9 hr. 6. Change to inches: a 19 yd. b 27 yd. 11 in. c 33 yd. 2 ft. 9 in. d 38 yd. e 37 ft. 10 in. / 28 yd. 1 ft. 6 in. g 45 yd. h 68 ft. 11 in. i 43 yd. 2 ft. 7 in. 7. Change to feet: a 14 rd. b 14 rd. 4 yd. c 16 rd. 4 yd. 2 ft. d 22 rd. e 24 rd. 5 yd. / 42 rd. 3 yd. 1 ft. g 30 rd. h 32 rd. 3 yd. i 54 rd. 2 yd. 2 ft. 8. Change to pence: a 19 b 3 18s c 13 4s 6d d 24 e 7 16s / 25 9s 8d g 37 h 9 15s i 53 6s 7d 180 WALSH'S BUSINESS ARITHMETIC 9. A field contains 85 acres 137 sq. rd.; how many sq. rd. are there in the field? PROCESS 15? Write, if necessary, 160 65 A. 137 sq. rd. (^h e num ber of square rods 10,537 sq. rd. Ans. to the acre) as a help. Use it as the multiplier. Think (6 times 65), 7 (adding in 7); write 7 sq. rd. Think 80 (16 times 5), 83 (adding in 3); write 3. Think 96 (16 times 6), 104 (carrying 8), 105 (adding in 1); write 105. CHECK Check by dividing 10,537 by 160, using short division. 10. Change to square rods: a 16 A. 127 sq. rd. b 43 A. 84 sq. rd. c 23 A. 109 sq. rd. d 54 A. 96 sq. rd. e 32 A. 132 sq. rd. / 62 A. 75 sq. rd. 11. Change to days: (a) 2 years 7 months 12 days, (b) 3 years 11 months 21 days. PROCESS (a) 2 yr. = 720 da. , (6) 3 yr. = 1080 da. 7 mo. = 210 " 11 mo. = 3330 " 12 da. = 12 " 21 da. = 21 " Ans. 942 da. Ans. 1431 da. NUMBERS AND PROCESSES 181 In reducing the following, employ either method, using the other one as a check. 12. Change to days: a 2 yr. 7 mo. 19 da. b 3 yr. 10 mo. 28 da. c 4 yr. 8 mo. 24 da. d 5 yr. 11 mo. 17 da. e 6 yr. 9 mo. 13 da. / 7 yr. 10 mo. 24 da. CHANGING TO HIGHER DENOMINATIONS 1. A certain quantity of coal was consumed in a factory in 2514 hours. How many weeks, days, and hours did it last? PROCESS 24 hr.)2514 hr. Divide 2514 7 (da.) 104 (da.) 18 hr. hr. by 24 hr. Ans. 14 (wk.) 6 (da.) 18 hr. The 1 uotient is 104 (the number of days), and 18 hr. remaining. Divide 104 da. by 7 da. The quotient is 14 (the number of weeks), and 6 da. remaining. To avoid the appearance of a concrete quotient with concrete divisor and dividend, write da. and wk. in parentheses. Bring down 18 hr. the first remainder. Insert the proper denominations. 2. Change to weeks, days, and hours: a 1500 hr. b 2759 hr. c 1699 hr. d 2508 hr. e 3007 hr. / 1594 hr. g 2306 hr. h 3240 hr. 182 WALSH'S BUSINESS ARITHMETIC 3. Change to pounds and ounces: a 375 oz. b 495 oz. c 1629 oz. d 1746 oz. e 594 oz. / 687 oz. 2345 oz. h 3369 oz. 4. Change to years, months, and days: a 1984 da. 6 1763 da. c 2746 da. d 1195 da. e 3265 da. / 1429 da. g 1876 da. h 2344 da. 5. Change to bushels, pecks, and quarts: a 695 qt. b 879 qt. c 1015 qt. d 1244 qt. 6 389 qt. / 467 qt. g 1137 qt. h 1878 qt. 6. Change to yards, feet, and inches: a 690 in. 6 798 in. c 1246 in. d 1095 in. e 587 in. / 937 in. g 1315 in. h 1457 in. 7. Change to pounds sterling, shillings, and pence a 698 d. 6 884 d. c 1847 d. d 2358 d. e 987 d. / 576 d. g 3015 d. h 4444 d. CHAPTER FOUR SIGNS AND OPERATIONS The following diagram shows the several arithmet- ical operations with their signs, the names of the terms, etc. Operation Expression 16 is called Addend 2 is called Result is called Addition 16 + 2 = 18 Addend Sum Subtraction 16 - 2 = 14 Minuend Subtrahend Difference, or Remainder Multiplication 16 X 2 or 16 2 = 32 Factor, or Multiplicand Factor, or Multiplier Product Division 16 -*- 2 = 8 Dividend Divisor Quotient Ratio 16:2 = 8:1 Antecedent Consequent Ratio Involution 16 2 = 256 Base Exponent Power Evolution ^16 = 4 Base Index Root The expression 16 X 2 is read "16 times 2," or "16 multiplied by 2." When one of the terms is concrete, it is generally read as the multiplicand; thus $16 X 4 is generally stated "$16 multiplied by 4." A person desiring to use the word "times" reads it "4 times $16," regardless of the order of the terms in the expression. 183 184 WALSH'S BUSINESS ARITHMETIC In arithmetical subtraction, the larger number is considered the minuend in such an example as "Find the difference between 316 and 500." That 16 is to be divided by 2 may also be indicated by % or 2)16. SIGHT EXERCISES 1. Give the value of each: a 75 + 19 + 25 6 75 + 25 + 19 c 19 + 25 -h 75 d 25 X 6K X 4 e 25 X 4 X && f 4 X 6# X 25 It will be noted that the values of a, b, and c are the same, showing that addends may be taken in any order; that the values of d, e, and / are the same, showing that factors may be taken in any order. 2. Give the values of the following: a 16% X 8 X 6 b 12K X 3% X 8 c 33% X 5 X 6 PRECEDENCE OF SIGNS It is agreed among mathematicians that when an expression contains a multiplication (x) or a division (-i-) sign, and also one of addition (+) or subtraction ( ), the product or quotient must first be found. Thus, a 12 X 8 + 2 means 96 + 2 6 40 + 8 x 2 " 40 + 16 c 18 -j- 6 - 2 " 3-2 ^ 30 - 18 - 9 " 30-2 To avoid misleading a person unacquainted with this convention, such quantities should be placed in a parenthesis (12 X 8) + 2 a (12 X 8) - 2 b 40 - (8 X 2) c (18 *- 6) + 2 . d 30 + (18 + 9) NUMBERS AND PROCESSES 185 A better plan for the last two would be to write them thus: c *% + 2 d 30 + l % SIGNS OF AGGREGATION A parenthesis denotes that the value of an expres- sion contained in it is to be taken as a whole in per- forming an operation. A vinculum, which is a horizontal line over an ex- pression, has the same meaning as a parenthesis. In dictating an expression containing a parenthesis or a vinculum, care must be taken to avoid misleading the hearer. Thus, it is difficult to distinguish between (3 X 8) 4, announced as 3 times 8, minus 4, and 3 X (8 4), announced as three times, 8 minus 4, notwithstanding the difference in the pauses. A better plan would be to dictate the first "From 3 times 8, take 4," and the second "3 times the differ- ence between 8 and 4." SIGHT EXERCISES 1. Read the following: a (9 X 5) - (6 - 3) - 10 b 24 - 9 - (24 ^- 4) c 9 X (5 - 3) - 16 + (6 - 2) d (8 -s- 4) + (3 x 5) - 2 14 + 10 3 + 7* 8 + 16 . ---^ / ___ + 23 -* Notice, in e and /, the line between two expressions has the effect of a vinculum. 2. Give the value of each. 3. Which of the foregoing marks of aggregation could be omitted? 186 WALSH'S BUSINESS ARITHMETIC INDICATING OPERATIONS PREPARATORY EXERCISES State the operations needed to obtain each of the following: 1. After spending $1.50 for a hat, and 30 cents for a necktie, John has 5 cents left. How much had he at first? 2. How much would Mary have left out of $1.50 after spending 30 cents for ribbon and 5 cents for pins? 3. A drover sold 150 sheep to one farmer, and 30 sheep to another. How much did he receive in all at $5 a head? 4. How many cubic feet of water are there in a rectangular pond 150 feet long and 30 feet wide when the water is 5 feet deep? 5. A man had a farm of 150 acres. How many acres would he have after he had sold 30 acres to Mr. A and 5 acres to Mr. B? 6. A grocer had 150 pounds of sugar. After selling 30 pounds, he put up the remainder in 5-pound pack- ages. How many packages were there? 7. A woman had $150 in the bank. How much would she have in the bank, exclusive of interest, after making 30 weekly deposits of ^5 each? 8. At the opening day of school it had 150 pupils. During the month 30 pupils were admitted, and 5 left. How many pupils belonged to the school at the end of the month? 9. A planter raised 150 bales of cotton in 5 fields of 30 acres each. How many bales did he average to the acre? NUMBERS AND PROCESSES 187 10. Five children picked 150 quarts of blackberries and 30 quarts of blueberries. How many quarts of berries did each child pick on the average? 11. A farmer had 150 pigs. He kept 30 and sold the others at $5 each. What did he receive for those he sold? SIGHT EXERCISES Combine numbers inclosed in a parenthesis before combining them with the other number. 1. Give answers: a 150 -h 30 + 5 b (150 + 30) + 5 c 150 + (30 + 5) d 150 X 30 X 5 e (150 X 30) X 5 / 150 X (30 X 5) 2. What answers are the same (a) in the first line? (b) In the second? 3. Give answers: a 150 - 30 - 5 6 (150 - 30) - 5 c 150 - (30 - 5) d 150 -=- 30 -:- 5 e (150 -=- 30) -=-5 / 150 ^- (30 -f- 5) 4. What two expressions in example 3 are equivalent to each other (a) in the first line? (b) In the second? 5. What parentheses could be removed without affecting the result in example 3? In the following examples treat two numbers connected by the sign of multiplication or of division as if they were inclosed in a parenthesis. 6. Give answers: a 150 + 30 x 5 b 150 X 30 + 5 c 150 X (30 -f 5) d (150 + 30) x 5 e 150 - 30 X 5 / 150 X 30 - 5 g 150 X (30 - 5) h (150 + 30) -r- 5 i 150 + 30 -* 5 j 150-30+5 k 150 + (30 + 5) I (150 - 30) X 5 m 150 - 30 ^ 5 n 150 *- 30 - 5 o 150 -5- (30 - 5) p (150 - 30) * 5 q 150 - 30 - 5 r 150 - (30 - 5) 188 WALSH'S BUSINESS ARITHMETIC When an expression is composed of numbers con- nected by signs of addition and subtraction ( + and ) exclusively, the result may be obtained by com- mencing at the right and making the combinations in the order in which they are given. 1. In determining the value of the expression 20 - 12+ 16 8 4 the successive steps may be 8 (20 12); 24 (adding 16); 16 (subtracting 8); 12 (sub- tracting 4). Ans. 12. The same result is obtained when these numbers are taken in any other order, such as a 20-8-4 + 16-12 b 16-8-4+20-12 etc. As an algebraic expression the order may be -12-8 + 20-4 + 16 In dictating (1) say 20 minus 12 plus 16 minus 8 minus 4 In evaluating an expression of this kind, it is cus- tomary, however, to combine the addends, and from their sum to deduct the sum of the subtrahends. This may be expressed in the following form: 20 + 16 - (12 + 8 + 4) the parenthesis indicating that the value of the ex- pression within the parenthesis is first to be ascer- tained. Note the change of the signs prefixed to 8 and 4 when they are placed within the parenthesis. NUMBERS AND PROCESSES 189 2. An expression containing numbers connected by signs of multiplication and division ( X and -7- ) may be evaluated in the same way. Thus in 16x4-i-8xlO-r-5 the successive steps may be 64 (16 x 4), 8 (dividing by 8), 80 (multiplying by 10), 16 (dividing by 5). Ans. 16. The same result is obtained by making the succes- sive operations in any order. The following are examples : a 16-5-8x10x4-5-5 b 10 + 8xl6-:-5x4 etc., etc. In practice, however, divide the product of the multipliers by the product of the divisors, thus , c 16 x 10 x 4 + (8 x 5), writing it as shown below: 16 x 10 x 4 d T^y~ Then, shorten the work by cancellation. Note the change of the sign preceding the 5 when it is placed in the parenthesis in c and below the line in d. CHAPTER FIVE ADDITION COUNTING EXERCISES Count by 6's, beginning (a) with 6. (6) With 7. (c) With 8. (d) With 9. (e) With 16. (/) With 17. 2. Count by 7's, beginning (a) with 7. (6) With 8. (c) With 9. (d) With 17. (e) With 19. (/) With 27. 3. Count by 8's, beginning (a) with 8. (6) With 9. (c) With 18. (d) With 19. (e) With 28. (/) With 29. (0) With 22. (A) With 23. 4. Count by 9's, beginning (a) with 9. (8) With 19. (c) With 29. (d) With 21. (*) With 22. (/) With 23. (0) With 24. (A) With 25. (i) With 26. ORAL DRILLS One type of the daily "warming-up" drill is a count- ing exercise. The teacher announces "Counting Drill." The class stands. A scorer at the blackboard records the time. The teacher says "By 6's." Successive pupils say 12, 18, 24, 30, etc., each taking his seat as he answers. When 102 is reached, the teacher says "7," and the pupil whose turn it is to answer says " 13," and the others continue 20, 27, etc. to 103. The scorer's duty is to call "time" at the expiration of 3 minutes, and to note the number of combinations that have been correctly made in the period. Each 190 NUMBERS AND PROCESSES 191 result should be compared with previous ones to de- termine the rate of progress made by the class in rapid work. SIGHT DRILLS Give the total of each column: a 66,666 b 77,777 c 88,888 d 99,999 66,666 77,777 88,888 99,999 66,666 77,777 88,888 99,999 66,666 77,777 88,888 99,999 66,666- 77,777 88,888 99,999 66,666 77,777 88,888 99,999 66,666 77,777 88,888 99,999 66,666 77,777 88,888 99,999 66,666 77,777 88,888 99,999 66,666 77,777 88,888 99,999 66,666 77,777 88,888 99,999 98,765 56,789 97,586 45,678 Drills similar to the foregoing should be written in large figures on manila paper for occasional use. The foregoing sight drills contain the same combi- nations as occur in the counting exercises. The num- bers are> however, in sight, which is of great help to many pupils; it is also the way in which most of their adding is done. MENTAL WORK Some drills should be employed in which the num- bers are not in sight. Answers to these combinations may be given orally by individuals at one recitation. At another, answers may be written by all the pupils. 1. Miss Bollin spent $1.67 for muslins and for gloves. Find the total. 192 WALSH'S BUSINESS ARITHMETIC Think two, thirty-seven (1.67 + -70); two, forty- two (adding .05). Give the answer as two, forty- two. If the answer is to be written, first write 2 42, then insert the decimal point and prefix the dollar sign. 2. Give sums: a 39 + 46^ 6 47^ + 84^ c $1.59 + $.33 d Mi + 38 e 18 + 96 f 4.17 + .67 g 63^ + Hi h 75 + S8f* i 6.36 + .45 j 45^ + Z5t k 37 + 63^ I 8.67 + .28 m 54^ + 36^ n 95 + 78^ o 3.78 + .16 p 18 + 68 q 28^ + 84ff r 7.45 + .39 s 73 + 19^ t 57^ + 58^ u 5.80 + .18 v 81^ + 13^ w 67 'i + 87^ x 2.28 + .56 3. Carl Hall has two farms, one containing 368 acres and the other containing 475 acres. How many acres are there in both? PROCESS Think 768 (368 + 400), 838 (adding 70), W (adding 5). ^43 A Ans. 4. Give sums : a 459 + 83 6 659 + 183 c 378 + 659 d 684 + 17 e 198 -f 247 / 456 -f- 548 g 852 + 49 h 484 + 176 i 737 4- 837 j 275 + 29 k 145 4- 693 / 295 4- 926 m 729 + 95 n 838 + 129 o 816 4- 495 p 369 + 38 q 134 + 568 r 648 4- 372 s 546 + 57 * 356 + 155 u 189 4- 818 v 138 + 68 w 119 + 777 x 576 4- 654 NUMBERS AND PROCESSES 193 5. Edward traveled 268 miles on Monday and 197 miles on Tuesday. How far did he go in the two days? METHOD Since 197 is 3 less than 200, deduct 3 from the sum of 200 and 268. Think 468 (268 + 200), 465 (subtracting 3). 465 mi. Ans. 6. Give sums: a 347 + 99 b 568 + 399 c 784 + 499 d 568 +98 e 245 + 698 / 426 + 899 g 848 +97 h 785 + 197 i 189 + 999 j 289 +96 k 318 + 596 / 538 + 698 m 627 + 39 n 609 + 299 o 616 + 597 p 465 +29 q 177 + 598 r 256 + 898 s 719 + 59 t 644 + 297 u 838 + 299 v 153 +49 w 437 + 496 x 347 + 998 ORAL PROBLEMS 1. Dr. Bragg paid $975 for a car and $98 for addi- tional equipment. What did he spend in all? 2. Find the total amount of the bill for a $75 grapho- phone and $19 worth of records. 3. A farmer had last year 265 acres in wheat. This year his wheat acreage is 69 acres larger. How many acres has he in wheat this year? 4. Before the war a certain grade of paper was sold at $95 a ton. During the war the price increased $38. Find the later price. 5. A pile of wood contains 78 cubic feet more than 194 WALSH'S BUSINESS ARITHMETIC a cord, which is 128 cubic feet. How many cubic feet are there in the pile? 6. Newton is 654 miles from Chicago, and La Junta is 370 miles beyond Newton. How far is La Junta from Chicago? 7. A man has $675 in the bank. How much will he have in the bank after he deposits $175? 8. In 1917 a man's salary was $1575. In 1918 he was paid $250 more. What was his salary in 1918? 9. A man born in 1843 died at the age of 69. In what year did he die? 10. The capacity of a shoe factory was 465 pairs a day. By better management this was increased by 78 pairs. What was its later capacity? 11. An employee was paid a monthly salary of $285 and certain commissions. How much did he receive in all in a month during which his commission amounted to $178? WRITTEN EXERCISES ADDITION 1. A farmer's account book shows the following expenses an acre in connection with his potato crop: Plowing $3.47 Spray Material $1.23 Fertilizing 6.50 Spraying, twice .25 Disking 1.37 Digging 1.83 Harrowing .52 Picking up 2.70 Seed 13.12 Sacks 4.05 Cutting seed 1.75 Sewing & Loading .45 Planting 1.05 Transporting 1.35 1st Cultivating .57 Interest 15. Cultivating, 4 times 4.20 Taxes 3.10 NUMBERS AND PROCESSES 195 a Find the total expenses an acre. PROCESS $3.47 Write the items in a column. Beginning 6.50 at the bottom, think 10, etc., ... 61 1.37 and write 1, carrying 6; think 7, 10, etc. .52 When the total is found by adding up- etc. ward, cover the answer with a piece of 1.35 paper and write on the latter the column 4.05 totals found by adding downward. Think 14, 16, 18, etc. Carrying 6, think 10, 15, 18, 23, etc. Compare the two results. If they agree, the addition may be taken as correct. In adding aloud follow a similar procedure. Ignore the cipher in the first column (and in all others) and announce 10, the sum of the first two significant figures, without mentioning five and five. When the final total 61 is announced write 1 and carry 6 without saying anything about it. That 6 has been carried is shown by its combination with 1 of the second column to make 7. NOTE: Omit superfluous words and figures. b If the gross receipts were $95.20 an acre, what was the profit on 130 acres? c. What was the value of the land an acre if the rate of interest paid was 6%? 2. The following is an itemized statement of the expense account of Fleming & Co. for a month: Salaries $2304.75 Labor 409.50 Traveling expenses 45.83 Taxes 29.60 196 WALSH'S BUSINESS ARITHMETIC Insurance 18.24 Office supplies 118.66 Advertising 265.40 Telegrams 463.27 Telephone 245.18 Postage 295.87 Light, heat, etc. 162. Painting and repairs 230. Cartage 56.84 Rent 375. Miscellaneous 46.89 What is the total for the month? When the addends are numerous and composed of large numbers, write the total of each column alongside, then write the figures in the footing. In checking the result cover the side totals as well as the footing. On a strip covering the side totals, write the new ones. Compare the two. See that the footing agrees with the second set of side totals. In case of disagreement between two results, the side totals render it unnecessary to go back more than a column to make sure of the number to be carried to the column in which a discrepancy exists. 3. Find sums. Test answers. - a 97,864 6 124,756 c 32,785 d 37,694 7.987 325,675 137,393 82,969 2,767 39,248 145,358 130,402 89,574 7,878 72,364 69,735 32,478 17,669 8,442 77,496 6,724 347,896 83,739 84,968 5,978 73,059 321,452 198,695 86,456 8,877 37,242 6,956 59,472 56,893 836 92,729 8,769 6,425 45,878 234,919 68,245 447 8,384 268,948 7.988 8,348 48,927 17,963 47,747 82,720 3,229 25,698 8,486 53,587 16,279 8,778 748 2,352 131,832 8,969 69 178 4,075 576 NUMBERS AND PROCESSES 197 e $6,837.42 / $53,819.37 g 468.987 h 5,628.3478 924.85 16,445.86 37.5384 353.68 6,193.74 2,437.75 1,428.3 1,753.0809 33,448.93 827.54 926.74 4,736.249 217.68 54,394.68 8,394.8945 37,459.08 437.56 37.25 7,534.3 3,485.6052 5,827.38 876.34 48,269.057 4,796.804 5,672.84 6,786.91 2,736.8052 6,248.72 54,984.93 827.36 8,548.291 645.0783 847.62 42,345.89 3.0787 486.57 9,382.49 2,651.48 65.45 3,467.343 3,483.57 753.43 382.345 25,895.8 37,896.82 48,269.27 37.0006 28,378.56 6,438.75 36,854.82 826.623 243.93 52,417.24 91.76 4,327.14 7,284.075 432.66 3,824.53 2,557.8346 762.88 13.89 826.62 ' 68,349.05 8,234.9 4.75 34,327.14 7,654.345 28,351.0402 23.64 2,557.83 23.68 3.006 4. The following are the receipts for a week in the specified departments : Dry Goods Millinery Notions Shoes Total Monday $1,928.75 $346.42 $289.85 $358.77 (e) Tuesday 1,056.34 275.98 305.64 323.84 (/) Wednesday 1,328.69 304.69 316.38 336.91 (g) Thursday 1,046.78 236.77 337.49 305.83 (*) Friday 984.67 251.09 250.08 298.64 (*) Saturday 2,345.56 546.57 375.97 475.86 (j) Totals (a) (6) (c) (<*) (*) Find the total for each department (a) to (d). For each day, (e) to (j) . The grand total for the week (k) . NOTE: Check by comparing the grand total, (k), found by adding the daily totals, (e) to (j), with that found by adding the department totals (a) to (d}. 198 WALSH'S BUSINESS ARITHMETIC 5. From the following, find the cost to the govern- ment of the outfit of an infantry private for clothing and shelter: 6.25 1 bedsack 3 blankets @ 1 waist belt 2 pr. breeches @ 4.45 2 service coats " 7.60 1 hat cord 3 pr. drawers @ .50 3 " " 1.62% 1 " gloves 1 hat 2 pr. shoe laces @ .02% 1 " leggings $0.98 2 flannel shirts @ $3.64 .25 2 pr. shoes 5 " stockings " 4 identification 5.10 .30 .08 tags @ 3 undershirts @ .00% .50 4 " " 1.22 1 overcoat .61 1.70 1.05 5 tent pins @ 1 " pole 1 poncho 1 shelter tent .04 14.92 3.55 2.95 6. Find the cost to a midshipman of the following articles with which he must provide himself upon his admission to the Naval Academy: 1 box soap .30 1 hair brush .65 stationery 1.75 12 white handker- chiefs @ .20 1 pr. suspenders .40 4 suits pajamas @ .70 1 tooth brush .18 thread and needles .75 brush and blacking .50 nail brush .50 6 pillow cases @ .13 name plate .15 2 bedspreads @ 1.25 1 slop jar 1 . 2 spatter cloths @ .50 1 white cap and anchor $2.45 1 dress jacket 20.78 1 blouse 15.22 1 pr. dress trousers 11.83 1 "service " 6.68 1 overcoat 26.98 1 reefer 12.18 1 mackintosh 11.50 1 cap cover .24 2 pr. leggings @ $.70 1 parade cap 3.10 1 mug .07 1 soap box .18 1 laundry book .25 1 pr. blankets 3.75 NUMBERS AND PROCESSES 199 1 pair overshoes .83 2 " high shoes @ 4.80 8 white shirts " .50 12 collars " .10 2 white blouses "4. 12 pr. cuffs " .18# 12 " socks " .20 8 towels " .20 1 shaving outfit 2.65 12 pr. drawers @ .40 12 undershirts @ .36 1 hand glass 1.15 1 blue sweater 3.15 2 " jerseys @ 2. 1 pr. white shoes 1.80 1 requisition book .40 1 pass book .30 3 stencils @ .25 1 basin and pitcher .90 1 P r - gymnasium slippers .87 1 whisk broom .17 1 coarse comb .12 7. Add horizontally and 2,259,969 + 313,225 30,631,114 + 4,624,231 15,192,362 + 3,657,641 1,241,410 + 132,640 650,599 + 220,299 2,336,043 + 156,708 62,997,808 + 8,444,473 14,070,829 + 1,160,278 19,380,698 + 1,822,756 27,796,815 + 6,799,875 1 hair pillow .75 1 rug .75 1 hair mattress 4.85 1 broom .35 3 khaki blouses 1.67 4 " shirts "2.30 1 " belt .17 1 waste paper basket .65 3 white hats @ .35 1 jackknife .25 2 lanyards @ .12 6 sheets @ .65 hammock clews .50 1 pr. bathing trunks .15 3 pr. white gloves @ .40 1 trousers hanger .30 6 coat hangers @ .06 1 strong box 1.60 1 pr. ear protectors .20 2 manuals @ .41% 1 pr. collar anchors .75 2 clothes bags @ .25 vertically : 2,835,546 67,384,012 32,702,416 2,421,798 1,334,004 3,271,787 + 127,914,369 + 23,466,950 + 32,610,057 + 42,621,617 (d) () (/) (?) (*) (*) ffl (m) = (n) 200 WALSH'S BUSINESS ARITHMETIC ADDING FRACTIONS DRILL EXERCISES 1. Give answers rapidly. a % b % c % d y 2 e % f % h % i X j % k % I % m % n +% + % + X +X + X p % q V* r % s % t % u % 2. Give sums. a 6 X c i % j / 2 k % I % m % ORAL PROBLEMS 1. Last year a farmer's crop of wheat averaged bushels to the acre. This year's was 1% bushels greater. What is the average to the acre this year? METHOD Think 22% (21%+ 1), 22% (adding %) 22% bu. Ans. 2. Before the war copper brought 12%f a pound. A few months later the price was increased 3%. What was the new price? 3. One pile of wood contained 2% cords, another contained 1% cords. How much wood was there in the two piles? 4. Pohick is 23Ko miles from Seminary. Falls NUMBERS AND PROCESSES 201 Church is 8%o miles farther. How far is Falls Church from Seminary? 5. Two pieces of silk contained 18% and 10% yards, respectively. How many yards were there in both? 6. After 7% pounds of butter were sold from a tub it contained 48% pounds. How many pounds did it contain originally? 7. A man worked 8% hours on Monday and 7% hours on Tuesday. How many hours did he work on both days? 8. A woman bought 7% pounds of beef and 3% pounds of veal. How many pounds of both did she buy? 9. A girl's expenses for a week were $8%, and her savings were $2%. What did she earn? 10. The distance between the first plant in a row and the last is 87 feet. These plants are each 1% feet from the end of the row. (a) How long is the row? (6) How many plants 3 feet apart are there in the row? SIGHT EXERCISES When the mixed numbers are in the view of the pupils, those who desire to begin the work by adding the fractions may be permitted to do so. When the answers to the following are to be written, the result should be obtained by the pupil before he begins to write. 1. How many acres are there in two fields, one containing 40% acres and the other containing 7% acres. METHOD Think 47% (40%+ 7), 48% (adding %). 48% A. Ans. 202 WALSH'S BUSINESS ARITHMETIC 2. Give sums: a 17% b 18% c 19% d 20% + % + % + % + % e 15% / 16% 20% h 21% 15% n 16% o 20% + 11% i 15% j 16% fc 20% Z + 10% +10% +10% +10% 3. Give sums: a 10% b 11% c 12% d 13% c 20% / 21% g 22% /* 23% + 5% +4% +5% +6% 2 30% j 31% & 32% Z m 41% n 42% o 43% p 44% <7 52% r 53% 5 54% t 55% i* 65% 64% w 63% a; 62% + _!% +_2% +_3% +J% WRITTEN EXERCISES In wholesale dry-goods houses 12% is written 12 1 , is written 13 2 , 14% is written 14 3 , the denominator, 4, being omitted. 1. Add the following. Write answers directly from the book: b 7 2 yd. c 31 2 yd. d II 1 yd. e 2 3 16 3 40 2 18 2 34 3 25 2 3 1 6 3 28 3 4 3 19 3 33 2 10 2 21 1 22 3 20 1 I 2 37 2 39 2 26 3 38 2 NUMBERS AND PROCESSES 203 a 14 1 yd. b 7 2 yd. c 31 2 yd. d II 1 yd. e 2 3 yd. 8 3 36 2 5 1 17 1 Check each result by adding downward, if the first result is obtained by adding upward. In writing pounds and ounces, grocers sometimes use small figures to express ounces, writing the latter as frac- tions of a pound, but omitting 16, the denominator. 2. Add the following, writing answers directly from the book: e 8 3 Ib. 14 13 " 31 io a 38 1 Ib. b 21 15 Ib. c 19 2 Ib. d 6 14 261 1 " 22 5 " 33 28 4 39 7 " 20 8 " 5 6 " 34 6 371 4 " j 4 36 3 " 18 9 91 3 " 1Q 12 25 2 " 40 12 17 5 " 33 9 310 16 15 Fractions in business are generally limited to halves, quarters, eighths, sixteenths, etc. 3. Add. Write answers directly from the book. a 16% b 23% c 25% d 9% 8% 9% 42% 18% 23% 42% 42% 6% 5% _6Ke J% 17M. e 23K / 37% flf 48% A 50% 7% 8% 9% 10% 8X2 204 WALSH'S BUSINESS ARITHMETIC 4. Find the total weight of six pieces of meat weigh- ing, respectively, 16^ lb., 8% lb., 9% lb., 11% lb., and lb. 16/2 lb. 8% 9% 11% Ans. 60% lb. PROCESS g Write the addends in a col- 2 umn and draw a perpendicular 4 line on the right to separate the Q new numerators from the origi- 3 nal fractions. In the second 37 _ QIV column, write 16, the least common denominator, on a line below the last addend in the second column, and write over this the sum of the new numerators when found. Write the new numerators alongside the corresponding fractions. Write 43, their sum, over 16 previously written. Reduce % to 2%. Write % under the origi- nal fractions, and carry 2 to the whole numbers. A Shorter Method A pupil that notes that the sum of % and % is 1%, which makes 2 when united with %, has left only two fractions to combine, % and %e, whose sum is %, which he writes. He then carries 2 to the whole numbers. Use this method to check the sum of the fractions. In adding mixed numbers containing such fractions, for example, as %j, & %, % 6 , %, and %, accountants frequently re- arrange the addends, especially in testing a result, to bring the fractions together in this order: %, %; %$, %j, & %. Even when combinations making 1 are not possible, as in & %, %, %, %, %, they rearrange the addends in some such way as this: %, %,%;%, %> %', combining the first three mentally into % or 2^, and the next three into % or etc. NUMBERS AND PROCESSES 205 5. Add: a S6& b 28% c 86% d 125% 8% 86% 8% 20% 93% 7%s 95% 354% 27% 20% 5& 68% 45% 9% 66% 98% 8% 5.3% 8% 7% 6. Find the sum of 3% days, 5% days, 7% days, 9% days, 11% days, 13& days. PROCESS In finding the least common multiple of the denominators of these fractions, omit from con- sideration 2, which is a factor of 4; 3, a factor of 6; 4, a factor of 8; 6, a factor of 12. Find the least common multiple of 8 and 12, by considering multiples of 12, beginning with 24. As this is a multiple of 8, it is the least common denominator. 7. Add the following: a 5% b 75% c 33% d 432% 7% 9% 80% 83% 9% 23% % 157& 11% 8%, 36% 28% 13% 13% 5% 7% 8% 6 29% 18% 8. A person made purchases of pencils as follows: 2% gross, 3% gross, % gross, 8% gross, % gross, and 9% a gross. How many gross did he buy in all? 206 WALSH'S BUSINESS ARITHMETIC gross 177 PROCESS After rejecting denominators that are multiples of others, there remain the following: 4) 8 - 9 - 12 2-9- / L. C. M. = 4 X 2 X 9 = 72 If you do not notice that 8 and 9 are prime to each other, which makes 72 their least common multiple, and that 72 is also a multiple of 12, find the least common multiple of 8, 9, and 12 by writing these numbers in a line. Then divide by 4, which is a common factor of 8 and 12. Write under 8 and 12 then* quotients, bringing down 9. Cancel 3, which is a factor of 9. Since 2 and 9, the remaining numbers, are prime to each other; that is, since they have no common factor, multiply their product by the divisor 4, which gives 72, the least common multiple. 9. How many pens are there in 2K gross, 4% gross, v/t gross, X gross, 5% gross, IX gross, 3# 6 gross, 7#s gross, % 4 gross, 9X 6 gross, and 8# 2 gross? 10. Add the following: a 18& b 6X c 22% d 125%, 9%4 27% 5% 14X 16X 85% 16X 8% % 8# 30% Xo 20% 26% 8% 27% NUMBERS AND PROCESSES 207 11. (a) Express in years and a fraction the sum of % year, % year, % year, %o year, and fa year. (6) Change each to days (taking 360 days to year), and find their sum. 12. A machine consists of four parts, which are manufactured from steel "blooms," weighing 290 pounds each. A bloom will make either 7 of one part, 9 of the second, 20 of the third, or 25 of the fourth. (a) Express the weight of each part as a mixed num- ber, and find their sum. (6) Express each as a mixed decimal and find their sum. (c) Change the fractional part of (a) to a 2-place decimal. PROCESS 41% Ib. Since there is no factor 41.4286 Ib 32% " common to any two of 32.2222 " 14% " the denominators the 14.5 11% " L. C. D. is their continued 11.6 Ib. / , product, x X & X 7 X y / 630 13. (a) Find the sum of IK, 2%, 3%, 4%, 5%, 6%, and 9Ko. PROCESS Find the least common multiple of 6, 7, 8, 9 and 10, rejecting the others. (b) Give the answer as a mixed decimal, two places- (c) Change the fractions to four-place decimals, 208 WALSH'S BUSINESS ARITHMETIC add the numbers as mixed decimals, and express the result as a mixed two-place decimal. PROCESS \% .5 % .3333 Write the decimal equivalent along- etc. etc. side. Increase the fourth place of the 5% .1667 decimal equivalent of % and of y, since 6)7 .1429 the next figure in each is greater than 5. etc. etc. 17. Add the following, changing the fractions to decimals. Give answer as a mixed decimal. 1% + %% + 3% + 4% + 5% + 6% + 7% + 8% + 9% ADDING COMPOUND NUMBERS SIGHT EXERCISES 1. How many pounds and ounces are there in two pieces of meat, one of which weighs 5 pounds 10 ounces and the other 3 pounds 8 ounces? METHOD Think 8 Ib. 10 oz. (5lb. 10 oz. + 3 lb.), 8 lb. 18 oz. (adding 8 oz.), 9 lb. 2 oz. (reducing) Ans. 9 lb. 2 oz. 2. Add: a 3 lb. 10 oz. b 4 lb. 9 oz. c 6 lb. 10 oz. +2 lb. 6 oz. +4 lb. 9 oz. +2 lb. 11 oz. NUMBERS AND PROCESSES 209 d 4 yd. 2 ft. e 5 yd. 2 ft. / 9 yd. 1 ft. +3 yd. 1 ft. +6 yd. 2 ft. +7 yd. 1 ft. g 6 gal. 1 qt. h 7 gal. 1 qt. i 8 gal. 3 qt. +2 gal. 2 qt. +3 gal. 3 qt. +1 gal. 3 qt. j 4 bu. 2 pk. fc 5 bu. 2 pk. I 3 bu. 2 pk. +4 bu. 2 pk. -f 3 bu. 3 pk. +2 bu. 3 pk. ??i 5 10s n 8 12s o 6 18s +6 10s +9 12s +2 10s p 6 ft. 3 in. g 8 ft. 10 in. r 9 ft. 8 in. +4 ft. 9 in. +1 ft. 10 in. +2 ft. 7 in. WRITTEN EXERCISES Add the following. Write answers from the book a 24 16s 3d b 32 yd. 1 ft. 10 in. 896 526 15 10 10 18 1 7 c 16 gal. 2 qt. 1 pt. d 62 bu. 1 pk. 6 qt. 35 3 534 911 24 2 41 613 e 43 Ib. 8 oz. / 8 ft. 10 in. g 2 mi. 90 rd. 18 10 63 5 10 120 65 89 3 84 CHAPTER SIX SUBTRACTION PREPARATORY EXERCISES MAKING CHANGE 1. What change does a clerk hand a person who gives a $20 bill to pay for articles amounting to $16.85? METHOD The clerk hands a nickel, saying "sixteen, ninety"; a dime, saying "seventeen dollars"; a dollar, saying "eighteen dollars"; and a 2-dollar bill, saying "twenty dollars." He gives 5{ + 10^ + $1 + $2 = $3.15 2. State the denominations of the money used to make change from $1 tendered in payment for pur- chases amounting to the sum specified below. State also, in each case, the total amount given in change. a Si b 76t c S9t d 45ff e f It g ISt h Sit i Mf j k 4 I 94^ m 6ty n WRITTEN EXERCISES 1. A man earned $1800 during the year. He spent $1475.35. How much did he save? 210 NUMBERS AND PROCESSES 211 PROCESS $1800. To subtract, begin with 1475.35 - 1475.35 (the subtrahend). Think 5 and 5 $324.65 Ans. (writing 5) are 10. Think 4 (carrying 1) and 6 (writing 6) are 10. Think 6 (carrying 1) and 4 (writing 4) are 10. Think 8 (carrying 1) and 2 (writing 2) are 10. Think 5 (carrying 1) and 3 (writing 3) are 8. CHECK Cover $1800 (the minuend) and add $324.65 (the remainder) to $1475.35. 2. Find remainders. Check. a 345.1 b 473 c 1016.82 - 57.064 - 389.49 - 893.9 3. Subtract without rearranging. a - 29.86 b - 146.5 c - 383.47 157.328 212.17 1000. d $9245.18 e 16,059 / - 764.58 - 264.83 - 1,088 1113.2 g - $321.69 h 10,193.8 i 12,657 1523.07 - 654.95 - 9,879 j 101,087 k -93,847 I $1364.57 - 65,564 104,305 - 890.09 m - 172,654 n - 18.25975 o 293,647 200,001 106.0005 - 188,898 4. The following is a statement of Mr. Fallen's account with Gaston and Carroll at the close of busi- ness Jul. 31, 1920. WALSH'S BUSINESS ARITHMETIC MR. C. FALLEN TUCSON, ARIZ., Aug. 1, 1920 2562 Georgetown Boulevard In Account with G ASTON and CARROLL Jul. 6 To Mdse. 273 46 9 58 95 11 187 84 15 36 92 18 375 14 20 263 88 29 95 44 () Cr. Jul. 12 By Mdse. 256 40 18 " Cash 100 22 " Mdse. 310 89 29 63 75 30 " Cash 100 (6) Bala nee d ue (<0 Copy the foregoing statement inserting at (a) the sum of the debits, at (6) the sum of the credits, and at (c) the balance due Gaston and Carroll. 5. A farmer's receipts and expenditures, respec- tively, for the year are shown in the following table: Receipts Expenditures Balance January $187.43 $138.98 = $48.45 February 156.14 125.47 = w March 195.80 156 = (d) April 163.44 135.29 = (e) May 201.59 163.88 = (/) June 198.65 148.77 = (d) July 302.88 205.93 w August 356.<).'5 216.84 = (i) September 298.67 225.98 = (j) October 215.42 160.56 = (*) November 198.68 123.15 0) December 125.94 112.68 = (*) Totals (a) (b) = (n) NUMBERS AND PROCESSES 213 Find (a) his receipts for the year. (6) His expendi- tures. (c to m) His monthly balances, (n) The balance at the end of the year. Find (n) by adding the last column. Check by covering (n) and writing on the paper the difference between (a) and (b). ORAL DRILLS 1. Anna had 85^. How much will she have after spending From S5i take 40^f, then take 9^f. Do not follow the method used in your Written Exercises in subtraction. 2. Give remainders. a 65 - 27 6 91 - 62 c 84 - 36 d 73 - 56 e 54 - 16 / 86 - 47 70 - 29 h 82 - 17 i 93-65 j 40-24 k 52 - 18 I 63 - 24 3. Miss Bruen paid $3.42 for muslin and gloves. The gloves cost $1.75. What did the muslin cost? Think $2. 42 (deducting $1), $1.72 (deducting 70$, $1.67 (deducting 5$. Ans., $1.67 4. Give remainders: a 121 - 75 b 190 - 175 c 253 - 164 , d 137 - 94 e 183 - 116 / 270 - 195 g 110 - 26 h 174 - 138 i 265 - 187 j 142 - 88 k 162 - 125 I 210 - 173 m 246 - 77 n 395 - 316 o 321 - 135 p 315 - 68 q 572 - 544 r 432 - 146 s 420 - 37 t 783 - 717 u 511 - 154 v 511 - 54 w 964 - 909 x 613 - 165 6. From a crop of 1216 bushels of corn, Mr. Popkins sold 658 bushels. How many bushels has he left? Think six, sixteen (deducting six hundred) ; five, sixty-six (deducting fifty) ; five, fifty-eight (deducting 8). Ans. 558 bu. 214 WALSH'S BUSINESS ARITHMETIC COMBINING ADDITION AND SUBTRACTION WRITTEN EXERCISES 1. A dealer had 1000 bushels of oats. How many bushels would he have after he had sold 154 bushels, 368 bushels, and 87 bushels? PROCESS From 1000 bu. Beginning with the last subtra- 154 hend, think 15 (7+8), 19 (add- Take 368 " ing 4), and 1 (writing 1) are 20. 87 " Think 10 (carrying 2), 16 (adding Ans. 391 " 6 )> 21 (adding 5), and 9 (writing 9) are 30. Think 6 (carrying 3) 7 (adding 1), and 3 (writing 3) are 10. CHECK Cover 1000 with a piece of paper. On this write the sum of 391 and the three subtrahends. 2. Write answers to the following directly from the book. (a) (6) (c) (d) From 1000 1234 3256 5167 159 216 1038 369 Take 87 157 887 2588 355 99 95 1269 3. Give the value of each of the following: a 756 - (184 + 95 + 367) d 4430 - (1234 + 345 + 68) 6 1239 - (257 + 388 + 86) e 3754 - (2345 + 456 + 77) c 2000 - (1234 + 277 + 95) / 5473 - (3456 + 567 + 84) NUMBERS AND PROCESSES 215 4. Write answers to the following directly from the book or blackboard : a $10.50 - ($2.75 + $.89 + $3.) b 26.43 - ( 9.50 + .75 + 1.28) c 35.19 - ( 7.63 + .67 + 2.29) d 43.26 - ( 8.79 + .93 + 3.14) e 50.20 - ( 6.28 + .52 + 5.67) 6. Supply missing items (a) to (i): $137.86 + $75.93 + $288.79 = (e) (a) + 168.76 + 45.63 = (/) 289.65 + (b) + 195.84 = (g) 48.76 + 253.92 + (c) = (h) 123.45 + 88.87 + 216.77 = (i) $819.30 + $916. + $989.98 = (d) 6. A merchant's cash account shows the following receipts and payments for eleven months, and the totals for the year. \ Receipts Payments Balance January $4,748.56 $3,949.82 $798.74 February 4,294.87 3,870.89 (a) March 4,655.18 4,327.65 (b) April 4,693.25 4,784.57 (c) May 4,705.93 4,259.85 (d) June 4,456.88 4,078.68 (e) July 4,327.65 3,963.26 (/) August 4,278.58 3,859.85 (g) September 4,683.95 3,965.78 (h) October 4,727.53 4,218.65 (i) November 4,515.78 3,887.79 (j) December (k) (I) (m) $54,837.63 $48,684.13 (n) 216 WALSH'S BUSINESS ARITHMETIC Find the balances for the eleven months (a) to (j) , the receipts for December (&), the payments for December (/), December's balance (m), the balance at the end of the year (ri). The following table shows the sums appropriated for a year for the specified items, also the expenditures for % year: Items Appropriations Expenditures Balance remaining Telephone $150 80.25 (a) A Repairs 1600 1267.80 (b) B Equipment 1500 1350. (c) C Supplies Manual Training 600 244.68 (d) D Janitors' Supplies 500 366.90 (e) E Domestic Science Supplies 400 241.40 (/) F Printing 500 317.10 (g) G Water, Light, Gas 550 239.80 (h) H Fuel 2075 726.25 (i) I Books 500 434.60 (j) J Helpers 1000 441.52 (k) K Janitors' Salaries 4000 2114. (I) L Drawing Supplies 350 173.95 (ra) M Athletics 300 274.56 (n) N Miscellaneous 1525 969.90 (o) O Science Supplies 800 507.36 (p) P Incidentals 250 184.62 (q) Q Music 300 105.30 (r)_ R^ I II III IV I. Find the total amount appropriated. II. The expenditures. III. The balance remaining of each appropriation, (a) to (r). IV. The per cent each balance is of the sum appropriated, (A to R). (Carry out to two decimal places.) NUMBERS AND PROCESSES 217 TAKING ONE NUMBER FROM THE SUM OF TWO OR MORE NUMBERS PREPARATORY EXERCISES 1. A boy who had $1.75 earned 50 cents and spent 98 cents. How much had he then? METHOD $1.75 + .50 His balance is found by taking $1 - 1. from the sum of $1.75 and $0.50, + .02 and adding 2f to the remainder. $1.27 Ans. ~ pl. / O In practice the $1 is not written, -50 but the deduction is made neverthe- less. $1.27 THE COMPLEMENT OF A NUMBER The 2 thus added is called the complement of 98,. the complement of a number being the difference between it and a unit of the next higher order. Thus, the complement of 9 is 1 (10 minus 9), of 79 is 21 (100 minus 79), of 675 is 325 (1000 minus 675). To find the complement of 783.951 take 7, 8, 3, 9 and 5 from 9; and 1 from 10, writing the successive remain- ders from left to right. 2. A girl who had $1.75 received 50^ from her aunt, and then spent $1.88. How much had she left? 218 WALSH'S BUSINESS ARITHMETIC METHOD $1.75 Use the complement of $1.88, .50 which is $8.12. Add the three 8.12 numbers. Before writing the total $ Ans. f the last column, deduct $10. WRITTEN EXERCISES 1. At the beginning of work in the morning, the factory had on hand 475 tons of steel. During the day 350 tons were made and 587 tons were sold. How many tons remained? PROCESS 475 T Write the subtrahend in the regu- + 350 " lar way, but use its complement, ' 587<< Think 3 (10 - 7), 8 (adding 5); write 8. Think 1 (9 - 8), 6 (adding 5), 13 (adding 7) ; write 3. Think 4 (9 - 5), 5 (carrying 1), 8 .(adding 3) 12 (adding 4) ; write 2, omitting the 1. 2. There were in a warehouse on Monday morning 649 barrels of flour. During the week 488 barrels were received and 574 were withdrawn. How many remained in the warehouse at the end of the week? NUMBERS AND PROCESSES 219 PROCESS 649 bbl. Write 574 bbl. but use its comple- + 488 " ment, 426. Begin at the bottom so 574 that you will be less likely to over- look the fact that you are dealing with the complement. 3. Give the value of 746 -f 184 + 95 - 367. PROCESS Beginning with 367, and using its complement, think 3 (10 - 7), 8, 12, 18; write 8. Carrying 1, think 4 (adding the complement, 9 - 6), 13, 21, 25; write 5. Carrying 2, think 8 (adding the comple- ment, 9 - 3), 9, 16; write 6. Omit the 1. Ans. 658. 4. Write the answers to the following directly from the book or the blackboard. a $4.50 + $2.75 - $1.89. g 3217 + 3087 + 234 - 3628. b $12.60 + $8.50 - $10.89. h 4382 + 2342 + 689 - 1367. c 1875 + 387 + 96 - 448. i 3562 + 4056 + 408 - 6924. d 2015 + 86 + 250 - 1234. j 2341 + 6027 + 824 - 5833. e 1887 + 2460 + 329 - 2563. k 1766 + 5150 + 569 - 3426. / 2065 + 1265 + 157 - 4257. I 2598 + 3006 + 736 - 4762. WRITTEN EXERCISES The following is a statement of the exports and imports of each business day for three weeks, begin- ning Jul. 17. 220 WALSH'S BUSINESS ARITHMETIC Copy this statement, and complete it by inserting for each day its excess (a) of exports or (6) of imports, (c) the total exports for three weeks, (d) the total im- ports, and (e) the net excess of the exports. Exports Imports Excess Exports Excess Imports Jul. 17 7,728,468 4,601,395 3,127,073 18 12,558,896 2,902,051 etc. 19 8,440,177 4,322,549 (a) 20 8,701,825 2,751,883 21 6,263,634 2,394,123 22 9,172,369 839,442 24 10,748,034 5,472,260 25 10,082,167 5,048,748 26 3,568,542 3,711,062 142,520 27 1,043,375 2,800,355 etc. 28 1,964,560 4,385,087 (b) 29 4,865,135 3,704,030 31 8,815,609 3,791,273 Aug. 1 20,128,921 5,864,208 2 14,178,438 4,503,504 3 6,580,265 6,776,233 4 5,271,135 5,105,781 5 1,471,401 2,737,628 Totals (c) (d) (e) GROSS WEIGHT, TARE, NET WEIGHT The gross weight of merchandise includes the weight of the barrel, tub, wagon, etc. The tare is the weight of the covering, wagon, etc. The net weighty which is the difference between the two former, is the weight of the merchandise. The buyer weighs the packages when he receives them and compares the weight of each with that marked on the package. When the package is emptied, NUMBERS AND PROCESSES 221 he weighs it and compares the weight with the marked one. 1. Find (a) the total gross weight. (b) The tare. (c) The total net weight of the following purchase of sugar, 15 barrels. 327 - 20 336 - 18 340 - 21 335 - 17 339 - 20 332 - 18 332 - 19 337 - 19 336 - 18 340 - 21 327 - 17 330 - 19 331 - 18 329 - 17 328 - 17 2. The following are the gross weights and the tares of 12 tubs of lard. Find (a) the total gross weight, (b) the total tare, and (c) the total net weight. 74 - 15 70 - 14 71 - 16 60 - 13 70 - 15 68 - 13 68 - 13 71 - 14 70 - 15 72 - 16 73 - 14 69 - 14 3. From the following data find (a) the total gross, (b) the total tare, (c) the total net of 18 loads of coal, and (d) its value at $7.50 a ton of 2000 pounds. Gross Tare Gross Tare Gross Tare 4764 1236 4756 1216 4912 1248 4588 1232 4972 1232 4636 1272 4648 1240 4568 1244 4592 1284 4720 1248 4884 1312 4756 1268 4936 1264 4728 1296 4872 1236 4652 1256 4632 1272 4928 1308 In the vicinity of a market to which farmers bring their produce, there is generally a public scale in charge of a sworn weigher. When a farmer sells a load of hay, he drives it on the scales. The weigher enters the weight of the load and wagon, and when 222 WALSH'S BUSINESS ARITHISIETIC the hay is removed, he weighs the wagon. To the farmer he gives a statement in the following form: CERTIFICATE OF WEIGHT Lawrence, Michigan, Aug. 30, 1920 LOAD OF. . .Hay GROSS WEIGHT .... 3250 Ib. . OWNER. . . John Ziegler TARE " 1130 " . . . . SOLD TO D wight Braman NET " 2120 " . Samuel Goldstone City Weigher. 4. Find the value of the foregoing load of hay at $1.35 a hundred pounds. 5. During the day Mr. Goldstone issued certificates for loads of hay weighing as follows. Find the value of each at the price specified. Gross Tare Rate per 100 Gross Tare Rate per 100 a 3325 1165 $1.25 b 3575 1525 $1.40 c 3430 1210 $1.30 d 3360 1240 $1.35 e 3245 1085 $1.15 / 3410 1150 $1.20 SUBTRACTING FRACTIONS DRILL EXERCISES 1. Give answers rapidly: a % b % c % d % e % f % g % -X -X -% -X -X -X -X h % i % j K k % I % mX n % -% -X -% -X -X -X -X NUMBERS AND PROCESSES 223 2. Give remainders: al b I c 1 d I el f 1 g I -_/ 2 -J4 -_X -_X -J -_X -_% A 1% i IX j IX fc 1 Z 1% m 1% n 1% -J -_X -_K -_X -_% -_ti -% o 1% p VA q IK f 1% 5 l/ 2 IX w l/ 6 -_^ -J -_% 5% -_% -_^ -_x 3. (a) From 1% take%. (6) From 1% take %. METHOD (a) Think & (1 - %), % (adding %). Ans. %. (6) Think Ks (1 - %), ! Ks (adding %). Reduce %to%. Ans. %. 4. Subtract : a 1% 6 1% c 1 / 1% <7 1% fc 1% i 1% j 1% WRITTEN EXERCISES 1. A dealer's stock of buttons at the beginning of the week was 905% gross; at the end of the week it was 356% gross. If none were bought during the week, how many gross were sold? 224 WALSH'S BUSINESS ARITHMETIC A LONG METHOD 905 % gross 356% 548% gross 4 13 22 After writing the numbers and drawing the vertical line, = y 2 as in addition, write 18 as the denominator of the frac- tion in the remainder, it being the L. C. I), of the other fractions. Change % to fa writing 4, the new numerator, to the right of the vertical line. Write 13, the numerator of the fraction in the sub- trahend, under 9. Since % is greater than fa, increase the latter by %, writing 22, the increased numerator, to the right of the 4. Subtracting 13 from 22, write 9 over 18, making the fraction % 8 and reduce it to J. Write % under the original frac- tions, increase 356 by 1, and complete the work. NOTE: The foregoing method gives all of the steps. The pupil should omit as many of them as possible. 2. Write answers from the book if possible: a 192} b 385% c 270% d 452% - 29% -137% - e 563% / 771% g 682%, h 843% -338% - 97% -129% - 65% 3. Subtract: a 158% b 862% c 329% d 613% - 99% - 593% - 98% - 267% e 261% / 706% g 510# h 432% - 104% - 69% - 238% - 75%, NUMBERS AND PROCESSES 225 SIGHT EXERCISES 1. From a field of 48% acres, 7% acres are sold. How many acres are left? PROCESS Think 41% acres (48% - 7), 40% (deducting %). Ans. 40% A. 2. Give remainders: a 20% 6 16% c 20% d 17% e 20% -19% / 17% -16% 9 21% -20% h 18% -17% i 20% - 9% 3 18% -_9% k 31% -_9% / 40% -J# m20% -16% n 18% -12% o 31% -25% p 40% -30% ORAL PROBLEMS 1. Last year a farmer's crop of wheat averaged bushels to the acre. This year it averaged 22% bushels What is the increase? PROCESS Think 1% (22% - 21), 1% (deducting %). Ans. 1% bu. 226 WALSH'S BUSINESS ARITHMETIC 2. Since the war copper has been sold at 15% a pound, an increase of 3%^. What was the former price? 3. Two piles of wood. contain 4% cords. One con- tains 2% cords; how many cords does the other con- tain? 4. A man starts for Falls Church, 32 miles away. How far has he to go after traveling 23Ko miles? 5. From a piece of cloth containing 41% yards 18% yards were sold. How many yards remain? 6. A tub of butter weighs, with the tub, 56 pounds. The tub weighs 7% pounds. WTiat is the weight of the butter? 7. A man worked on Monday 8% hours, on Tuesday 1% hours less. How many hours did he work on Tuesday? 8. A woman bought 12% pounds of meat, 8% pounds being beef and the rest mutton. How many pounds of mutton were there? 9. A girl earned $11X a week. What did she spend if her savings were $3%? 10. In a row 20 feet long, the distance between the end plants is 18^ feet. How many feet are there between each end plant and the end of the row if the two distances are equal? SUBTRACTING COMPOUND NUMBERS WRITTEN EXERCISES 1. A fanner has 32 bushels, 3 pecks, 7 quarts of seed. He requires 36 bushels, 1 peck, 4 quarts. How much is he short? NUMBERS AND PROCESSES 227 METHOD 32 bu. 2 pk. 7 qt. The question is to find the quantity by which 32 bu. 36 bu. 1 pk. 4 qt. 2 P k - ? qt- must be increased to make 37 bu. 1 pk. 4 qt. Write these quantities as shown above. Under 7 qt. write the number of quarts, which added to 7 qt. will make 12 qt. (1 pk. + 4 qt.) Carry 1 pk. to 2 pk., making 3 pk. In this column write the number of pecks which added to 3 pk. will make 5 pk. (1 bu. -f- 1 pk.). Carry 1 bu. to 32 bu. In this column write the number of bushels which added to 33 bu. will make 36 bu. Cover the last line with a piece of paper. On this write the sum of the two addends, adding upwards. Compare this result with the original sum, 36 bu., etc. In the following examples use the same method without changing the arrangement of the quantities. 2. Subtract. Write answers directly from the text book. a 40 3s. 6d. b 63 yd. 1 ft. 2 in. -19 16s. IQd. - 48 yd. 2 ft. 8 in. c 93 gal. 2qt. d 74 bu. 2 pk. 3 qt. - 44 gal. 3 qt. 1 pt. - 28 bu. 2 pk. 6 qt. SIGHT EXERCISES 1. (a) From 9 Ib. take 3 Ib. 9 oz. (b) From 8 bu. 2 pk. take 5 bu. 3 pk. 228 WALSH'S BUSINESS ARITHMETIC METHOD (a) Think 6 Ib. (9 Ib. - 3 lb.), 5 Ib. 7 oz. (de- ducting 9 oz.). 5 lb. 7 oz. Ans. (6) Think 3 bu. 2 pk. (8 bu. 2 pk. - 5 bu.), 2 bu. 3 pk. (deducting 3 pk.) 2 bu. 3 pk. Ans. 2. Give answers: a 18 6s. b 9s. 6d. c 4 lb. - 13 10s. - 5s. 9d. - 1 lb. 7 oz. d 25 bu. 1 pk. e 5 pk. 2 qt. / 8 gal. 1 qt. - 8 bu. 3 pk. - 1 pk. 7 qt. - 2 gal 3 qt. TIME BETWEEN DATES PREPARATORY EXERCISES 1. If a man begins work at the opening hour of May 5, and finishes at the closing hour (a) of May 6, (b) of May 21, how many days has he worked? 2. An importer receives some bales numbered con- secutively from 52 to 73. How many bales are there? 3. How many fence posts 8 feet apart will be needed for a strip of fence (a) 8 feet long? (b) 16 feet? (c) 80 feet? (d) 160 feet? 4. If there are 21 fence posts 8 feet apart, what is the distance between the first and the last? The difference between two dates, say March 1 and March 31, is 31 days if both days are included, 29 days if both days are excluded, and 30 days if one is included and the other is excluded. When both days are included, the time is stated as March 1 to March 31, inclusive; when both days are excluded, it is stated as March 1 to March 31, exclusive; when one is NUMBERS AND PROCESSES 229 included and the other is excluded, the time is stated merely as March 1 to March 31. In some places, however, interest for 2 days is charged on money borrowed on March 1, and repaid on March 2, both days being included. Ascertain the practice prevalent in your locality. In the following examples, include only 1 day. Time less than a Year When dates are less than a year apart, the time between them is usually found in days. WRITTEN EXERCISES 1. How many days' interest is due on a loan made Jul. 3, 1919, and paid May 16, 1920? METHOD Jul. 28 days Write the time remaining in Aug. 31 " July by deducting 3 days from 31 Sep. 30 " days, thus excluding July 3. Oct. 31 " Write the number of days in each Nov. 30 " of the other months to April, Dec. 31 " inclusive, remembering that 1920 Jan. 31 " is a leap year. For May, write Feb. 29 " the number of days expressed by Mar. 31 " the date, thereby including May Apr. 30 " 16. May 16 A method of checking is to Total 318 days take the time as 10 months 13 days, which would make 313 days if each month had 30 days. Adding 6 extra days for July, August, October, December, January, and March, and deducting 1 for February makes 5 days more than 313. 230 WALSH'S BUSINESS ARITHMETIC 2. Find the time between: a Dec. 28, 1919 and Jan. 16, 1920 b Mar. 19, 1920 " Feb. 29, 1920 c Jan. 22, 1919 " May 12, 1919 d Aug. 17, 1918 " Jun. 12, 1919 e Jan. 31, 1919 " Aug. 24, 1919 / May 29, 1918 " Mar. 22, 1919 g Feb. 23, 1920 " Jun. 18, 1920 h Jul. 25, 1919 " Apr. 20, 1920 i Sep. 27, 1918 " Jul. 15, 1919 j Apr. 30, 1919 " Sep. 21, 1919 Bankers use a table to ascertain the time between two dates. WRITTEN EXERCISES 1. Find the time that has elapsed between May 15, 1917, the date on which a note was drawn, and Jan. 3, 1920, the date on which it was paid. In this case, also, the practice varies. Some states require that first the whole number of years be taken (2 years from May 15, 1917, to May 15, 1919); then the whole number of months (8 months from May 15, 1919, to Dec. 15, 1919); finally, the number of days from Dec. 15, 1919, to Jan. 3, 1920, viz. 19 days. The more common practice is the one given below, which assumes that each month contains 30 days. PROCESS 1920 - 1 - 3 Write 1920, first month, third 1917 5 15 day, as the minuend; and 1917, fifth month, fifteenth day, as the subtrahend. Find the difference by the method given for subtracting compound numbers (com- pound subtraction). NUMBERS AND PROCESSES 231 2. Find the difference in time between a Apr. 17, 1916 and Sep. 10, 1919 b Sep. 30, 1917 " Jul. 12, 1920 c Jul. 28, 1914 " Apr. 15, 1918 d Nov. 19, 1916 " Jun. 11, 1919 e Feb. 17, 1915 " Aug. 15, 1920 / May 22, 1918 " Mar. 20, 1921 g Jan. 16, 1919 " May 12, 1922 h Oct. 20, 1916 " Feb. 18, 1920 i Aug. 25, 1918 " Mar. 22, 1921 j Jun. 18, 1919 " Jan. 13, 1922 SIGHT EXERCISES Find the number of days that elapsed between the planting and the first picking of the following: a Beans, planted May 12, first picking Aug. 10 b Beets " Apr. 15, " " Jun. 15 c Corn May 5, " " Aug. 1 d Melons " May 15, " " Aug. 20 e Peas " Apr. 5, " " Jun. 10 / Tomato, " May 1, " " Aug. 1 g Squash, " May 25, " " Sep. 1 h Radish " Apr. 1, " " May 10 i Onion, " Apr. 10, " " Aug. 15 j Leek, " Apr. 15, " " Aug. 15 CHAPTER SEVEN SPECIAL TESTS AVOIDING MISTAKES Legible Figures "Blind" figures are one source of error. Learn to make figures that are easily read, and to write each figure in its proper place. Do not make a correction by writing a second figure on top of the first one. Draw your pen through the original figure, write the correct one, and assume the responsibility for the change by affixing your initials. Do not erase anything in a business document. Erasures beget suspicion at times. Make a necessary change in the manner suggested above. TESTING A RESULT In testing any result, look first at its reasonableness. The product of 37 by 27 should be less than 1200 (40 X 30). It should be more than 925 (37 X 25). Count the number of figures in a result. The product of 2 X 4 contains 1 figure, that of 4 X 3 contains 2; the product of 23 X 30 contains 3 figures, that of 40 X 25 contains 4, etc., the number of figures in a product of two factors being equal to the total number of figures in the two factors or 1 less. In the latter case examine the product. 99* NUMBERS AND PROCESSES 233 A pupil in multiplying 316 by 307 might, by mistake, place the first figure of the second partial product in the tens' place instead of in the hun- Error dreds', obtaining the incorrect result 316 11,692. When he finds X 307 that this product has Correct ^ ve fig ures > ne fewer 316 than the total of the x 307 two factors, he should observe that a 5-figure product must be greater than 90,000. Of course, if he makes the test by using 316 as the multiplier, he will discover his mistake. This will not be the case if he applies the test of "casting out 9's." In testing the product of 43 X 67, of 274 X 689, or of any other two factors containing the same number of figures, obtain a second product by reversing the factors. 43 67 274 689 X 67 X 43 X 689 X 274 When you obtain the product of 72 X 28769 by multiplying by 72, test it by using 8 and 9, the factors of 72. 28769 (a) 28769 X 72 72 (6) 258,921 " 9 times (a) 57538 2,071,368 8 " (6) 201383 2071368 234 WALSH'S BUSINESS ARITHMETIC If you obtain the product originally by using 9 and 8 as the factors, find the second product by chang- ing the order to 8 and 9. The product of 73 X 34568, when first obtained by the method shown at the left, is tested by the one shown at the right. (a) 34,568 X 73 (c) 34,568 x 73 (6) 103,704 3 times (a) (d) 276,544 8 times (c) 2,523,464 70 times (a) + (6) 2,523,464 9 times (d) + (c) Explanations of these abbreviated processes will be given later. "CASTING OUT 9's" It has been seen that a number is divisible by 9 if the sum of the digits is divisible by 9. By the "excess" of 9's in a number is meant the remainder left when a number is divided by 9. To obtain this excess, find the sum of the digits in the number, and divide this total by 9. The "excess" of 9's in 3460875, for instance, is the remainder left when 3 + 4 + 6 + 8 + 7 + 5, or 33, is divided by 9; namely, 6. It is not even necessary to divide 33 by 9 to obtain this remainder, the "excess" of 33 being 3+3. In practice reject 9 when the sum of two or more digits is 9 or more. Think 7 (3+4), 13 (adding 6), 4 (rejecting 9), 12 (adding 8), 3 (rejecting 9), 10 (adding 7), 1 (reject- ing 9), 6 (adding 5). This process of finding the excess of 9's in a number is called "Casting out 9V NUMBERS AND PROCESSES 235 TESTING A SUM A sum may be tested by comparing its excess with the sum of the excesses of the ad- 3461 (Exc.) 5 dends. In the given example the 822 " 3 excesses of the addends are 5, 3, 1753 " 7 anc } 7 j the sum of which is 15, of 6036 (Exc.) 6 w hich the excess is 6. The excess of 6036 is 6. That is, the excess in a sum equals the excess of the total of the excesses of the addends. SUBTRACTION TEST A difference may be similarly tested. In this example, the excess of 9's in the , , i i iti i >/ o4OJ. (li 221 x 41 i 32 X 412 j 612 X 24 A: 24 X 444 / 202 x 36 Test products by writing on a second strip the suc- cessive products obtained by using the factors of the multiplier. MULTIPLYING AND ADDING ORAL PROBLEMS 1. How many quarters are there in 21%? 2. What is the cost of five pounds of 8-cent sugar and 25 cents' worth of eggs? 3. How many inches are there in 10 feet 11 inches? 4. Change 9% to an improper fraction. Each of the foregoing requires the finding of a prod- uct and the combination of the latter with a given number. SIGHT EXERCISES 1. A farmer paid a debt by giving 12 tons of hay at $15 a ton and $20 in cash; how much did he owe? 2. Give the value of the following: a 16 25 + 59 b 34 + (6 x 50) c 83 + 12 X 33% d (9 x 12) + 20 e (9 X 12) +20 / 12% X 48 + 67 Remember that the product of the numbers connected by a sign of multiplication is to be added to the remaining number. In a, add 59 to the product of 16 by 25; in c add 83 to the product of 12 times 33%, combining the numbers con- nected by a sign of multiplication before performing the indicated addition. NUMBERS AND PROCESSES 245 In 6 and in e the parenthesis is unnecessary, but its use serves to indicate to a person unaware of the effect of the multiplication sign that the numbers within it are to be com- bined into a single number. WRITTEN EXERCISES 1. How many square inches are there in the surface of a steel plate containing 8 square feet 96 square inches? PROCESS 8 sq. ft. 96 sq. in. There are 144 square inches 1248 sq. in. i n a square foot. In 8 square feet there are 8 times 144 square inches. To the product add 96 square inches. Do this in one operation. . Think 32 (8X4), 38 ("adding-in" 6); write 8. Think 32 (8X4), 35 (carrying 3), 44 ("adding- in" 9); write 4. Think 8 (8 X 1), 12 (carrying 4); write 12. TEST Divide 1152 (1248 - 96) by 8. 2. Find the value (a) of (9 X 86) + 129. (6) Of 237+ (7X 97). PROCESS a (9 X 86) + 129 b 237 + (7 X 97) Ans. 903 916 Ans. Write the result under the number to be "added- in." 246 WALSH'S BUSINESS ARITHMETIC 3. Find the value of each of the following: a (4 x 38) +95 b 77 + (9 x 83) c (10 x 87) + 261 d (5 x 46) +87 e 55 + (8 x 67) / (20 X 43) + 129 g (6 x 54) + 66 h 68 + (7 x 95) i (30 X 52) + 104 j (7 X 62) +59 k 86 + (6 X 79) I (40 X 23) + 115 SIGHT EXERCISES 1. (a) How many times 87 is 261? (b) How many times 87 is (10 X 87) + 261? 2. How many times 43 is (20 X 43) + 129? 3. How many times 52 is (30 X 52) -f 104? 4. How many times 23 is (40 X 23) + 115? Business Ways The pupil who thinks it impossible for him to dis- pense with any of the crutches he learned to employ in the lower grades should at least become acquainted with the fact that there are other and shorter ways of performing operations. Even if he cannot use all of those suggested, he should occasionally try some of them. The methods recommended are used by elementary pupils somewhere. They do not include types of combinations that have only a limited application. MULTIPLIERS OF MORE THAN ONE FIGURE WRITTEN EXERCISES 1. How many square rods are there in a rectangular plot 87 rods long and 43 rods wide? NUMBERS AND PROCESSES 247 PROCESS One Way 87 (rd.) Place the right-hand X 43 (rd.) figure of the product by 261 3 under 3, of the product 348 by 4 under 4. Combine 3741 (sq. rd.) Ans. the P artial Products. Saving a Line 87 (rd.) Write the product by 3. 43 " Under it draw a line, and then TTT multiply 87 by 4 (tens). 3741 (sq. rd.) Instead of writing this partial product, combine it with the first partial product. First bring down 1, the one's figure of the product by 3. Think 28 (4x7), 34 (adding 6); write 4. Think 32 (4X8), 35 (carrying 3), 37 ("adding in" 2); write 37. ANS. 3741 (sq. rd.) TEST Multiply 43 by 87. 2. Find products. Test. Try the short method. a 94 X 86 b 73 X 57 c 63 x 84 d 78 X 74 e 28 x 69 / 94 X 96 g 54 X 72 h 86 x 36 i 46 x 54 j 29 x 27 A: 87 X 93 / 56 x 52 m 68 x 83 n 48 X 43 o 65 x 26 p 39 X 79 q 37 X 67 r 35 X 62 s 42 X 42 t 24 X 58 u 53 X 47 v 89 X 38 w 76 x 34 a; 32 X 82 248 WALSH'S BUSINESS ARITHMETIC 3. Find the cost of 76 acres of land at $85 an acre. METHOD $85 Many accountants begin mul- 76 tiplication with the left-hand 595 figure. $6460 Ans. Write the first figure of the product by 7 under 7, etc. Draw a line, multiplying by 6; think 30 (6x5); write 0. Think 48 (6x8), 51 (carrying 3), 56 (adding 5); write 6. Carry 5 to 59 and write 64. 4. Multiply. Save a line. a 27 X 34 b 23 X 37 c 75 X 43 d 38 X 92 e 53 X 96 i 79 X 27 / 54 X 57 j 59 X 98 g 45 X 49 k 56 X 74 h 67 X 59 / 93 X 58 m 64 X 63 n 47 X 64 o 82 X 68 p 97 X 82 q 38 X 59 r 57 X 47 s 32 X 49 t 93 X 84 u 28 X 63 v 72 X 74 w 67 X 46 a: 59 X 45 Omit as many figures as you can. aa 28 X 35 X 73 bb 24 X 38 X 64 cc 76 X 45 X dd 54 X 97 X 29 ee 55 X 58 X 76 // 57 X 73 X gg 78 X 26 X 64 hh 97 X 95 X 94 ii 83 X 69 X jj 65 X 37 X 56 kk 48 X 63 X 35 II 33 X 48 X mm 39 X 58 X 43 nn 58 X 46 X 73 oo 68 X 74 X 5. Edward Regan bought 127 covers from Mr. Plumridge at $2.85 apiece, (a) How much was paid? (b) What would be the cost of 712 covers? NUMBERS AND PROCESSES 249 PROCESS (a) $2.85 x 127 First multiply by 7, then by - 12 (tens); combine this prod- uct with the first. $361.95 Ans. Multiply by 12; then by 7 (hun- ^ dreds). Bring down 20, the ones and - the tens of the product by 12. $2019.20 w Note in (6) that 5, the right-hand figure of the product of 7 times 5, belongs in the hundreds' place (under the 7) ; hence, combine it with 4 of the first partial product, to make 39; etc. 6. Find products. Try to limit the number of figures you use. a 127 X 195 6 138 X 234 c 149 X 321 d 116 X 586 e 129 X 639 f 117 X 845 9 316 X 432 h 169 X 543 i 178 X 232 j 712 X 591 k 912 X 396 I 711 X 458 m 611 X 685 n 512 X 345 J 812 X 942 P 134 X 347 q 615 X 235 r 184 X 374 s 414 X 253 t 161 X 357 u 418 X 224 V 156 X 624 w 417 X 192 X 149 X 328 Learn to multiply numbers below 10 by numbers below 20. aa 128 X 196 X 163 bb 117 X 537 X 152 cc 812 X 642 X 711 dd 314 X 628 X 143 250 WALSH'S BUSINESS ARITHMETIC 7. A school used in a year 134 gross of pens. (a) How many pens were used? (6) How many pens are there in 56 gross? METHOD (a) 134 (gro.) X 144 1608 (12 X 134) 19296 (pens) (12 X 1608) Ans. (b) 144 pens X 56 1008 (7 X 144) 8064 pens (8 X 1008) Ans. In (a) use the factors 12 and 12; in (b) use 7 and 8. TEST (a) 134 (gro.) X 144 2144 (16 X 134) X9 19,296 (pens) (9 X 2144) (b) 144 pens X 56 1152 (8 X 144) 8064 pens (7 X 1152) Ans. In (a) use 16 and 9 as factors; in (b) reverse the order of the factors. Do not write the expressions in parenthesis (12 X 134), (12 X 1608), (7 X 144), etc. Some accountants think that they' save time by the employment of the factors of the multiplier. These can frequently be used to advantage in testing a product obtained in another way. NUMBERS AND PROCESSES 251 8. Find products, using factors: a 32 X 647 b 56 x 389 c 52 X 587 d 36 x 328 e 64 X 267 / 72 x 456 g 63 x 195 h 28 X 419 i 96 X 853 j 78 X 323 k 54 X 635 I 42 x 926 9. An agent bought 308 horses at an average of $209 a head. How much did they cost? One Way $209 Place the right-hand figure of the product by 8 under 8, of the product by 3 under 3. Ignore the cipher in the multiplier. $64,372 Ans. The Other Way Bring down 72. Multiply 209 $209 by 3 and "add in" 16, the remain- 308 ing figures of the first partial prod- 1672 uct - $64,372 Ans. Test by multiplying 308 by 209. 10. Find products a 709 X 805 b 208 x 906 c 307 x 709 d 406 X 608 e 505 X 409 / 609 X 209 g 708 X 507 h 807 X 306 i 906 x 408 j 706 X 409 k 607 X 407 1 306 X 603 m 405 X 907 n 504 X 506 o 704 X 407 p 609 X 208 q 805 X 508 r 809 X 908 s 906 X 305 t 207 X 702 u 908 X 607 252 WALSH'S BUSINESS ARITHMETIC 11. Find the cost (a) of 213 acres of land at $164 an acre. (b) Of 321 acres at $416 an acre. A Short Way (a) $164 Multiply by 3, placing the right- X213 hand figure of the product under 3. 492 Obtain the product by 21 (tens) by 3444 multiplying 492 by 7 (tens). Why? $34 932 Pl ace the right-hand figure of this product under 1. (b) Multiply by 3 (hundreds), (b) $416 placing the right-hand figure of X 321 the product under 3. Obtain 1248 the product by 21 by multiplying 8736 1248 by 7. Place the right-hand $133)536 Ans . figure of the product under 1. A Shorter Way (a) $164 Bring down 2, then prefix 7 (tens) times 492 with 49 (tens) added in. $34,932 Ans. b $416 (b) Combine 1248 (hundreds) X 321 with 7 times 1248. 1248 " " $133,536 Ans. 12. Find products: a 122 X 189 b 123 X 279 c 153 X 355 d 246 X 497 e 212 X 918 / 312 X 927 g 315 X 535 h 624 X 749 i 427 X 568 j 567 X 364 k 459 X 328 / 287 X 546 m 742 X 856 n 756 X 436 o 945 X 832 p 728 X 564 NUMBERS AND PROCESSES 253 13. Find the cost of 3868 pounds of Rio coffee at 12.84 cents a pound. PROCESS 3868 $.1284 46416 Exc. 7 Exc. 8 Exc. 1 Exc. 1 Write 12.84^ as dollars, four decimal places. Although it is a concrete number, use it as the multi- plier. First multiply by 12, placing the right-hand figure of the product under 2. Multiply this product by 7, placing the right-hand figure of the product under 4. During the multiplication "add in" 46416. In giving the answer retain only the two decimal places representing cents. TEST BY CASTING OUT ll'S Casting out ll's, the excess in the multiplicand is 7; in the multiplier, 8; the product of these excesses is 56, of which the excess is 1. The excess of the product, 4966512, is 1. In finding this last excess include 12, the figures can- celed in giving the answer. 14. Multiply. Test by reversing the factors. a 1177 X 4206 d 3612 X 1296 b 8407 X 1272 e 8811 X 1248 c 12,144 X 11,132 / 12,132 X 11,088 254 WALSH'S BUSINESS ARITHMETIC 15. At an average of 765 pounds to the acre, what will be raised (a) on 18 acres? (b) On 81 acres? (c) On 102 acres? (d) On 201 acres? (c) On 316 acres? PROCESS When there is a 1 in the multiplier, write the latter alongside the multiplicand, and make it one of the partial products without writing it a second time. Do this whether you "add-in" the second partial product or not. (a) 18 X 765 Ib. (b) 81 X 765 Ib. 13,770 Ib. Ans. 61,965 Ib. Ans. (c) 102 X 765 Ib. (d) 201 X 765 Ib. 78,030 Ib. Ans. 153,765 Ib. Ans. (e) 316 X 765 Ib. In W use 765 for the 2295 first partial product of 4590 765 by 1 (ten). Mul- J40lb. Ans. ^fr by S Hundred) for the second partial product. Multiply this by 2 for the third partial product, placing the right-hand figure in the ones' column. Accustom yourself to begin with any figure of the mul- tiplier. There are advantages at times in beginning with the left-hand figure rather than with the ones' figure. 16. Multiply: a 879 X 17 b 789 X 107 c 978 X 316 d 786 X 71 e 687 X 701 / 876 X 613 NUMBERS AND PROCESSES 255 17. What is the weight of a piece of armor plate containing 374 cubic feet, at the rate of 476 pounds to the cubic foot? PROCESS 476 Ib. When you require three X 374 partial products in performing 1904 a multiplication do not "add 3332 in." Check the product by 1428 reversing the factors or by Ib. Ans. castin S out u ' s - 18. Multiply. Test by casting out ll's: a 379 X 286 b 973 X 421 c 845 X 754 d 417 X 278 e 536 X 768 / 784 X 230 g 903 X 518 h 623 X 319 i 473 X 926 j 245 X 397 k 724 X 839 I 956 X 680 m 638 X 817 n 413 X 947 o 365 X 365 p 429 X 398 q 219 X 609 r 937 X 346 s 158 X 415 t 538 X 709 u 498 X 794 v 734 X 457 w 673 X 295 x 462 X 897 ONE FRACTIONAL FACTOR DRILL EXERCISES 1. Give answers: a %of84 6 96 x % c YQ of 54 d 78 xYz e % " 48 / 64 x% g % "36 h 84 X K2 i % "84 j 48 X % k % "72 I 60 X % w % "48 n 56 X 7 /s o % " 81 p 96 X Ke g X "84 r 96 X Yi2 s % "45 / 80 X %5 tt X " 96 48 x & w % " 63 x 64 X 256 WALSH'S BUSINESS ARITHMETIC 2. Multiply: a M of 83 b 97 X X c % of 13 d 15 X % e X " 21 / 33 x X % " U h 11 X % i % " 95 j 17 x X fc X " 82 Z 85 X X 6 m X " U n 13 X % o % " 43 p 27 x Ke q % " 88 r 95 X /i2 * X " 16 < 15 X KG w % " 35 v 13 X ^12 w X " 17 x 13 X KG SIGHT EXERCISES 1. What is the cost of (a) 12 pounds of sugar at (6) Of 4% pounds of meat at 32j PROCESS (a) Think S (tf of 12), 9 (3 times 3). Think 84 (7 times 12), 93 (carrying 9). Write 93. 93^ Ans. (b) Think 128 (4 X 32), 144 (carrying 16, % of 32). Write 144. $1.44 Ans. 2. Give products: a 66 X VA b 1/2 X 52 c 63 X l)i d 84 X IX IK X 84 / 66 X 1% g 56 X IX /i IX X 60 i 84 X IX j 20 X 1% k IX X 88 Z 81 X IX m 24 X 1% n 1% X 81 o 36 x 1% p 48 X IX q 1% X 45 r 54 X \% s 32 X 1% t \% X 56 w 40 X 1% tr 16 X IX w 1% X 27 x 60 X 1% 3. Multiply: a 20 X IX b 14 X 2/ 2 c 15 X 2X d 17 x IX 15 X 3^ / 16 x 3/3 9 19 X IX * 16 X 2X i 17 X 2X j 22 X IX & 30 X 3X * 21 X 3% NUMBERS AND PROCESSES 257 m 23 X 1% n 18 x 2% o 13 X 2% p 37 x IKo ? 16 X 3% r 17 X 3% 5 25 X 1& < 27 X 2% u 28 X 2% 33 X IMe to 20 X 4Xo x 21 X 4Mo WRITTEN EXERCISES 1. How many pounds of flour are there in 18 bags containing 24% pounds each? PROCESS Think 9 (18 halves). Think 72 (18 times 4), 81 (carrying 9); write 1. Think 36 (18 times 2), 44 (carrying 8); write 44. 441 Ib. Ans. Test by using 2 and 9 as factors. NOTE: By taking 2 as the first factor, the first product is an integer. 2. Write answers from the book. Test: a 12X110% 6 110)4X24 c 8 X 112% d 231% X 15 e 10 X 346% / 108K X 20 g 6 X 109% h 322% X 18 3. Mr. Schlaefer raised an average of 112% bushels of potatoes to the acre. What was the yield of a 24- acre field at that rate? PROCESS 112% bu. Think 18 (% of 24) X 24 Think 48 (24 X 2), 66 (carrying 2706 bu. Ans. 18). Write 6. Think 24 (24 X 1), 30 (carrying 6); write 0. Think 24 (24 X 1), 27 (carrying 3); write 27. 258 WALSH'S BUSINESS ARITHMETIC 4. Write answers from the book: a 8 X 246% 6 246% x 12 c 212% X 24 d 9 X 246% e 325% X 12 / 111% X 32 g 6 x 246% h 418% X 12 i 101% x 48 j 8 X 275% k 522% X 12 / 321% X 18 m 8 X 317% n 607% X 12 o 321% X 15 5. How many yards are there in 29 pieces of ging- ham averaging 35% yards to the piece? PROCESS 35% yd. X 29 Multiply % by 29, by multi- 4)87~ Paying 29 by 3 and dividing the product by 4 (do not write n% 4). To the result, 21%, add 9 times 35, and 2 (tens) times 35. 1036% yd. Ans. 29 TEST X 35% Multiply 29 by 36, JZi_ Product by _6 and from the product 1044 * 36 deduct % of 29. -7/4 _% 1036% " " 35% 6. Multiply: a 45% X 79 6 74 X 73% c 16% X 129 d 32% X 83 e 53 X 81% / 17% X 135 g 63% X 67 h 65 X 64% i 18% X 215 j 24% X 55 A: 81 X 43% I 19% X 223 m 58% X 91 n 95 X 52% o 15% X 329 7. What is the cost (a) of 123 shares of stock at $83% a share? (6) Of 137 shares at $85% a share? NUMBERS AND PROCESSES 259 PROCESS (a) 123 ^ se ^ e P r d" $83% uct b ^ 3 as T> J 4. 1 O tne fi rSt P ar ~ 369 Product by 3 . . , ( f tial product. 984~' " " s'ftens) Divide this b y 4 for the prod- $10301% Ans. uct by % First multiply 137 $ 85 5/ by 5, then by % by - j' *j- 4.1, ^ 695 Product by 5 dividing the first / oD $11741% Ans. 8. Multiply: a 13% x 25 b 126 x 15% c 237 X 23% d 27% x 37 e 217 X 37% / 369 X 42% 9. Multiply 267 (a) by %. (b) By 9%. (c) By 19%, (d) By 39%. (e) By 49%. PROCESS (a) 267X% (b) 267 X 9% Less % 33% 2670 Product by 10 Ans. 233% Less 53% " " % 2616% Ans. (c) 267 X 19% (d) 267 X 39% 5340 Product by 20 10680 Product by 40 Less_89 " " % 66% " " % 5251 Ans. 10613% Ans. 260 WALSH'S BUSINESS ARITHMETIC 10. Find products: a %X365 6 %X291 c 9% X 58 d 19% X 98 e %X213 / %X577 9 9% X 63 h 29% x 83 i % X 415 j % X 364 k 9% x 95 / 39%x71 m % X 127 n % X 427 o 9% x 89 p 49% X 65 g %o X 567 r % X 336 s 9% X 77 t 59% X 77 w % X 643 v % X 616 w> 9% X 97 x 69% X 83 MULTIPLYING FRACTIONS GENERAL METHOD WRITTEN EXERCISES 1. How many square yards of oil cloth are there in a piece 57% yards long and (a) 2% yards wide? (fr) 3% 6 yards wide? PROCESS 43 7 gf QQI (a) 57^ X n = ^ X - -= 150}^ (sq. yd.) Ans. p 2 Omit the denomination. Change each mixed number to an improper fraction. Cancel. Write the product of the new numerators over the new denominator. Reduce to a mixed number. After the result write sq. yd. in a parenthesis. Use no figures beyond those shown above. (6) 57XXSXe= - -X" = ? o ID NUMBERS AND PROCESSES 261 2. Find products: a 44% X 9% b 75% X 12% c 124% X 9% d 18% X 8% e 65% X 10% / 105% X 8% g 27K x 7% ft 59% X 11% i 132% X 7% SPECIAL METHOD SIGHT EXERCISES 1. Find % (a) of 1%. (6) Of 2%. (c) Of 3%. PROCESS (a) Change 1% to %\ % of %=%. Ans. (6) Change 2% to %\ % of % = %. Ans. (c) Change 3% to % % of *% = % = %. Ans. 2. Give answers: a % of 1% b % of 2% c % of 3% d % of 4% * % of 1% / % of 2% g / 4 of 3K A % of 5% m X of 1% n X of 1% o X of 3/ 4 p % of 7% 3. Write answers from the book: a % of 1% b % of 8% c % of 9% d % of 25% e % of 125% / % of 2% p % of 8% h % of 9% i % of 25% j % of 125% fc % of 3% Z % of 8% m % of 9% n % of 25% o % of 125% p % of 4% q % of 6% r % of 7% 5 % of 25% t % of 126% WRITTEN EXERCISES 1. A dealer had four pieces of cloth containing (a) 57% yd., (6) 57% yd., (c) 57% yd., and (d) 57% yd., re- 262 WALSH'S BUSINESS ARITHMETIC spectively. He sold % of (a), % of (6), % of (c), and of (c?). How many yards of each did he sell? PROCESS (a) % of 57% yd. = 19% yd. Ans. (6) % of 57% yd. = 14X 2 yd. Ans. Divide 57% by 4. This gives a quotient of 14 (write 14), and a remainder of 1%, or %. % of % is %>. Write %> (c) # of 57% yd. = 11% yd. Ans. Write the quotient 11. Reduce 2%, the remain- der, to % % of l % is %. Write %. (d) % of 57% yd. = 9% yd. Ans. Write 9, the quotient. Reduce 3%, the remain- der, to % % of % is %. Write %. TESTS Check the results by covering the answers. In (a) multiply 19% by 3. In (6) multiply 14& by 4. In (c) multiply 11% by 5. In (d) mul- tiply 9% by 6. 2. Write answers from the book: a % of 269% 6 K of 374% c % of 475% % of it (6) " 72% (% " " ) " 8. (c) 70Xs (X " " ) " 10. l % = 3% 3 % = 4X 5 % 5% " " " " 7. Find products: a 3% X 126} b 4% X 126% c 5% X 126% d 2% X 126^ e 6X1 X 126% / 7% x 126)^ y 8X1 X 126^ h 9Xi X 126X i 2% X 253^ j 3^ x 315% fc 4% X 407^ / 5^ X 512% NUMBERS AND PROCESSES 265 8. Multiply 215% (a) by 2%. (6) By 3%. (c) By 5%. PROCESS (a) 215% X 2% (b) 215% X 3% 646% Product by 3 861% Product by 4 Less 53% " }{ Less 71% " % 592 % Ans. 789% Ans. (c) 215% X 5% 1292% Product by 6 Less 26% " % 1265% Ans. 9. Multiply: a 8% X 215% b 9% X 136% c 7% X 257% d 3% X 427% e 4% X 215% / 5% X 123% g 5% X 224% h 1% X 152% i 3% X 306% SOME SHORT METHODS ALIQUOT PARTS A number that is a factor of another number is said to be an aliquot part of the latter. Thus 50^ is an aliquot part of a dollar; 10 days is an aliquot part of a month of 30 days; 6 hours is an aliquot part of a day. Seventy-five cents, which is $%, is called an aliquant part of a dollar, although it is an aliquot part of $3. While 20 days is not an aliquot part of a month it is an aliquot part of a year. 266 WALSH'S BUSINESS ARITHMETIC In performing computations, any number may be decomposed into others that are aliquot parts. MULTIPLYING BY ALIQUOT PARTS OF 100 25 = H* 12% = -HP- 33% = 16% = i 50 = SIGHT EXERCISES 1. What is the cost of 25 rugs (a) at $48 each? (b) At $35 each? PROCESS (a) At $48 each, 100 rugs, would cost 48 hundred dollars; % of 100 rugs would cost % of 48 hundred dollars or 12 hundred dollars. $1200 Ans. (b) At $35 each, 100 rugs would cost 35 hundred dollars; % of 100 rugs would therefore cost % of 35 hundred dollars, or 8% hundred dollars. $875 Ans. 2. Multiply by 25: a 27 b 33 c 46 d 85 e 124 / 165 38 h 49 i 83 j 96 fc 169 Z 205 3. Multiply by 33%: a 27 6 15 c 17 d 29 e 31 / 154 # 39 h 62 z 66 j 69 fc 97 / 128 4. (a) In multiplying 48 by 12%, what fraction of 48 hundred is the result? (b) What is % of 49 hundred? (c) What number is equal to % hundred? (d) To % hun- NUMBERS AND PROCESSES 267 dred? (e) To % hundred? (/) To % hundred? (g) To % hundred? (K) To % hundred? (i) To % hundred? 5. Multiply by a 24 b 32 c 25 cZ 34 e 169 / 249 2 44 h 69 i 89 j 51 k 321 Z 404 6. What is (a) % of 100? (6) %? (c) % ? (d) %? (e) X? 7. Multiply by 16%: a 24 6 25 c 32 d 37 e 48 / 185 g 19 /i 29 i 50 j 66 & 69 I 241 WRITTEN EXERCISES 1. What is the cost (a) of building 25 miles of rail- road at $8765 a mile? (b) Of building 125 miles? PROCESS (a) $8765 Divide 8765 hundred by 4,which X 25 gives 2191% hundred $219125 Ans. Substitute 25 for % hundred (b) Since 125 is % thousand divide $8765 8765 thousand by 8, which gives X 125 1095% thousand. $1095625 Ans. Substitute 625 for % thousand Write answers directly from the book: 2. Multiply by 25: a 1625 b 3463 c 2345 d 1296 e 3579 / 1143 g 2305 h 4425 i 3617 j 1234 k 4061 I 3582 268 WALSH'S BUSINESS ARITHMETIC 3. Multiply by 125: a 1627 b 3565 c 2347 d 1298 e 5064 / 2076 g 2316 h 3666 i 2468 j 5670 fc 4492 J 3786 , 4. Multiply by 33%: a 1628 6 3464 c 2349 d 1297 e 4565 / 1116 g 4538 h 4016 i 3527 j 1357 k 2348 / 3691 6. Multiply by a 1626 6 3665 c 2248 d 1089 e 2033 / 1854 2316 h 1444 i 1246 3458 fc 2244 J 5687 6. Multiply by 16%: a 1629 b 3352 c 2234 d 1185 e 2468 / 1965 g 3427 /i 2555 i 1357 j 4569 A; 3251 / 5408 WRITTEN EXERCISES 1. Mr. Sterrett sold 1465 shares of stock in the Corrigan Paper Mill for $175.25 a share. What did he receive? PROCESS Multiply 1465 by 25 by taking 1465 % of it. Bring down 25. Find 175.25 the product of 1465 by 175 by 36625 (a) multiplying (a) by 7. Add in $256,741.25 Ans. 366 > the remaining figures of the first partial product. NUMBERS AND PROCESSES 269 2. Multiply by 17,525: a 1245 b 2467 c 3488 d 4179 e 5234 / 6432 3. Multiply by 25,175: a 2346 6 3578 c 4569 d 5283 e 6345 / 7543 4. Multiply by 7525: a 3457 6 4689 c 5671 d 6394 e 7456 / 8654 5. Multiply by 2575: a 4568 b 5792 c 6783 d 7405 e 8567 / 9765 OTHER SHORT METHODS SIGHT EXERCISES 1. Find the cost of 88 shares of stock (a) at $99 a share, (b) At $99^. (c) At $99%. (d) At $99%. PROCESS At $100 a share, 88 shares would cost 88 hun- dred dollars. Diminish 88 hundred: in (a) by 88; in (b) by 44, Y 2 of 88; in (c) by 22, # of 88; in (d) by 11, Y 8 of 88. 2. Give products: a 24 X 99 b 24 X 99% c 24 X 99% d 24 X 99% e 99 X 99 / 24 X 99% g 24 X 99% h 24 X 99% i 99 X 48 j 48 x 99% A: 48 X 99% I 48 X 99% m 57 x 99 n 84 X 99% o 99 X 99% p 66 X 99% g 99 x 63 r 16 x 99% s 84 X 99% 88 X 99% M 98 X 99 o 36 X 99% w 99 X 99% x 72 X 99% 270 WALSH'S BUSINESS ARITHMETIC 3. Find the cost of 48 yards of ribbon (a) at a yard. (6) At 26^. (c) At 13}^. (d) At () At PROCESS The price a yard is 1 cent more than $% in (a), than $K in (6), than $% in (c), than $% in (d), and than $%in (e). Add, therefore, 48^ to % of $48 in (a), to % of $48 in (6), to X of $48 in (c), to % of $48 in (d), and to % of $48 in (e). 4. Give products: a 86 X 51 6 88 X 13% c 17% X 24 d 36 x 34% e 26 X 84 / 32 X 13X 2 flf 17%x72 h 99 x 34% i 46 x 51 j 64 X 13% k 17%x42 / 69 x 34% m 26 x 24 n 96 X 13% o 17%x54 p 39 x 34% q 51 X 72 r 72 X 13% s 17%x66 t 66 X 34% w 28 X 26 v 56 X 13% w 17% X 78 x 96 X 34% 6. What is the cost of 48 yards of embroidery (a) at 49ff a yard? (b) At 24 jj? (c) At ll^ff? (cQ At 32%^? (e) At PROCESS The price a yard is 1 cent less than $% in (a), than $K in (6), than $% in (c), than $% in (d), and than $% in (e). Deduct, therefore, 48^ from % of $48 in (a), from Y 4 of $48 in (6), from % of $48 in (c), from % of $48 in (d) and from % of $48 in (e). NUMBERS AND PROCESSES 271 6. Give products : a 86 X 49 b 88 X 11% c 15% X 72 d 36 x 32^ e 24 X 84 f 32 X l\% g 15% X 42 /i 99 X 32& i 46 x 49 j 64 X UK fe 15% X 24 Z 69 x 32} m 24 X 24 n 96 X IV& o 15% X 54 p 39 X 32} q 72 X 49 r 72 X 11/2 s 15% X 66 < 66 x 32^ u 24 X 28 v 56 X UK w 15% X 78 z 96 X 32% WRITTEN EXERCISES 1. Find the area of a rectangle 344 yards long (a) 99 yards wide, (b) 97 yards wide, (c) 95 yards wide. PROCESS (o) 344 (yd.) X 99 (yd.) Deduct 344 from 100 times 34056 (sq. yd.) Ans. 344 without writin S the latter product. In (b) deduct 3 times 344 from 100 times 344. (6) 344 (yd.) X 97 (yd.) Think 12 (3 X 4) and 8 33368 (sq. yd.) Ans. (writing 8) are 20. Think 12 (3x4), 14 (carrying 2) and 6 (writing 6) are 20. Think 9 (3 X 3), 11 (carrying 2) and 3 (writing 3) are 14. Think 1 and 3 (writing 3) are 4. Bring down 3. 2. Multiply: a 456 x 99 b 98 X 375 c 576 x 999 d 567 X 97 e 96 X 486 / 389 X 998 g 678 X 95 h 96 X 598 i 437 X 997 j 789 X 94 k 95 X 864 / 684 X 996 m 234 X 98 n 97 X 864 o 886 X 995 272 WALSH'S BUSINESS ARITHMETIC 3. At $248 an acre, find the cost (a) of 37% acres, (6) Of 35 acres, (c) Of 27% acres, (d) Of 26% acres, (e) Of 75 acres, (/) Of 87% acres, (g) Of 97% acres, (h) Of 62% acres. PROCESS (a) 25 A. $6200 (6) 25 A. ? + 12% " ? +10 " ? 37% A. ? Ans. 35 A. ? Ans. (c) 25 A. ? (d) 25 A. ? + 2% " ? + IX " ? 27% A. ? Ans. 26% A. ? Ans. (e) 100 A. ? (/) 100 A. ? - 25 " ? - 12% " ? 75 A. ? Ans. 87% A. ? Ans. (g) 100 A. ? (h) 50 A. ? - 2% " ? + 12% " ? 97% A. ? Ans. 62% A. ? Ans. In (a) find the cost of 12% A. by taking % the cost of 25 A. In (b) find the cost of 10 A. by multiplying $248 by 10. In (c) the cost of 2% A. is Mo the cost of 25 A. etc. 4. Multiply: a 136 x 37% b 212 X 75 c 384 X 87% d 444 X 43^ e 516 x 35 / 639 X 66% 712 X 62% h 883 X 45 i 969 X 76% j 842 X 47% & 715 X 97 J 624 X 17% NUMBERS AND PROCESSES 273 5. Find the cost of 1347 1 yards of prints (a) at cents a yard. (6) At 10% cents. METHOD Save time and figures by and of %. using aliquot parts of % 6 (a) Atl / 1347^ (6) 1347K 1^ $161.22tf %t 6.73% (I) ^ 84% 2 (II) At 10^ $134.75 " % 3.36% (III) " X 1.68^6 (IV) $168.80 Ans. $139.80 Ans. For (II) take Y 8 of (I) For (IV) take }{ of (III) 6. Find products : a 2% X 484 d 3% X 576 g 4%> X 328 j 5Ke X 254 6 6%j X 184 e 7% X 908 h 8% X 736 k 9% X 864 c 10% x 272% / 18% X 104/ 2 i 12% x 364% 1 16J4, X 406^ DECIMALS ONE DECIMAL FACTOR WRITTEN EXERCISES 1. What is the area of a plot (a) 7 rods long 6.85 rods wide? (b) 15 rods long 8.4 rods wide? METHOD (a) 6.85 (rd.) (6) 8.4 (rd.) X 7 " X 15 " Ans. 47.95 (sq. rd.) Ans. 126.0 (sq. yd.) When the product can be written at once, insert the decimal point when it is reached in performing the multiplication. 274 WALSH'S BUSINESS ARITHMETIC 2. Write answers from the book: a 8 X 13.52 b 12 X 2.345 c 32 X .0204 d 6 X 2.345 e 15 X 12.34 / 13 X 120.5 g 5 X .1768 h 21 X 3.421 i 16 X 24.31 SIGHT EXERCISES 1. Multiply by 10: a 34.26 b 4.32 c .897 d .0345 e .0059 / 4.6 g 19.84 h 5.67 i .603 j .0567 & .0006 I 5.2 2. Multiply by 100: a 62.43 6 9.84 c .789 d .0534 e .0095 / 6.4 g 35.18 A 5.23 i .264 j .0402 k .0007 / 8.3 3. Multiply by 1000: a 26.43 6 8.49 c .978 d .0435 e .0062 / 5.7 g 17.09 A 3.46 i .104 j .0926 & .0004 I 9.1 WRITTEN EXERCISES 1. The coin value of a franc is $.193. What is the value (a) of 10 francs? (6) Of 20 francs? (c) Of 60 francs? PROCESS (a) To multiply $.193 by 10, shift the decimal point one place to the right. For (b) multiply by 2 the result obtained in (a). NUMBERS AND PROCESSES 275 2. Write answers from the book: a 40 X 3.1416 b $4.8665 X 100 c 70 X 2.345 d 50 X .1975 e .3937 X 200 / 80 X 13.81 g 60 X 123.4 h 2.2046 X 300 i 90 X 347.2 3. (a) How many pounds are there in 900 kilos of 2.2046 pounds each? (b) Find the coin value of 4000 at $4.8665 to the . METHOD (a) 2/20.46 lb. (b) $4/866.5 X 1984.14 lb. Ans. $19466.0 Ans. In (a), multiply 2.2046 by 100 by shifting the deci- mal point two places to the right. Multiply the changed multiplicand by 9. In (b) multiply 4.8665 by 1000 by shifting the deci- mal point three places to the right. Multiply the changed multiplicand by 4. Cancel the decimal cipher. 4. Multiply. Test: a 900 X 174.9862 b 1200 X 14.756 c 700 X 1374.64 d 2400 X .02345 e 600 X 24.385 / 3000 X 3.0098 MULTIPLYING DECIMALS WRITTEN EXERCISES 1. Multiply (a) .243 X .37. (b) 3.65 X "8.6. Changing the decimals to common fractions the problem becomes 276 WALSH'S BUSINESS ARITHMETIC 243 37 8991 x wo- =- 0899lAns - The numbers of ciphers in the denominator of the product is equal to the combined number in both factors. PROCESS Ignoring the decimal points, multi- ply 243 by 37. Since there are three * decimal places in the multiplicand 729 and two in the multiplier, point off .08991 Ans. five (3 + 2) decimal places in the product. To point off this number, prefix a decimal cipher to the original product. (6) 3.65 (6) Cut off 3 decimal places. X 8 6 Cancel the terminal cipher 2920~ 31.890 Ans. TEST As a preliminary to the test of (b) note that the product must be more than 8 times 3 and less than 9 times 4. 2. Find products. Test: a 7.29 X 4.8 b 7.0234 X 819 c 25.09 X 8.32 d .0385 X 7.2 e 6.1408 X .042 / 531.75 X .484 NUMBERS AND PROCESSES 277 3. Multiply 513.583 (I) by 3.25, (II) by 23.25, (III) by 37.5 METHOD (I) a 513.583 X 3.25 b 128.39575 Product by % Ans. 1669.14475 " of (a by 3) + b In doing the work substitute % for .25 (II) 513.583 When the multiplier is a mixed 23.25 decimal containing such deci- 128 39575 ma ^ s as *^> ^^' etc *> some 1540 749 accountants prefer to place the 10271 66 latter beyond the last figure of the multiplicand, as they do in writing a mixed number. In this case they insert the decimal point in each partial product. (III) a 513.583 X 37.5 (300/8) b 154074.9 Product of a by 300 19259.3625 "b " % Test by using aliquot parts, multiplying first by 25, then by 12%. 4. Multiply: a .864 X .625 b 84.624 X S3% c 78.6 x .135 d 97.25 X .23 e 14.9375 x 34% / 437 X .995 g 27.055 x 3.4 h 8312.34 X .99 i .115 x 6.288 j .875 x 3.08 k 99.7 x 6.086 / 95.704 X 32} m 88.5 X .6248 n 74.2 X .375 o 437.6 x .099 p 18.75 X 2.94 q 63.8 X .0495 r 28.4 X .076 278 WALSH'S BUSINESS ARITHMETIC MULTIPLYING DENOMINATE NUMBERS WRITTEN EXERCISES 1. How many bushels of apples are there in 15 barrels averaging 2 bushels 3 pecks each? METHOD 2bu. 3pk. Think 45 pk. (15 X 3 pk.), 11 bu. 15 1 pk. (changing to bushels and pecks). Write 1 pk. bu. 1 pk. (carrying 11 bu.) Write 41 bu. Ans. 41 bu. 1 pk. 2. Write answers from the book: a 3 Ib. 9 oz. b 8 bu. 2 pk. c 4 pk. 3 qt. d 5 gal. 3 qt. X4 X3 X6 X5 e 4 8s. / 5s. 6d. g 6 qt. 1 pt. h 3 ft. 4 in. X7 X8 X9 XlO 3. A family uses 2 quarts 1 pint of milk a day. How much does it use (a) in a week? (b) During June? 4. Write products from the book: a 3 Ib. 10 oz. b 3 qt. 1 pt. c 3 yd. 1 ft. d 46s. X 18 X 16 X 24 X 12 e 10s. 6d. / 1 bu. 3 pk. g 3 pk. 4 qt. h 2 ft. 6 in. X 18 X 20 x 15 x 40 CHAPTER NINE DIVISION DIVIDING BY AN INTEGER SIGHT DRILLS A B C D E F G H a 45 54 102 104 105 106 108 140 b 56 65 110 111 114 116 117 143 c 69 76 118 119 120 121 123 144 d 78 87 125 126 128 130 132 145 e 86 98 133 135 135 136 138 147 1. Name rapidly (I) by columns, (II) by lines, the multiples (a) of 2. (b) Of 4. (c) Of 8. (d) Of 3. (e) Of 9. (/) Of 6. (g) Of 5. (h) Of 7. (i) Of 11. 2. State (I) by columns, (II) by lines, the remainders when the following numbers are divided: (a) By 3. (6) By 5. (c) By 9. (d) By 11. (e) By 4. (/) By 8. (<7) By 25. ABCDEFGH a 345 554 102 504 905 506 109 543 b 656 165 210 611 814 416 217 677 c 469 987 325 729 623 321 423 709 d 278 887 425 826 735 239 332 821 3. Give two factors of: a 65 b 69 c 86 d 133 e 106 / 111 87 h 46 i 57 j 119 k 143 I 121 m 51 n 95 o 62 p 145 q 134 r 118 s 93 * 58 M 91 v 158 w 155 * 146 279 280 WALSH'S BUSINESS ARITHMETIC ORAL PROBLEMS 1. In how many weeks will a man earn $1440 when his weekly earnings are (a) $15? (b) $16? (c) $18? (d) $24? (e) $30? (/) $36? 2. How many pounds are there in (a) 96 oz.? (b) 144 oz.? (c) 80 oz.? (d) 112 oz.? (e) 176 oz.? (/) 128 oz.? 3. How many feet are there in (a) 132 in.? (b) 168 in.? (c) 96 in.? (d) 192 in.? (e) 288 in.? (/) 960 in.? 4. (a) At 60 pounds to the bushel, how many bushels of potatoes weigh 9600 pounds? (b) How many bushels of oats, weighing 32 pounds to the bushel, will have the same weight? SIGNS OF DIVISION To indicate that 15 is to be divided by 3, write 3, o\ -I * the divisor, then a curved line, then the dividend. Write 5, the quotient, under- neath. This form may be read "3 into 15 (goes) 5 times." Or, write the dividend above a line and the divi- sor underneath. Follow with a sign of - ~ equality and then the quotient. This form - = 5 may be read "15 over 3 equals 5." Or, write the dividend, then the division sign (-s-), then the sign of equality, concluding 15 -j- 3 = 5 with the quotient. This form is read "15 divided by 3 equals 5." The other two forms may also be read in this way. The second form is generally employed when either term is compound or contains literal numbers. NUMBERS AND PROCESSES 281 3X 16 ab y 2 - 16 2 c ' y + 4 In many European countries the colon, which in this country is employed to denote ratio, is used as the division sign. In some of them our division sign (-T-) indicates subtraction. SHORT DIVISION WRITTEN EXERCISES 1. (a) When 15 barrels of sugar weigh 4620 pounds,, what is the average weight per barrel? (6) How many overcoats at $15 each will cost $5250? PROCESS (a) 15)4620 Ib. Divide 4620 Ib. by 15, the Ans. 308 Ib. number of barrels. (6) $15)$5250 Divide $5250 by $15, the Ans. 350 (coats) cost of a coat. The quo- tient, 350, is the number of coats. Write coats in a parenthesis. Test each result, covering the dividend with a strip of paper on which you write the product of the quotient by the divisor. Remove the paper and compare this product with the dividend. Be careful to place the first quotient figure under the right-hand figure of its partial dividend, and to place a quotient figure or cipher under each remaining figure of the dividend. 2. Write quotients from the book. Under each write its product by the divisor: 282 WALSH'S BUSINESS ARITHMETIC a 32)1024 b 18)5418 c 15)3600 d 19)4408 e 21)2331 / 14)2002 g 13)3952 h 17)8517 i 16)2128 j 24)2952 k 23)7590 I 25)5375 DIVIDING BY A MULTIPLE OF 10 PREPARATORY EXERCISES 1. At $200 an acre how many acres of land will cost $2800? 2. At 2000 pounds to the ton, how many tons are there in 86000 pounds of coal? 3. At 160 square rods to the acre, how many acres are there in 3200 square rods? 4. (a) Why is the quotient of 2800 -f- 200 the same as the quotient of 28-7-2? (b) By what number are both terms of 2800 -=- 200 divided to change them to 28 -T- 2? Dividing the divisor and the dividend by the same number makes no change in the quotient. WRITTEN EXERCISES 1. (a) At $60 each, how many cows will cost $57,600? (b) What is the average cost of a rug when $52,000 is paid for 800 rugs? METHOD (a) 6 1 0)6760 10 (b) 8 1 00)$520|00 (cows) Ans. $ Ans. In (a) divide both terms by 10 by cutting off the final cipher. Divide 5760 by 6. In (b) divide both terms by 100 by cutting off the last two ciphers. Divide $520 by 8. NUMBERS AND PROCESSES 283 2. Write quotients from the book: a 120)67,800 b 800)36,800 c 1500)106,500 d 600)45,600 e 160)38,560 / 4000)292,000 REMAINDERS PREPARATORY EXERCISES 1. At $16 each, how many calves can be bought for $500, and how much money will remain? 2. At $16 a ton, how much iron ore can be bought for $500? Give answer as a mixed decimal. 3. How many miles an hour does a train travel when it goes 500 miles in 16 hours? Give answer as a mixed number. 4. If a vessel goes 16 miles an hour, how many hours and minutes will it require to go 500 miles? 5. How many persons can be properly accom- modated in a room having 500 square feet of floor space if each is to have at least 16 square feet? 6. How many auto cars are needed to transport 500 soldiers at one time if each can carry only 16 soldiers? 7. Why should the remainder be given in the answer to Ex. 1 and omitted in the answer to Ex. 5? 8. What is done with the remainder in the answer to Ex. 6? WRITTEN EXERCISES 1. Write answers from the book, giving each quo- tient as an abstract number and the remainder as a concrete number: a 17 lb.)8523 Ib. b $14)$4258 c 16 T.)8163 T. d 15 yd.)4539 yd. e 13 mi.)7973 mi. / 24 A.)7227 A. 284 WALSH'S BUSINESS ARITHMETIC 2. At 2000 pounds to the ton, give the number of tons and pounds (a) in 96,875 pounds of coal, (b^ In 97,000 pounds, (c) In 97,450 pounds. METHOD (a) 2|000lb.)96|875lb. 48(T.)875 Ib. Ans. When 96875 Ib. is divided by 1000, there is a remainder of 875 Ib. Write this remainder after 48, the quotient of 96 (thousand) divided by 2 (thousand). After 48, the number of tons, write T. in a parenthesis. (6) 2|QOOlb.)97lOOOlb. 48 (T.) 1000 Ib. Ans. 2 (thousand) is contained in 97 (thousand) 48 times with a remainder of 1 (thousand) (c) 2|000lb.)97|450lb. 48 (T.) 1450 Ib. Ans. Divide 97 by 2, writing 48, the quotient. Prefix 1, the remainder, to 450, the figures of the dividend that are cut off. To divide an integer by a number ending in one or more ciphers cut off the terminal cipher or ciphers in the divisor and the same number of figures from the right of the divi- dend. Divide the remaining figures of the dividend by the remaining figures of the divisor. Write as the remainder the figures of the dividend that have been cut off, prefixing the partial remainder, if any, left after performing the division. NUMBERS AND PROCESSES 285 3. Find quotients and remainders: a 120)57650 b 700)50200 c 1800)203500 d 210)25635 e 140)48320 / 3200)99805 DECIMAL QUOTIENTS When the quotient of two integers is to be given as a decimal, continue the division by mentally annexing decimal ciphers to the dividend. WRITTEN EXERCISES 1. (a) I paid $18 for 8 bushels of potatoes; what was the cost a bushel? (b) At $16 a ton, how many tons of straw can be bought for $250? PROCESS Place a decimal point after (a) 8)$18. $18. Place a decimal point $ 2.25 Ans. m the quotient under the one in the dividend. Place a decimal point after (b) 16)250 ^' ^ not wr * te ^ e deci- * , mal ciphers. Place a decimal ' Ans> point in the quotient under the one in the dividend. 2. Write quotients from the book, as mixed deci- mals: a 12)246 b 8)243 c 16)340 d 4)3926 e 14)175 / 6)201 g 18)405 h 2)4321 286 WALSH'S BUSINESS ARITHMETIC DECIMAL DIVIDENDS 3. Divide (a) 24.3 by 8. (b) .246 by 12. PROCESS (a) 8)24.3 (6) 12) .246 3.0375 .0205 Place a decimal point in the quotient under the one in the dividend. In (b) place a cipher under the 2 in the dividend. 4. Write quotients from the book: a 12)36.6 6 8)3.23 c 16). 344 d 9)34.2 e 12)4.86 / 8). 324 g 18)3.69 h 4)1.02 5. How many tons are there (a) in 96,875 pounds? (b) In 97,000 pounds? (c) In 97,450 pounds? Give results as mixed decimals. METHOD (a) gppp)96.875/ (6) 2PPP)97.PPP/ Ans. 48.4375 (T.) 48.5 (T.) (c) 2PPP)97.450/ Ans. 48.775 (T.) Since the answer is to be given as a decimal, cancel the three ciphers in the divisor (dividing it by 1000) and divide each dividend by 1000 by setting off three decimal places. NUMBERS AND PROCESSES 287 To show that the original dividend is an integer, place after it a decimal point, and cancel it when the new one is written. 6. How many tons are there in 14,760 pounds? 7. At 160 square rods to the acre, how many acres are there in 2440 square rods? 8. Express quotients in decimal form: a 120)426 b 800)1244 c 16000)4040 d 160)808 9. Divide (a) 62.4 by 120, (b) 14.84 by 16000. METHOD Divide the divisor by 10 by canceling the cipher. (a) 120)6.2/4 Divide the dividend by 10 by - moving the decimal point one Ans ' place to the left. Divide the changed dividend by the changed divisor. To move the decimal point in the dividend three places to the left, prefix (b) 16W).014/84 10. Express quotients in decimal form: a 300)4.26 b 6000)524.4 c 150). 606 d 90)47.7 FRACTIONAL QUOTIENTS When the result of a division is to be expressed as a mixed number, write the remainder over the divisor in the form of a fraction. 11. Express each quotient as a mixed number. Write answers from the book. a 11)37561 b 13)29400 c 12)39863 d 15)46702 288 WALSH'S BUSINESS ARITHMETIC 12. In the following give the fraction in the quotient in lowest terms. Write answers from the book. a 14)30107 b 16)50100 c 21)84639 d 18)90372 COMPOUND NUMBER QUOTIENTS The result of the division of a denominate number by an abstract number may be expressed as a com- pound number, as shown by the first example (a) below. 13. Divide (a) 54 bushels by 16. (b) 42 yd. 2 ft. 3 in. by 9. PROCESS 54 bu. divided by 16 gives a quotient of 3 bu. with a remainder of 6 bu. Change the latter to / \ I*\KA u 24 pk. This divided (a) 16)54 bu. * . by 16 gives a quotient Ans. 3bu.lpk.4qt. mainder of 8 pk. Change the latter to 64 qt. This divided by 16 gives a quotient of 4 qt. After dividing 42 yd. by 9, and writing the quo- tient, 4 yd., change 6 yd., the remainder, to 18 ft. (6) 9)42 yd. 2 ft. 3 in. To th / s add 2 'V . ak ; ing the next dividend Ans. 4 yd. 2 ft. 3 in. 2Q ft Wrfte % ft>> ^ quotient, and change the remainder, 2 ft., to 24 in. To this add 3 in., making the next dividend 27 in. Write 3 in., the next quotient. 14. Express each quotient as a compound denomi- nate number. Write answers from the book. NUMBERS AND PROCESSES 289 a 8)34 Ib. 6 6)39 Ib. 6 oz. c 12)51bu. 2 pk. 4 qt. d 9)40 yd. e 7)33 gal. 1 qt. / 10)95 yd. 1 ft. 10 in. g 8)37 bu. h 5)63 yd. 1 ft. i 11)86 gal. 2 qt. 1 pt. 15. Divide 65 yd. 10 in. by 10. METHOD 10)65 yd. ft. 10 in. Insert the missing denomi- nation. 16. Express quotients as compound numbers, a 10)62 yd. 8 in. b 12)76 bu. 4 qt. c 9)73 gal. 1 pt. FRACTIONAL DIVIDENDS SIGHT EXERCISES 1. Give quotients. a % -s- 2 b % -5- 2 c IX + 2 d 1/5 -f- 2 e % -5- 3 f % -H 3 many accountants use Ans. 984 (bu.) the factors. Test the re- sult by covering the divi- dend, and writing the product of 984 by 8, and this product by 7. 2. Find quotients: a 59,544 ^72 b 68,096 -=- 64 c 91,584 -* 96 d 99,616 -f- 88 e 88,816 - 56 / 78,197 + 49 3. Divide (a) 86,347 by 91 (6) 228,338 by 66. METHOD (a) 7)86,347 (b) 11)228,338 13)12,335 2 / 7 6)20,758 948% Ans. 3459% Ans. 292 WALSH'S BUSINESS ARITHMETIC 4. Express quotients as mixed numbers: a 68,551 -. 81 b 81,745 - 66 c 95,239 -j- 54 d 83,015 ^42 e 90,583 - 39 / 71,229 - 28 Decimal quotients are frequently limited to two or to three places. In such a case carry out the result to an additional place. When this last quotient figure is less than 5, reject it in stating the result; when it is 5 or more use it to increase the preceding figure by 1. 5. Divide (a) 34,885, (b) 24,703 by 96, giving quo- tients to nearest thousandth, to nearest hundredth. METHOD (a) 8)34,885 (b) 8)24,703 12)4360.625 12)3087.875 363.3854 257.3229 (I) Quotient to nearest thousandth (a) 363.385 Ans. (b) 257.323 Ans. (II) Quotient to nearest hundredth (a) 363.39 Ans. (6) 257.32 Ans. 6. Give quotients (I) to nearest thousandth, (II) to nearest hundredth. a 58,843 * 48 6 45,678 -r 72 c 62,943 - 77 d 37,945 -r- 56 e 86,745 4-84 / 76,849 -j- 63 7. Divide (a) 86,347 by 91, (b) 228,338 by 66; (I) expressing each result as a mixed number, (II) giving quotients and remainders. NUMBERS AND PROCESSES 293 METHOD (a) 7)86,347 (b) 6)228,338 13)12,335% 11)38,056^ (I) 948% Ans. 3459% Ans. (II) 948; rem. 79 Ans. 3459; rem. 44 Ans. In (a), the denominator of %, the fraction in the mixed number quotient (I), being the same as the regular divisor, 91, write 79, its numerator, as the remainder in (II). In (b) multiply %, the fraction in the answer (I) by 66, the regular divisor, which gives 44 as the remainder (II). By omitting to reduce the fractions % and % to lowest terms, the denominator of (b) 6)228,338 the latter would corres pond with 11)38,056% the regular divisor, and its numer- 3459% ator would be the remainder. 8. Divide; (I) expressing results as mixed numbers, (II) giving quotients and remainders. a 68,551 *- 81 d 34,672 -5- 77 g 11,572 -f- 33 j 48,312 -s- 42 b 83,015 + 42 e 53,219 4- 32 h 81,745 * 66 k 42,094 + 84 c 94,724 ^ 48 / 95,239 -*- 54 i 96,583 -*- 39 I 71,229 * 28 DIVIDING BY MULTIPLES PREPARATORY EXERCISES 1. At $1J each what will be the cost of 12 baseballs? 2. How many baseballs costing 3 half dollars each an be bought for 36 half dollars? 294 WALSH'S BUSINESS ARITHMETIC 3. (a) 3 halves)36 halves (b) IX) 18 (c) 3)36 ? ? T 4. (a) How many times IX is 3? (6) How many times 18 is 36? (c) How does the quotient of 18 * IX compare with the quotient of 36 + 3? Multiplying the divisor and the dividend by the same number makes no change in the quotient. 5. How many baseballs can be bought for $6 when they cost (a) $X each? (6) $M each? METHOD (a) X) 6 (b) }{} 6 X 2X 2 X 4X 4 1) 12 1) 24 Although you obtain the result in (a) by multi- plying 6 by 2, and in (6) by multiplying 6 by 4, you should realize that you are really dividing $6, the sum to be spent, by the cost of each, by $X or $& respectively, to ascertain the number that can be purchased. 6. Give quotients: a X)24 b X)36 c Xm d X)144 JQ31 X)72 h X)140 j X)33 NUMBERS AND PROCESSES WRITTEN EXERCISES 295 1. How many baseballs can be bought for $15 when the price is (a) $% each? (6) $lji each? (a) JO 15 X4 X4 METHOD (&) IK) 15 X4 X4 3) 60 20 (baseballs) Ans. 5) 60 12 (baseballs) Ans. Multiply the divisor and the dividend by the denominator of the fraction. Divide the new dividend by the new divisor. Test (a) by multiply- ing % by 20; (6) by multiplying 1% by 12. In practice omit such unnecessary figures as the multipliers shown above. Write only (a) JQ 15 (6) IK) 15 . 3)60 5)60 2. Find quotients. Write answers directly from the book: b / 4 a fc 3. Divide. Test: a l/2)112/ 2 6 DQ236/4 g 2)0242/3 h 2^)231% i 2/ 5 )200/ 5 296 WALSH'S BUSINESS ARITHMETIC 4. At $7% a ton, how many tons of coal can be bought (a) for $324? (6) For $318%? METHOD (a) 7)0824 (b) 7^)318% 15)648 15)637^ 43} (T.) Ans. 42^ (T.) Ans. 5. Divide. Test: a IflllOX b 1?Q108X d 1J0120X IK) 1^3% / 2)0163% 6. Divide 83647 by 65. Give quotient (a) correct to nearest hundredth, (b) As a mixed number. METHOD Multiply the divisor and 65)83,647 the dividend by 2 . Cancel 13P) 16,729.4 the cipher in the divisor and 1286.88 Ans. cut off one decimal place in the dividend. 7. Divide by 35, giving the result correct to the nearest hundredth : a 17,463 6 23,986 c 35,207 d 43,916 e 54,268 8. Divide by 45, giving the quotient as a mixed number: a 63,482 b 74,006 c 82,954 d 96,875 e 83,108 NUMBERS AND PROCESSES 297 9. Divide by 55, giving the quotient to the nearest thousandth : a 70,034 b 62,158 c 51,329 d 47,676 e 32,983 10. Divide (a) 43,816 by 25. (b) 3619.4 by 33% (c) 260.78 by 12%. (d) 16.547 by 16%. Give quotients as mixed decimals. METHOD (a) 25) 43,816 (6) 33%)3619.4 100)1752.64 Ans. 100)144.77/6 Ans. (c) 12^)260.78 (d) 16%) 16.547 100)16.86/24 Ans. 100). 99/282 Ans. Multiply divisor and dividend by 4 in (a), by 3 in (6), by 8 in (c), and by 6 in (d). Divide by 100 by shifting the decimal point in each new dividend two places to the left. 11. Divide by 25. Write answers from the book: a 164.5 b 321.25 c 2408 d 12.34 e 3750 / 477.5 12. Divide by 16%. Write answers from the book: a 123.5 b 506.75 c 4802 d 40.25 e 7250 / 307.5 13. Divide by 33%. Write answers from the book: a 106.4 b 312.25 c 3504 d 20.44 e 4360 / 206.5 14. Divide by 12%. Write answers from the book: a 125.5 b 273.25 c 1216 d 30.75 e 2430 / 512.5 298 WALSH'S BUSINESS ARITHMETIC 15. How many tons of armor plate can be bought for $55,440 when the price is (a) $175 a ton? (b) $225 a ton? (c) $275 a ton? METHOD (a) 175) 55,440 Multiply the divisor 700)221,760 an d the dividend by 4. ^ ns ~~ cp \ Give the result as a mixed decimal. Test the result by multiplying it by 175, using the aliquot part method. 16. Divide by 175: a 78,995 b 86,387 c 97,244 d 67,011 e 59,822 17. Divide by 225: a 39,798 b 28,368 c 48,438 d 79,326 e 65,286 18. Divide by 275: a 93,071 b 85,679 c 54,670 d 43,692 e 74,283 19. How many acres of land can be bought for $21,000 when the rate is (a) $37^ an acre? (b) $62% an acre? (c) $87% an acre? METHOD a 37K) 21,000 Multiply the divisor 300)168,000 and the dividend by 8. Ans. (A.) NUMBERS AND PROCESSES 299 20. Divide by 37%: a 24,000 6 31,500 c 42,360 d 54,813 e 62,172 21. Divide by 66% (multiply both terms by 3) : a 84,000 b 73,200 c 96,480 d 86,214 e 71,203 22. Divide by 62%: a 63,000 6 50,500 c 43,280 d 32,105 e 23,456 23. Divide by 75 (multiply both terms by 4) : a 18,000 6 23,400 c 36,070 d 42,315 e 50,306 24. Divide by 87%: a 63,000 6 75,600 c 89,530 d 97,293 e 86,436 25. Divide by 112%: a 72,000 b 60,300 c 53,820 d 53,065 e 32,148 26. Divide by 125. Give the quotient as a mixed decimal. Write answers directly from the book. (Multiply both terms by 8.) a 14,723 b 2345.6 c 325.19 d 40.876 e .51,234 27. Divide by 375: a 63,273 b 76,543 c 81,951 d 93,252 e 87,345 28. Divide by 625. Try to write answers from the book by multiplying both terms by 16: a 43,210 b 32,104 c 21,043 d 10,234 e 54,321 29. Divide by 875: a 30,387 6 26,614 c 43,638 d 60,501 e 10,605 300 WALSH'S BUSINESS ARITHMETIC 30. Divide by 133%: a 12,345 6 23,456 c 34,567 d 45,678 e 56,789 31. Divide by 166%. Write answers from the book. (Multiply both terms by 6.) a 63,421 b 70,416 c 86,235 d 91,314 e 82,031 DECIMAL DIVISORS WRITTEN EXERCISES 1. (a) A man pays annually as interest .06 of the sum he borrowed to help to pay for a house. If the interest is $135 a year, how much did he borrow? (b) Divide 8.36 by 1.6 METHOD (a) /06) $135/00 Multiply the divisor by Ans. $2250 100 by canceling the decimal point. Multiply the divi- dend by 100 by annexing two ciphers. Divide the new dividend by the new divisor. (6) Multiply the divisor by 10 by canceling the decimal point. Multiply the divi- (ft) } dend by 10 by shifting the decimal point one place to the left, cancel- ing the original one. (a) To show the change in the dividend, place a decimal point after 5. Cancel it when annexing the ciphers. NUMBERS AND PROCESSES 301 2. Find quotients: a 1.5)2.97 b .16)18 c .08)322 d .007). 1001 e .4)2.762 / .09)538.2 g 1.1)16.016 h .12)836.1 SIGHT EXERCISES When the decimal divisor is an aliquot part of 1, that is, when it equals & %, %, X 6 , change it to the equivalent fraction. 1. Give answers: a 3.1 + .5 b 62 + .25 c .81 4- .125 d 2.2 4- .0625 2. Divide: a 3.2 -i- .4 b 21 -=- .375 c 3.5 -v- .625 d .21 ~ .875 WRITTEN EXERCISES Change each of the following divisors to a whole number by multiplying it by 2, 4, or 8. 1. Find quotients. Write answers from the book: a 63.4 -h .25 b 216 -s- 2.5 c 9.03 -=- 1.25 (2 876 -^ .125 2. Divide: a 63.5 - .375 6 495 - .625 c 8.03 - .875 d 8.03 ^- 6.25 e 4.96 -v- 12.5 / 333 - 3.75 g 4.05 -r- 62.5 h 119 4- 875 DIVIDING BY 99 A computer would not use long division in dividing by 99 or 999. PREPARATORY EXERCISES 1. Give quotients and remainders: a 99)100 b 99)200 c 99)300 d 99)500 e 99)800 302 WALSH'S BUSINESS ARITHMETIC How does each quotient compare with each re- mainder? 2. In dividing (a) 103, (6) 305, (c) 509, (d) 713, (e) 937, by 99 how much more than 3 is the remainder in (a)? Than 5 is the remainder in (&)? Than 9 is the remainder in (c)? Than 13 is the remainder in (d) ? Than 37 is the remainder in (e) ? 3. In dividing 12 hundred by 99, what is (a) the quotient? (6) The remainder? 4. In dividing 24 hundred 72 (2472) by 99, (a) What is the quotient? (6) How much more than 72 is the remainder? (c) \Vhat is the remainder? To divide a three- or a four-place number by 99, cut off the two right-hand figures (tens and ones). The remaining figures give the quotient; to obtain the remainder add the quotient figures to those cut off. SIGHT EXERCISES 1. (a) At 99 cents each, now many baseballs can be bought for $12.75, and how much will remain? (6) Divide 2445 by 99. METHOD (a) 1275ff -f- 99^ = 12 (baseballs); remainder 87 (lit + 750 (6) 2445 + 99 = 24; remainder 69 (24 + 45) 2. Divide by 99. Give quotients and remainders: a 1841 6 2306 c 3560 d 4324 e 5009 / 6213 NUMBERS AND PROCESSES 303 3. Divide by 99 (a) 8514; (b) 7230. In (a) the quotient, according to the foregoing rule, is 85 and the remainder is 99; the correct quotient is, therefore, 86. In (b) the remainder 102 indicates that the number 72 should be increased by 1, making the quotient 73; the remainder is 3 (102-99). 4. Divide by 99. Give quotients and remainders: a 2080 b 3090 c 4060 d 2182 e 3180 / 4260 These examples are given to show pupils that such a divisor as 99, which seems a difficult one to them, is really a very simple one to computers; 999 is a still easier divisor. A similar method is used in dividing by 98 and 998; also by 89, 79, 69, etc. LONG DIVISION SIGHT DRILLS The guesses made by some pupils to obtain the successive quotient figures in a long division example show their need of sight drills similar to those given below : 1. Find quotients: a 20)140 b 30)270 c 40)160 d 50)250 e 60)420 / 70)210 g 80)480 h 90)360 i 80)560 j 70)490 k 60)360 I 50)450 304 WALSH'S BUSINESS ARITHMETIC Obtain the quotient of each of the foregoing by dividing 14 by 2, 27 by 3, etc., rejecting the cipher in each term. In the next set, think of 19, 29, etc., as less than 20, 30, etc. Since 20 is contained 9 times in 180, 19 must be contained 9 times with a remainder. 2. Give quotients, omitting remainders: a 19)140 b 29)270 c 39)160 d 49)250 e 59)420 / 69)210 g 79)480 h 89)360 i 79)560 j 69)490 k 59)360 I 49)450 Since 7 times 20 is 140, 7 times 21 is more than 140; the latter, therefore, will contain 21 only 6 times with a remainder. In giving the quotient, say 6, omitting the remainder. 3. Give quotients. Omit remainders: a 21)140 b 31)270 c 41)160 d 51)250 e 61)420 / 71)210 g 81)480 h 91)360 i 81)560 j 71)490 k 61)360 I 51)450 4. Omit a remainder when there is one: a 210)840 b 430)860 c 310)930 d 510)8570 e 209)840 / 429)860 g 309)930 h 509)3570 i 211)840 j 431)860 k 311)930 I 511)3570 NUMBERS AND PROCESSES 305 m 150)750 n 199)800 o 209)680 p 499)2510 q 149)900 r 202)800 s 129)390 t 391)2420 u 151)600 v 296)900 w 131)390 .T 411)3690 Before a set of long division examples is worked, these should be used as drills, in which successive pupils are asked to announce rapidly the first quotient figure of each. MULTIPLYING AND SUBTRACTING PREPARATORY EXERCISES 345 1. Express - as a mixed number. METHOD First write 7 as the integral part of the quotient ~ _ and 47 as the denominator of the frac- = 7 tion. Obtain the figures of the numer- 47 ator thus: Think 49 (7 times 7) and 6 (writing 6) are 55. Think 28 (7 times 4), 33 (carrying 5) and 1 (writ- ing 1) are 34. Ans. 7% 2. Give quotient as mixed number. Write answers from the book. a iff. b w e e^ d a W h^f- i ^ j 306 WALSH'S BUSINESS ARITHMETIC WRITTEN EXERCISES 1. At 59 tons to the car, how many car loads are there in 43,567 tons, and how many tons are there over? ONE WAY Ans. 738 (C. L.); remainder 25 T. 59 T.)43567 T. 413 226 177 497 472 In long division write the quotient above the dividend. The first partial dividend is 435. Ob- tain 7, the first quotient figure, by dividing 43 by 6 (the divisor being nearly 60). Write 7 above 5, the last figure of the partial dividend. After 738, the quotient, write C. L. (car load) in a parenthesis, followed by the remainder, 25 T. Thousands of European children are taught only the following method in long division. Surely Ameri- can boys and girls should be willing to use it if time can thus be saved. The greater concentration re- quired tends to secure accuracy. 2. Divide 417,739 by 59. NUMBERS AND PROCESSES 307 ABBREVIATED FORM Ans. 7080; remainder 19. This method con- 59)417739 sists in multiplying and 473 subtracting in one 19 operation, omitting the partial products. Having written 7, the first quotient figure, think 63 (7 times 9) and 4 (writing 4) are 67; think 35 (7 times 5), 41 carrying 6. This being the same as the remaining figures of the partial dividend, the remainder is 4. To 4, the remainder, annex 7, the next figure of the dividend, making 47 the next partial dividend. Since 47 does not contain 59, write a cipher in the quotient and bring down 3, the next figure of the dividend, making 473, the next partial dividend. Write 8, the next quotient figure, and think 72 (8 times 9), and 1 (writing 1) are 73; think 40 (8 times 5), 47 (carrying 7). To 1, the remainder, annex 9, making 19 the next partial dividend. Since 19 does not contain 59, write a cipher in the quotient. Be careful to locate properly the first quotient figure, and to write a figure (which may be a cipher) over each of the remaining figures of the dividend. Before making one of the tests specified below, note that the quotient has the required number of figures. 308 WALSH'S BUSINESS ARITHMETIC Test the foregoing result by multiplying 7080 (the quotient) by 59 (the divisor) and adding to the product 19 (the remainder). Or by casting out ll's, multiply 7 (the quotient excess) by 4 (the divisor excess). To this product, add 8 (the remainder excess), which gives 3 as the excess. The dividend excess is 3, which agrees with the other result. SIGHT DRILLS Before taking up the following examples there should be a rapid drill in giving the first quotient figure of each example and the number of figures in the quo- tient. WRITTEN EXERCISES 1. Divide, using either the abbreviated form or the longer one. Test each result: a 4000 -7-41 b 13,582 + 501 c 908,671 + 1023 d 5871 + 61 e 26,154 + 702 / 777,349 - 2056 g 6325 + 71 h 70,000 + 803 i 470,493 + 3142 ; 7320 + 81 k 52,610 + 423 / 839,264 + 4026 m 9065 H- 51 n 46,792 + 315 o 678,579 + 3205 p 5216 + 91 q 63,130 + 269 r 708,000 + 1684 s 9653 + 31 t 83,746 - 137 u 853,568 + 2245 v 6885 + 21 w 94,217 + 621 x 956,308 + 3189 2. At a railroad terminal 794 car loads of freight were received, weighing 63,018 tons. What was the average load per car? Give answer (a) to the nearest hundredth, (b) To the nearest tenth, (c) To the nearest integer. Test each result. NUMBERS AND PROCESSES 309 PROCESS 79.367 (a) 79.37 T. Ans. 794)63018. 7338 (6) 79.4 T. 2920 5380 (c) 79 T. 6160 Test (a) by adding 616 to the product of 7936 and 794. Test (b) by adding 538 to the product of 793 and 794. Test (c) by adding 292 to the product of 79 and 794. In giving the answer to (a) write 7 as the fourth figure of the quotient, since 7, the next figure, is greater than 5. In giving the answer to (b) write 4 as the third quotient figure, since 6, the fourth figure, is greater than 5. In giving the answer to (c) write 79, the next figure being less than 5. 3. Divide. Give each answer to the nearest integer: a 4000 -i- 43 b 23,582 -^ 431 c 129,456 -i- 531 4. Divide. Give answers to the nearest tenth: a 5871 - 51 6 36154 ^ 732 c 248,673 -* 727 5. Divide. Give answers to the nearest hundredth: a 6325 + 81 b 47,000 -*- 723 c 320,000 -5- 337 d 7974 -i-91 e 52,318 - 864 / 562,873 -5- 739 6. (a) How many kilos of 2.2046 pounds each are equivalent to 54.75 pounds? (b) What decimal of a meter, 39.37 inches, is a yard? 310 WALSH'S BUSINESS ARITHMETIC PROCESS Ans. 24.834 (kilos) Multiply the divi- (a) 2/2046.)54 /7500. sor by 10,000 by 10 6580 shifting the decimal 1 83960 point 4 places to the 75920 right. Do the same 97820 with the dividend, 9636 annexing two ci- phers. Carry the result to three decimal places. (b) Write the dividend as 36 inches, to give it the same denomination as the divisor. Give the result to 39/37.)36/00.0 the nea rest thousandth. 7. Give quotients to nearest thousandth: a 38.765 -*- 3.9 b 18,612 - .095 c 844.73 + .77 d 6.5772 -T- .85 e 511.347 - .67 / 105.28 4- 5.9 g 58.6 -5- .049 h 2406 -. .43 i 53.95 ^ .083 8. Divide 292.2331903 by 46.72352, giving the result correct to thousandths. 46.724)292.233 9. Give quotients correct to thousandths: a 18.54875 -*- 3.23852 b 76.824 -:- .74325 c 8.32346 -5- .72149 d 1634.7853 -r- 22.37425 e .093285 + .005873 / 398.647 + 93.0286 g .0065437 + .85436 h 73.0248 + 1.63387 NUMBERS AND PROCESSES 311 MULTIPLYING AND DIVIDING CANCELLATION PREPARATORY EXERCISES 1. (a) At $16 a week of 44 hours, what is the pay of a girl who works 33 hours? (b) What wages does a boy receive for 39 hours' work at the rate of $18 a week of 54 hours? METHOD In (a) multiply the weekly rate, $16, by %, the fraction of the week she works. In (b) multiply the hourly rate, $% by 39, the number of hours she works. 2. (a) What is the value of 321 eggs when they are worth 36 cents a dozen? (b) Of 360 eggs at the rate of 43 cents a dozen? 3. Give the cost (a) of 131 pounds of potatoes at $1.80 a bushel of 60 pounds, (b) Of 120 pounds at $1.70 a bushel. 4. Give answers : a 16 xff e W X 131 . 246 X 72 b |f X39 / 170 X J^ . 123 X 93 c 321 X ff 9 HX60 , 130 X 42 d spf. x 43 h 84 x W 24 X 125 82 82 X 72 J 279 123 X 279 65 65x42 120 120 X 125 24 312 WALSH'S BUSINESS ARITHMETIC WRITTEN EXERCISES 1. Find the cost of a rectangular plot 154 yards long 68 yards wide at the rate of $275 an acre (4840 sq. yd.)- ONE WAY First find the number of square yards by multi- plying 154 by 68, which gives 10472. Divide this by 4840 to ascertain the number of acres (2%$ A.). Multiply $275 by 2%*. A BETTER WAY 154 X 68 X $275 Indicate the area in square 4840 yards by writing 154 X 68. Draw a line and indicate the number of acres by writing 4840 underneath (as a divisor). Indicate that this result is to be used to multiply $275, by writing after it the latter preceded by a multiplication sign. Cancel. In computations involving only multiplication and division, indicate the operations, then shorten the work by cancellation. 2. Find answers: 12 X 7 X 153 85 X 126 X 13 454 X 198 X 72 19 X 49 17 X 91 81 X 63 X 35 3. Find the value of: 484 X .06 X 210 24.5 X 18.7 a ' 360 .238 NUMBERS AND PROCESSES 313 PROCESS .01 a 484 X .06 X 210 In canceling .06 and 36 by 6, 3()() ke careful to write .01 above g the former. b Since the divisor .238 contains 24/5 X 18/70 three decimal places, annex a terminal decimal cipher to one of the numbers above the line, giving a total of three places in the dividend. Cancel all the decimal points. This multiplies the divisor by 1000, and the dividend by 10 and again by 100. 4. Find the value of each of the following: 18.9 X 12 X 49 1.89 X 12 X 4.9 18.9 X .12 X .49 6.3 X 21 2.1 X .63 .63 X .21 DIVISION OF FRACTIONS PREPARATORY EXERCISES 1. How many times is 2 thirds contained in 3 thirds? Give answer (a) as a mixed number, (6) as an improper fraction. 2. Divide 1 by %, giving quotient as an improper fraction. 3. If % goes /2 times into 1, how many times does it go (a) into 5 times 1? (b) Into 7 times 1? (c) Into 9 times 1? 314 WALSH'S BUSINESS ARITHMETIC 4. Give quotients: a 3 halves)^ halves b %)% c %)1 d 1)01. e l+% f \^% 9 l+% hl+% The quotient of 1 divided by a number is called the reciprocal of a number. 5. Give the reciprocal of the following: a 1% b 2 c % d% e 5/ 5 / 2% To get the reciprocal of a common fraction invert its terms. WRITTEN EXERCISES 1. Find the average yield per acre (a) when 27 acres yield 496% bushels, (b) When 28% acres yield 693 bushels, (c) When 36% acres yield 790% bushels. (a) (D 496% * 27 = PROCESS (II) (HI) Cancel /s 8 1 8 27 (b) 693 -=- 28% = 693 231 T~ ~8~ 693 8 i Ssi Cancel 6321 147 6321 4 (c) 790% -r- 36% = -5- = JT- X Cancel (I) shows each example in the original form; (II) shows the divisor and the dividends written as fractions; (III) substitutes for each divisor its reciprocal and changes the sign of division to that of multiplication. TEST Multiply the result by the divisor. NUMBERS AND PROCESSES 315 2. Find quotients. Estimate the integral part of each result before beginning work: a 436 -r- 18% d 973 -=- 34% g 678 -r- 42% j 279 -5- 13% m 777 -^ 29% b 330% -:- 23 e 924% -r- 19 /i 788% - 57 A; 425% + 16 n 806% - 30 c 907% - 24% / 787% 6 - 42% i 870% - 36% / 665% - 16% o 231% - 10% p 357 -*- 14% g 528% - 21 r 404% - 13% s 825 -;- 31% / 291% + 18 u 545%. -s- 21% v 564 -s- 15% w 607% -s- 22 a; 374% -r 18% , 8% X 6% X 4% X 1% 3. Find the value of - 5% X 3% X 5% X 2% METHOD 2 % X 3 % X % X % X % 6 X K 5 X & X % Change the mixed numbers in the compound dividend to improper fractions. Then write as multipliers the reciprocals of the fractions in the divisor. Cancel. 4. Find the value of: 6% X 5% , 3% X 16% 60% X 3% 27 X 3% 2% X % 14% X % 5. At $% a yard, how many yards of dress goods can be bought for $127%? NOTE: In dividing by %, %, %, %, etc., business men frequently use the reciprocals in their mixed number forms, viz., 1& 1%, 1%, 1#, etc., instead of the respective improper fractions: %, %, %, %, etc. 316 WALSH'S BUSINESS ARITHMETIC 6. Divide 127% (a) by %, (b) by (c) by %. METHOD (a) 127% (-%) X IX (6) 127% (-s-jflx IK Add%42% AddK _ 170 Ans. 159% Ans. (c) 127% (*50X 1% AddK 25% 153 Inclose each divisor in a parenthesis and write its reciprocal as a multiplier. Multiply 127% by 1% in (a), by IK in (6), by 1% in (c), by adding to it %, X, K, respectively, of itself. Test the result in (a) by multiplying 42% by 4; in (6) by multiplying 31% by 5; in (c) by multiplying 25% by 6. 7. Find quotients: a 1356% 4- % b 6876% - % c 7594% - % d 2796% -s- X 7641% -=- % / 6463% -^ % 3475% +% h 8438% -:- % i 5929% -=- % j 4004 & 4- % & 9567% ^- % / 4613% -j- % m 5256% - % n 8360% + X o 3722% - % p 6234% +% q 7642% + X r 2363% - % s 7042% ^ % < 6907% -s- X u 1276% ^- Xo t; 8629% -5- % w 5005% + X 2563% -s- % 8. At $1% a bushel, how many bushels of potatoes can be bought for $127%? 9. Divide 127% (a) by 1%, (b) by IX, (c) by 1%. Test each result. NUMBERS AND PROCESSES 317 METHOD (a) 127X 2 (+ 1)0 X % Deduct X 85 Ans. (6) I27y 2 (-5- DO x % Deduct X 31 95% Ans. (c) 127% (* IK) X % Deduct X 21X 106% Ans. Inclose each divisor in a parenthesis and write its reciprocal as a multiplier. Multiply 127M by % in (a), by % in (6) and by % in (c), by deducting from it %, % and X, respectively, of itself. Test the result in (a) by multiplying 42% by 2; in (6) by multiplying 31% by 3; in (c) by multiply- ing 21% by 5. 10. Find quotients: a 1353% -s- 1% b 5005K -s- 1% c 7164%) * IX d 2496% 4- IK c 5005M -s- W / 8363% * 1% g 3075% -s- IK h 6328% ^ 1^ i 9009% *- iMo j 4238){ H- IX A; 7593% - Itf / 8657^ 4- IX SECTION IV PRODUCTION AND CONSUMPTION CHAPTER ONE PROBLEMS OF THE CONSUMER HOUSEHOLD EXPENSES The calling followed by the largest number of per- sons is that of home keeping. Success in this line, as in any other, requires the employment of business methods. Efficient management is just as important in spending the income as it is in earning it. FAMILY BUDGETS The following table shows the average outlay of a large number of families in various sections of the United States for food, for shelter, and for clothing, arranged by classes having incomes as specified. Expenditures for Remainder for Yearly operating ex- Income Food Shelter Clothing penses, savings, etc. $(500 $258 $114 $78 (a) 900 378 162 126 (6) 1200 444 204 180 W 1500 510 255 * 270 (d) 318 PRODUCTION AND CONSUMPTION 319 WRITTEN EXERCISES 1. Write from the book the sum represented by (a), by (6), by (c) and by (d), respectively, in the foregoing table. 2. Make out a table similar in form to the fore- going, but changing the money to per cents in the last four columns. 3. Before the war the following was Mrs. Kirby's estimate of the minimum food requirements of Mr. Kirby and herself, and their three children. Meats, etc. 5 Ib. beef l / 2 " " (stew) % " pork Y 2 " ham 1 " chicken 1% " fish " 36^ " 18^ " 12f5 Milk, Eggs, etc. 1 Ib. butter / 2 4< cheese " 20^ 2 doz. eggs " 32^ 16 qt. milk " 6^ Cereals, etc. 21 loaves bread @ 5ff 1 doz. rolls " 10^ 2 Ib. cake " 10 % " rice " 8^ 2 " flour " Z% " oatmeal " Sugar, Tea, etc. 1 Ib. coffee @ 2 " sugar " % pt. sirup " % Ib. tea " % pk. potatoes Turnips or carrots 2 Ib. onions Other vegetables Beans and peas Vegetables, etc. @ 64^ 1 can tomatoes 5^ ^ ' corn " 3^ Fruit " 66^ % Ib. prunes " 5ff Pickles, spices, etc. @ 20^ 4. Find the weekly cost (a) of the meats, etc., (6) of the cereals, etc., (c) of the milk, eggs, etc., 320 WALSH'S BUSINESS ARITHMETIC (d) of the sugar, tea, etc., (e) of the vegetables, etc. (/) Find the total weekly cost, (g) Find the cost for 52^ weeks. 5. How much did the yearly cost exceed 42% of Mr. Kirby's pay for 300 working days at $3 a day? 6. The following was the estimated cost of clothing. Mrs. Kirby's hats and coats, and Mr. Kirby's over- coat were supposed to last two years, one half the given price being allowed for one year. The prices were taken from a schedule issued before the war. Mother's Clothing Father's Clothing 2 hats 00 @ $3. 1 cap @ $0.25 1 coat (J0 8. 1 hat " .75 Isuit 8. 1 suit " 10. 3 waists .66% 1 overcoat 00 " 10 2 dresses 1.25 1 pr. trousers " 2. 2 petticoats .50 3 shirts * 1.50 3 aprons .15 2 shirts i 1 6 handkerchiefs .07/2 6 collars ' .10 6 prs. stockings .10 2 pr. overalls * .75 2 pr. shoes 2. 4 ties * .12)* Repairing shoes 1. 4 handkerchiefs * .05 3 suits underwear * .20 6 pr. socks * .10 P M 4 .70 Gloves and mittens * .50 Linen 6. 2 pr. shoes i 2. Rubbers .50 Repairing i 1.50 Sundries * 3. 2 suits underwear .50 o " " " .75 7. Find the annual cost of (a) the mother's clothing. (6) That of the father. (c) Find the total cost of the family clothing, in- cluding $23.35 for that of the girl and $16.30 for each of the two boys. PRODUCTION AND CONSUMPTION 321 (d) How much more did the clothing cost than 14% of $900? (e) What should have been the an- nual income, in order that 14% of it would purchase the specified clothing at the prices given? 8. The following are estimates of the other expenses for a year: Rent $156. Recreation Car fare 31.20 Church dues 10. Fuel and light 52. Utensils 15. Furniture 52. Spending money Insurance 52. (father) 5. Reading matter 5. Sundries 5. a What is the total of the foregoing items? b What was the total amount of the year's expen- ditures including those for food and clothing? 9. If Mr. Kirby's earnings of $900 were supple- mented by a year's interest at 4 % on $1000 he has in the savings bank, how much of his income should remain at the end of the year? Finding that a house in the suburbs with a piece of ground could be bought for a cash payment of $600 and monthly instalments of $15 each until the re- mainder, $1200, was paid, with interest at 6%, Mr. Kirby bought it, taking possession February 1. 10. Make out a statement of the first year's pay- ments, showing (a) the principal at the beginning of each month; (b) the interest for the month; (c) the amount due, including interest, etc.; (d) the payment made; (e) the balance remaining. (/) How much did his payments for the year exceed the total of the interest ? WALSH'S BUSINESS ARITHMETIC Date Principal Interest to date Amount at date Payment Bal. Mar. 1 $1200. $6. $1206. $15 $1191. Apr. 1 May 1 1191. 1181.96 5.96 5.91 1196.96 1187.87 15 etc. 1181.96 etc. etc. etc. etc. etc. etc. etc. NOTE: Use no side calculations. The monthly interest is %% of the principal. Do not give fractions of a cent in stating the interest; write $5.96 for $5.95& $5.91 for $5.9098, etc. 11. (a) How much did his interest payments amount to for the first year? For purposes of taxation, his property was assessed at $1400, on which he paid a tax of %%. (b) What were his taxes for the year? He insured his house for $1500 at 44 cents per $100 for three years. (c) What was the cost of the three years' insurance? He made most of his repairs himself with the help of his boys, paying $15 for material, and only $7 for outside help, (d) How much did he pay for interest, taxes, one year's insurance, and repairs? (e) How much less did these amount to than the yearly rent of his former residence? (/) What per cent of $1800, the cost of the house, was its assessed value of $1400 ? (g) For what per cent of its cost was it insured? 12. How much did he reduce his mortgage of $1200 by the end of the year? As soon as they were settled in the new house, Mr. Kirby with the help of the boys fenced off a portion of the land for chickens, and bought materials for a henhouse as follows: PRODUCTION AND CONSUMPTION 323 a 226 bd. ft. scantling b 850 " "lumber c 622 " "boards d 2 pr. hinges e 150 sq. ft. roofing paper / 5 Ib. nails g 56 sq. ft. poultry wire 13. Find the cost of each of the, foregoing items at $32 per M (1000 board feet) for the scantling, $30 per M for the lumber, $36 per M for the boards, 50 per pair for the hinges, 2K^ per square foot for the roofing paper, 6^ per pound for the nails, and \%i per square foot for the wire. 14. He bought 23 hens from a neighbor at 75 cents each, (a) Find the cost of the hens. The fol- lowing is the egg-production of a year, with the aver- age price prevailing during the month: Month Eggs Laid Value per doz. Month Eggs laid Value per doz. Feb. Mar. Apr. May Jun. Jul. 330 461 393 358 357 344 40^ 36 32 30 32 33 Aug. Sep. Oct. Nov. Dec. Jan. 334 129 99 104 153 254 34 36 40 42 44 42 (6) Find the number of eggs laid during the year, (c) their value, (d) the average value per dozen. 15. During the year the garden patch yielded the following : 324 WALSH'S BUSINESS ARITHMETIC 15 quarts of string beans 2 bushels of turnips 2K "lima 12 "tomatoes 2K " navy 100 heads " cabbage 3 bushels of beets 20 bunches " carrots 2 "onions 150 "radishes 3 ' peas 10 dozen cucumbers IK " " spinach Find the value of the foregoing at the prices pre- vailing in the vicinity of the school. 16. Mr. Kirby's payments for food were reduced $2.80 a week, owing to the home production of eggs and vegetables, the daily surplus being preserved for winter consumption. Find the saving of 52% weeks. "BALANCED" MEALS A day's meals should supply, in proper quantities, protein, carbohydrates, fats, mineral matter, water. Protein supplies the tissue building materials, to- gether with some of the heat and energy. It is chiefly obtained from the whites of eggs, lean meat, skimmed milk, gluten of wheat, etc. The best known of the carbohydrates are the sugar and the starch of foods. These yield energy in the form of heat and the power to do work. Fat is obtained from cereals, eggs, nuts, cream, etc. It yields a larger amount of energy according to its weight than does either of the other two groups. Mineral matter comes from green vegetables, fruits, cereals, and milk. PRODUCTION AND CONSUMPTION 325 The day's meals of a mechanic should provide about 4 ounces of protein and 3500 calories of energy. The following are the meals of a man doing clerical work: Kind of Food Weight Cost Protein Energy Breakfast Cereal Hominy 2 oz. %> .166oz. 206 calories Meat Sausage cakes 3 3% .390 " 398 Bread f Toast, 3 1 .273 " 210 Butter \ % cu. in. X IX 112 Beverage | g g ^ e X ft 57 Fruit Prunes 2 1 .042 " 175 Total for meal (a) (6) (c) GO Dinner Meat Beef stew 8 oz. 3%^ .449 oz. 330 calories Vegetable Rice 2 " 1M .160 " 324 " Green Spinach 2 " IK .042 " 32 Dessert ( Cherry roll 5K " 2% .217 " 353 \ Sauce \% " 1% 225 Bread ( 2 slices 2 " % .182 " 140 Butter \ % cu. in. X " IX 112 Total for meal W (/) (9} (h) Supper Animal food Cottage cheese 5 oz. 1%^ 1.145oz. 160 calories Vegetable Potato cakes 4 " 1 .088 " 96 " Bread f 3 slices 3 " 1 .273 " 210 " Butter \ % cu. in. % " 1% 140 " Beverage Cocoa 5% " 1% .216 " 193 Total for meal (0 0') (*) (0 Total for day () (n) (o) w WRITTEN EXERCISES 1. Find the weight of the food for each meal, (a), (e), and (i); the total for the day (m); the cost for 326 WALSH'S BUSINESS ARITHMETIC each meal (6), (/), and (j); the total cost for the day (n); the quantity of protein for each meal, (c), (g), and (fc); the total for the day (o); the amount of energy supplied by each meal, (d), (h), and (/); the total for the day (p). The following table gives the most important items of one type of a United States soldier's service ration for a day : Protein Calories per Ib. Protein Calories per item Bacon 16 oz. 15% 2080 (a) 0) Flour 18 11.5% 1680 (6) & Beans 2.4 ' 22.5% 1600 (c) to Potatoes 20 1.8% 320 (d) m) Prunes 1.28 ' 2.1% 1440 (0) () Sugar 3.2 ' 1868 (/) (o) Milk .5 " 9#% 784 (f) to Lard .64 " 4320 (h) (?) Butter .5 " 1% 3608 (*) w Totals w CO 2. From the foregoing, find the quantity of protein in each item, (a) to (i); the number of calories in each, (j) to (r); the total amount of protein, (s); and the total number of calories, (/). 3. How many times 4 ounces is (s)? 4. How many times 3500 calories is (<)? 6. Find the number of pounds of each of the follow- ing required for a detachment of 6000 men: (a) Bacon (6) Flour (c) Beans (d) Potatoes (e) Prunes (/) Sugar (g) Milk (h) Lard (i) Butter PRODUCTION AND CONSUMPTION 327 6. Find the total quantity of food required a day for the same detachment, including the following: Coffee 420 Ib. Pepper 60 Ib. Vinegar 120 " Cinnamon 21 " Sirup 120 " Lemon Extract 21 " 7. Find the daily quantity allowed to each man. A SAMPLE UNITED STATES MENU The cost to the Government of the standard ration is now 38Kj a day. For the various specified items, the use of other articles is authorized when the latter supply the proper nourishment, and the cost of the ration does not exceed the Government allowance. The following table gives the cost of a day's meal to 1700 men at a training camp: BREAKFAST Cereal Milk Toast $19.60 Meat Ham Omelet 55.60 Vegetable Fried Potatoes 20.00 Bread Rolls and Butter 25.00 Beverage Coffee and Milk 36.00 Total (a) DINNER Soup Beans $24.60 Meat Fried Liver 80.00 Vegetable Baked Potatoes 36.00 Fried Onions 22.80 Bread Bread 16.00 Dessert Coffee Cake 30.00 Beverage Lemonade 33.00 Total ~W~ 328 WALSH'S BUSINESS ARITHMETIC Meat Vegetable Bread Dessert Beverage SUPPER Beef Roll $32.00 Sweet Potatoes 21.00 Bread and Butter 17.00 Cake 30.00 Lemon Sauce 12.65 Coffee with Milk 20.00 Total (c) WRITTEN EXERCISES Find the cost of each meal, (a), (6), and (c). Find (d) the total cost for the day. Find (e) the daily cost per soldier. Find (f) the difference for 1700 soldiers between (d) and the Govern- ment allowance of a day. SOLDIERS AT MESS EFFICIENCY IN HOME KEEPING No matter how small the sum available for food, the efficient manager supplies the necessary nourish- ment. She purchases cheaper cuts of meat, and makes them just as palatable as the higher-priced ones. By carefully watching the market she is able to give her table the needed variety. She is careful to require the butcher to give her all PRODUCTION AND CONSUMPTION 329 the fat and the bone that have been weighed and charged for. The water in which vegetables have been boiled, and which contains important mineral con- stituents, she uses in making soup. No 'stale bread is wasted, being made into tasty desserts. THE NUMBERS ON THIS PICTURE LOCATE VARIOUS CUTS OF BEEF High Cost of Meat The most expensive item in food is frequently the meat, even when care is taken in its purchase. The following shows the weight of the various cuts, and the retail price per pound: 1. Porterhouse 2. Sirloin 3. Round 4. Top Sirloin 5. Rib Roast 54 Ib. 32^ 45 " " 30" 37K " " 28" 24 " " 26" 40 " " 24" 330 WALSH'S BUSINESS ARITHMETIC 6. Rump 21 " " 24" 7. Cross Rib 12^ " " 24" 8. Flank 4} " " 20" 9. Chuck 52^ " " 20" 10. Blade 15 " " 20" 11. Shoulder 12 " " 19" 12. Neck 12 " " 18" 13. Brisket 20 " " 15" 14. Plate 72 " " 15" 15. Navel 48 " " 15" 16. Shin 30 " " 12 " WRITTEN EXERCISES 1. Find (a) the total weight of the foregoing cuts; (6) the amount paid; (c) the average price a pound. (d) How many pounds are sold above the average price? (e) How many below? 2. What is the total amount obtained by the butcher if he receives 6 cents a pound for 25 pounds of suet, 3 cents a pound for 25 pounds of scraps, and % cent a pound for 40 pounds of bones? 3. What is the average price a pound received for the entire carcass, including suet, scraps, and bone? 4. What per cent of the live weight of 1000 pounds is the weight of the carcass? 6. (a) What did the butcher pay for the meat at $7.50 per 100 pounds? (6) How much more did he receive for it? 6. How many live cattle weighing 1000 pounds each will be required to supply a day's rations for PRODUCTION AND CONSUMPTION 331 6000 men at 1% pounds per man if the dressed weight of the cattle is 60 % of the live weight? 7. Complete the following table, which shows the daily food of 528 students in a Government school, at contract prices before the war: Article Total Food Oz. per pupil Price per Ib. Total Cost Bread 891 Ib. 5 Beef 379% " 8^ Oatmeal 33 " 40 Potatoes 247% " 2jf Sugar 10% '" 60 Sirup 5% " 80 Corhstarch 11 " So Corn Bread i c ) i H Butter 16% " 30^f Flour 88 " 4%^ Milk 181% " 3 Coffee 5% " 16^ Tea 1/J52 " 32^ Onions 11 " 4^ Raisins 11 " V Tomatoes 5% " ji Total (a) (6) ( c ) 8. Find (a) the total weight of the daily rations for 528 pupils; (b) the number of ounces to a pupil's daily ration; (c) the total cost of 528 rations; (d) the cost for each pupil each day. ORAL PROBLEMS 1. How many cents a day is the cost of a wife's food if it is .8 of the cost of her husband's food, which is 30 cents? 332 WALSH'S BUSINESS ARITHMETIC 2. How many times the cost of the father's food is that of the family consisting of the parents and their three children, if the mother's food is .8 of that of the father, and the food of the children is .7, .6, and .5, respectively, that of the father? 3. Multiply 30 cents by 3.6. 4. When three ounces of sausage cake cost 3% cents, what was the cost (a) of an ounce? (b) Of a pound? 5. How much starch is lost by peeling a 4-ounce potato before boiling, if it loses 2.7% when peeled and .2% when boiled with skin? 6. (a) When round roast costs 30 cents a pound, and 4 ounces are lost in the bones and fat not eaten what is the cost an ounce of the cooked meat that is eaten? (b) What per cent is waste? 7. If rib roast beef costs 40 cents a pound un- cooked, and the waste is 50% what is the cost (a) of a pound of cooked meat? (b) Of an ounce? 8. How much is saved on a pound of cooked meat if round roast costing 30 cents a pound uncooked is used instead of rib roast? 9. To a detachment of 6000 men the following items are issued: Tomatoes, 7500 Ib. Dried peaches, 48 Ib. Onions, 1500 Ib. Jam, 75 Ib. Express the weight of each for a man (a) in pounds or decimal of a pound, (b) In ounces or decimal. 10. Give the per cent of waste in a pound of st< ak that contains ten ounces of lean meat. PRODUCTION AND CONSUMPTION 333 RED CROSS ARTICLES WRITTEN EXERCISES 1. Find the value of the materials used by the children of a small school in making the following articles for soldiers' use: a 24 pajamas, each requiring 6 yards outing flannel at 12 cents a yard; 7 buttons at 10 cents a dozen; 1% yards of tape at 4 cents per 4-yard piece. The following were used in making all of the pajamas : iy 2 doz. spools of cotton at 45 cents a dozen; 50 needles at 5 cents a paper of 25; 2000 pins at 10 cents a M; 5 24 operating gowns, each requiring 5 yards twilled muslin at 26 cents a yard; \% yd. tape at 4 cents a 4-yard piece. The following were used in making all of the gowns : 1 doz. spools of cotton at 45 cents a dozen; 50 needles at 5 cents a paper of 25 ; 1000 pins at 10 cents a M. c 20 bed shirts, each requiring 4% yards of twilled muslin at 26 cents a yard; 1% yards of tape at 4 cents a 4-yard piece. The following were used in making all of the shirts: 10 spools of cotton at 45 cents a dozen; 50 needles at 5 cents a paper of 25; 800 pins at 10 cents a M. d 120 operating caps, each requiring % yard of twilled muslin at 26 cents a yard. 334 WALSH'S BUSINESS ARITHMETIC The following were used in making all of the caps : 10 spools of cotton at 45 cents a dozen; 50 needles at 5 cents a paper of 25; 500 pins at 10 cents a M. e 80 operating helmets, each requiring % yard of cheese-cloth at 22 cents a yard; 1 yard of tape at 7 cents a 4-yard piece; Cotton, needles, and pins as in (d). / 80 ice-bag covers, each requiring % yard canton flannel at 20 cents a yard; 2 yards of tape at 4 cents a 4 -yard piece; Cotton, needles, etc. as in (d). g 120 comfort bags, each requiring % yard of cre- tonne at 25 cents a yard; 1% yards of tape at 7 cents a 4-yard piece; Cotton, needles, etc. as in (d). 2. Find the value of the contents (a) of a bag, (6) of 120 bags. 1 spool of cotton, white $0.05 1 " " " khaki .05 1 " " darning cotton .05 1 paper of needles .05 5 darning needles at 5 cents per paper of 25 1 doz. white buttons .05 1 " khaki .05 1 thimble .02 1 pr. scissors .10 1 cake of soap .05 1 paper of pins .05 1 paper of safety pins .05 PRODUCTION AND CONSUMPTION 335 1 comb .15 1 tooth brush .25 1 small mirror .25 6 handkerchiefs @ 25{ a package of 3 1 lead pencil .02 1 writing pad .10 24 envelopes @ 3 a dozen 10 postal cards @ 2^ 1 collapsible drinking cup .10 1 pen knife .50 2 pr. tan shoe laces @ 10^ 3. How many articles were made? 4. Find the total value of the materials, and the contents of the bags, all of which were contributed by friends of the school. THE MILLINERY CLASS 1. Find the cost of the materials used in making a silk-covered hat as follows: % yd. buckram at $3.08 a roll of 16 yd. 3 " brace wire at 12 cents a roll of 30 yd. }s " crinoline at 7 cents a yd. \% " satin at $1.48 a yd. (trimming) For 20 hats there were needed : 4 spools Kerr's thread at 14 cents 40 milliners' needles at $1.125 a M. 2. Find the cost of a straw hat, as follows: 10 yd. brace wire at 12 cents a 30-yd. roll % " cape net at 25 cents 1% pc. straw braid at $1.25 336 WALSH'S BUSINESS ARITHMETIC 3. Find the cost of the materials used in making a spray of three poppies, each flower requiring: % yd. ribbon at 52 cents 3 centers at 72 cents a gross 1% yd. tie wire at 11 cents a 25-yd. spool 1 spray of leaves at 65 cents a dozen. 3 stems at 36 cents a gross (144) ONE FORM OF A HOUSEHOLD ACCOUNT Mrs. Goldstone keeps her accounts in an ordinary blankbook. She gives a double page to each month, and groups the monthly summaries on the thirteenth page, from which she ascertains the receipts and the expenditures for the year. The receipts are chiefly Mr. Goldstone's regular weekly salary of $25, which is supplemented by pay for extra work, and by interest on his savings. Mrs. Goldstone makes her entries at the close of each day. On June 1, she first writes 37.34, the balance remaining at the close of May 31. She then enters her two expenditures, from the total of which she finds that the balance then on hand should be 35.84. Finding that this agrees with the cash, she knows that she has omitted no expenditure. Then she enters 1.50 in the "Total" column, and 35.84 in the last one. In making her entries at the close of June 7, she writes 28.00 in the second column, as the day's cash receipts, placing 9.38, the previous day's balance, in the first column. PRODUCTION AND CONSUMPTION 337 In the monthly "Summary," she inserts the total of each column except the first, the third, and the last. In the first, she writes the balance on hand at the close of May. In the third she writes the sum of this balance and the total receipts of the month. In the last column she writes the difference between the summary of the third column and that of the next column to the last, which gives the total expenditures of the month. On succeeding pages is shown the June page of Mrs. Goldstone's account. WRITTEN EXERCISES 1. (a) Find the total of each day's expenditures, and the balance at the close of each day. (6) Find the monthly summary of each item of expenditure, and of the total expenditure, (c) Write the summary for June; underneath it, write the May summary, as given below; on the following lines insert the in- crease or the decrease with respect to each item. (d) Determine the balance on hand at the close of April 30, from the data given in the May summary. 2. Mr. Goldstone's income for the year was $1440. (a) What per cent of this sum was spent during the year for rent at the monthly rate of $18? (6) What per cent of the June income was spent for food during that month? (c) What per cent was spent for food during the year if the monthly average was $43.20? 3. The cost of the family's clothing for the year was $352. What per cent of Mr. Goldstone's income was expended for this purpose? 338 WALSH'S BUSINESS ARITHMETIC JUNE, 1919 C-21 On Hand Expenditures Day Balance Receipts Total Food Rent Clothing Fuel Light 1 37.34 2 35.84 3.14 18. 3 .20 4 4.30 5 6 .15 7 9.38 28. 37.38 9.80 8 9 2.60 7.25 10 .65 11 5.70 .63 12 13 14 25. 8.74 15 1.10 16 17 1.15 18 8. 19 20 21 29.40 9.20 22 23 .12 24 25 26 .27 27 28 25. 7.65 29 30 .59 Summary 113.10 150.44 Last month 37.34 136.10 48.15 18. 16.30 2.10 1.30 Increase Decrease PRODUCTION AND CONSUMPTION 339 Balance Insur- ance Ch'rch Ice Read- ing Uten- sils Recre'- tion Health Sun- dries Bank Dues Total .35 1.15 1.50 35.84 .35 .15 21.64 14.20 .20 .17 .35 9.38 9.80 27.58 .40 2. .35 .15 .25 1. 1.63 .40 5. .30 .35 .15 $8.40 40 .30 .42 .35 .15 .25 .24 5. .10 .40 .23 2.10 1.50 .95 1.01 3.15 3.80 3.10 15. 1. 37.34 340 WALSH'S BUSINESS ARITHMETIC THE HOUSEHOLD INVENTORY The following excerpt is taken from the Standard Fire Insurance Policy, used in some states: A FIRE SCENE If fi re occur, the insured shall forthwith separate the damaged and undamaged personal property . . . make a complete inventory of the same, stating the quantity and the cost of each article and the amount claimed thereon. . . . In order to be able to comply with this requirement in the event of a fire in his home, Mr. Helm has listed in a blankbook an inventory of the personal property contained in his residence. This book Mr. Helm keeps with his policy in his office downtown in order PRODUCTION AND CONSUMPTION 341 that they escape destruction in a fire that may destroy his property. A page is given to each room and one to the reca- pitulation. Other pages contain itemized lists of the "Books," "Pictures," "Cut Glass," etc. A page of "Pictures," for instance, would give the title and value of each of the eleven (11) totaled in the parlor page as worth $174, together with the number and the value of all of the others in the house, specifying the room in which each is hung. The inventory gives the cost of each item with the date of purchase. From the latter may be determined the sum that should be deducted for depreciation. The following is a list of articles contained in the parlor when the inventory was made. As articles are added or removed, changes are noted. PARLOR Number Article Date of Purchase Cost Remarks 1 Carpet XI-16-1908 $40. 7 Chairs 82. 1 Clock XII-23-1910 20. Gift 4 Curtains X-15-1909 12. 3 Electric Fixtures XI-16-1908 25. 1 Jardiniere 5. Gift 1 Lamp 12. Electric 1 Mirror 25. 1 Music Cabinet 15. 1 Piano and Cover 375. 1 Piano Stool 5. 84 Piano Music Var ous 37.50 See List 11 Pictures 175. < 1 Portiere IX-15-1911 10. 1 Rug 12. 4 Shades XI-16-1908 4. 2 Sofas " 40. 1 Statue XII-23-1915 12. Gift 2 Tables XI-16-1908 10.- 342 WALSH'S BUSINESS ARITHMETIC WRITTEN EXERCISES 1. Find the original value of the contents of the parlor. 2. The following shows the last page. Include the value of the contents of the parlor, and ascertain the original value of all the furniture. RECAPITULATION Halls $127 Servants' Room $48 Parlor Bath Room 25 Dining Room 647.50 Laundry 39.50 Living Room 765. Attic 168. Kitchen and Pantry 129. Linen Closet 94.50 Bedroom 1 347.50 Chests, etc. 47.80 2 263.25 Miscellaneous 123. 3 189.50 Total $ 3. Mr. Helm insures the foregoing articles for $3000, at the rate of 55 cents a $100, for three years. What is the cost of the insurance? 4. In the event of the total destruction of all of the articles by fire, what sum should he receive from the insurance company if it deducts for depreciation 25 % of the original value of the articles? CHAPTER TWO PROBLEMS OF THE PRODUCER FARMING AS A BUSINESS Everybody, whatever his calling, is interested in the success of the 6% millions of farmers, upon whom devolves the part of feeding and clothing, not only themselves and the remain- ing 70% of our population, but also many mil- lions in other parts of the globe. The world's welfare depends upon a maxi- A FARM HOUSE mum produc- tion, at reasonable cost, with prices that yield the farmer interest on his capital and a fair compensa- tion for his time, muscle, and brains. FARM ACCOUNTS While the farmer's accounts must necessarily be few in number and easily kept, they should show him 343 344 WALSH'S BUSINESS ARITHMETIC the expense of production and the profit or the loss made by the sale of his products, giving as much detail as possible. THE INVENTORY Many farmers limit their accounts to the making of an annual inventory, each of which they compare with the preceding one to ascertain what may be the profit or loss for a year. The following are two annual inventories. INVENTORY OF BURGUNDY FARM Jan. 1, 1919 Jan. 1, 1920 T . items Quantity Value Quantity Value Real Estate 400 A. $38,000. 400 A. $40,000. Cows, etc. 59 3,750. 6 3,573. Hop 27 346. 37 396. Donea 7 1,200. 9 1,850. Sheep 87 624. 100 875. Hens 167 107. 132 83.50 Machinery, etc. 1,500. 1.350. Corn 80 bu. 120. 125 bu. 187.50 Oats 200 " 180. 90 " 81. Potatoes 40 " 36. 80 " 80. Hay 15 T. 390. 24 T. 576. Silage 90 " 360. HOT. 440. 1-W.I IK " 45. 8KT. 195. Bills Receivable 46. Cash 670. 2,148. Total (a) () Less Mortgage 8,500. 6,500. (6) (d) Last year (6) Increase for year () PRODUCTION AND CONSUMPTION 345 WRITTEN PROBLEMS 1. (a) Find the value of the land and equipment on Jan. 1, 1919. (b) The net value after the deduction of the mortgage, (c) The gross value Jan. 1, 1920. (d) The net value at this date, (e) The increase in a year. 2. Find the total value of the following items, which have not been included in the farm equipment: Furniture, $2475; automobile, $1800; 2 buggies at $75 each; harness, etc., $95. 3. Find the value of the machinery, as follows: 1 thresher $340 1 manure spreader 1 binder 135 1 wheat drill, hoe 75 1 mower, 5-ft. 35 1 " " , disk 60 1 " 4-ft. 30 2 harrows, disk 50 1 roller 12 2 " , spring tooth 27 1 dray 2 2 " , spike tooth 24 1 hay loader 60 2 plows, 2-horse 12 2 hay racks 20 2 plows, 3-horse 18 1 weeder 12 2 double cultivators 50 2 wagons, 4-horse 120 2 single 14 1 wagon, 2-horse 50 4 double shovel plows 10 1 corn planter, dbl. r. 40 1 smoothing harrow 12 1 " " , single 12 1 weeder 12 1 horse rake, side del. 40 1 horse rake, spring tooth 20 4. If 10% should be charged off for a year's de- preciation, (a) what is the value on Jan. 1, 1920 of machinery worth $1500 on Jan. 1, 1919? (6) What will be its value on Jan. 1, 1921? 5. (a) How much is 5 % of the inventory value of Jan. 1, 1919? (b) How much does the year's increase exceed this sum? 346 WALSH'S BUSINESS ARITHMETIC 6. Besides the profits shown by the inventory, there should be added $32.50 a month for the use of the house, $450 for the vegetables, eggs, etc., sup- plied by the farm, and $35 for wood, etc., used as fuel. How much do these items amount to in a year? RECEIPTS AND EXPENDITURES The following table gives Mr. and expenditures for five years: Appich's receipts Items 1st year 2dyear 3d year 4th year 5th year Receipts Cattle $2084.30 $200. $500.10 $1937.60 $720.80 Sheep, lambs, wool 460. 590.40 550. 550. 750. Wheat 1230. 751. 1557. 1157. 1682.40 Corn 969.50 620. 1000. 750. 906. Oats 60. 75.40 Hay 709. 860. 905. 980. Live hogs 135.60 309.80 200. 475. 756.20 Poultry & dairy pro- ducts 375. 403. 462. 690.10 698.40 Wood 180.25 Apples 506. 1427. 512.40 1680.80 Total Receipts (a) (6) (<0 (<*) _w__ Expenditures Labor $400. $450. $500. $700. $700. Taxes 150. 138. 145. 140. 168. Farm Supplies 300. 300. 300. 200. 400. Interest 360. 360. 344. 260. 240. Fertilizer 135. 116.50 147.86 185.39 185.39 Seed 550. 400. 600. 750. 600. Feed 212. 150. 150. 197.50 188. Cattle (for Feeding) 1763. 781.24 Hogs (for Feeding) 36. Extra Labor 900. 418. Total Expenditures (/) (d W (0 (;) Net Income (*) (0 (m) (n) () PRODUCTION AND CONSUMPTION 347 7. Find the receipts for each year, (a) to (e). 8. Find the expenditures, (/) to (j). 9. Find the net income, (k) to (o). MILK PRODUCTION The following table shows the quantity of milk yielded by a herd of 27 cows on the farm of Mr. Pop- kins, who arranges to have the winter production as great as possible: Month Quarts Rate Receipts Month Quarts Rate Receipts Sep. 4,606 yy April 11,226 si Oct. 5,708 3K May 9,342 3 Nov. 5,983 4 Jun. 6,253 3 Dec. 10,510 4 Jul. 4,142 2/4 Jan. 13,008 4 Aug. 4,280 3 Feb. 11,858 4 Sold 1,460 4 Mar. 12,467 4 - Used 2,190 s l A Total (a) (&) 10. Find (a) the number of quarts produced during the year; (6) the receipts, including the value of the milk used in the families of the owner and two hired men. (c) Find the average value a quart, (d) Find the total weight of the milk at 2Xe pounds a quart. (e) Estimate the average number of quarts a cow for the year. SIGHT PROBLEMS 1. A farm worth $40,000 is assessed for purposes of taxation at $24,000. (a) What per cent of the actual value is the assessed value? (b) The taxes for a year are $168; what is the tax rate on each $1000 of the assessed value? 348 WALSH'S BUSINESS ARITHMETIC 2. Give the value of each of the following a bushel or a ton, from these data. 80 bu. worth $120 200 " " 180 40 " 96 90 " 81 80 " " 100 150 " " 180 15 tons worth $390 90 " " 360 W " 45 24 " " 576 110 " " 440 VA " " 195 3. In a year $150 is expended for food for a family of five, and the farm supplies food worth $450. (a) What is the total value of the food? (6) What per cent of the total is supplied by the farm? 4. The fuel consumed in a year is worth A BARN AND SILO Of this there is spent $25 for coal. The re- mainder is supplied by the farm. What per cent of the annual expense does the latter constitute? 5. If an apple tree occupies a space 2 rods by 2 rods, (a) how many square rods does it occupy? (b) How many trees would there be to an acre (160 square rods)? (c) To 30 acres? 6. Give the value of 2400 bushels (a) at $1 a bushel, (b) At % cents a bushel, (c) At 97# cents a bushel. PRODUCTION AND CONSUMPTION 349 7. What would be the cost of 5 bushels of seed at $5% a bushel? 8. What is the value of 40 acres of land at $120 an acre? If it is assessed at 60% of its value, what is the assessed value? 9. Give the interest for a year on $400 at 6 %. COST OF A CROP Some farmers desire to know more about their business than is disclosed by a comparison of inven- tories, or even by a statement of receipts and expen- ditures. They wish to ascertain (a) the cost of producing certain crops, and (6) the profit, if any, of selling them at market prices. WRITTEN EXERCISES The following is a memorandum of expenditures before the war for labor in the production of corn on 40 acres: ! Labor Cost Items Dates Man Hours Horse Hours Man Horse Total Plowing Mar. 25-Apr. 2 80 320 (a) (b) (e) Disking Harrowing Apr. 7-Apr. 29 " 29-May 4 90 25 360 50 (a) (a) 1 w Planting " 30- " 5 30 60 (a) (6) (c Harrowing May 10- " 14 35 70 (a) (b) (c Cultivating " 27- " 30 60 120 (a) (b) (c " Jun. 3-Jun. 6 55 110 (a) (b) (e) " " 14- " 18 50 100 (a) (b) (*) " 23-Jul. 5 60 120 (a) (b) (c) Picking seed Sep. 27-Oct. 7 60 (a) (b) Husking Nov. 2-Nov. 22 300 600 (a) (b) (c) (d) (e) (/) (9} (A) 350 WALSH'S BUSINESS ARITHMETIC 1. Find the cost (a) of the man labor on each item at 20 cents an hour; (b) of the horse labor at 12K cents an hour; (c) of the total expense for labor on each item, (d) Find the total number of man hours; (e) of horse hours. (/) Find the cost of the man labor; (g) of the horse labor; (h) the total labor cost. NOTE: Find (/) by adding the (a) column. Check the result by multi- plying 20 cents by (d). Find (g) by adding the (6) column. Check the result by multiplying 12^ cents by (e). Find (h) by adding the (c) column. Check the result by comparing this total with the sum of (/) and (0). 2. Find (a) the interest at 6% on the value of the land, 40 acres at $120 an acre; (b) the taxes at $7 a $1000 on the assessed value of $2880; (c) the cost of 5% bushels of seed at $5 a bushel; (d) of 8 tons of fertilizer at $16 a ton; (e) the interest at 6% on $400, the value of the machinery used. 3. Make out a statement in the following form showing the receipts, expenditures, and profits from the foregoing crop. FIELD B 40 ACRES CORN Sold 2400 bu. @ 97J# (a) Value of Stalks 29 u Total Receipts Labor costs (c) ft) Fertilizer (d) Seed (e) Interest on Land (Rent) Taxes 1 Interest on Equipment (h) Other Expenses 19 25 Total Expenses (0 Pro fit 0*) (b) Write the total value of the crop. Insert at (c), (d), etc., the several expenditures specified in PRODUCTION AND CONSUMPTION 351 previous examples, and the separate item, $19.25. At (i) write the total expenditures. At (j) write the profit. 4. From the data given in the previous examples, find the cost of production (a) an acre; (b) a bushel. 5. Fill in the missing items in the following account, with an acre of grapes during 3 years: One Year Cleaning land Plants Setting plants Fertilizers Cultivating Total Interest on (a) for 1 yr. at 6 % Carried forward $25. 10. 1. 12. 5. Two Years Forward Stakes Setting stakes Fertilizers Cultivating Total Interest on (d) for 1 yr. at 6 % Total Deduct sales of 5 2 crates $2.50 Balance forward (c) 7.50 3.50 15.50 16. Three Years Forward Cultivating Fertilizers New stakes Crates and pick- ing Total Interest on (i) for 1 yr. at 6 % Total Deduct sales of 75 crates $2.50 Balance (*) 16. 15.50 2. 42.75 (a) (&) (4) to (0 00 (c) (/) (<7) (*) (1) (A) (m) All of the permanent laborers on Mrs. Bruen's farm are men with families. Each is supplied with a house, an acre of ground for a garden, a cow with pasture, and firewood. SIGHT PROBLEMS 1. Frank Kerr receives $200 a year in cash; the use of a house, which he considers as the equivalent of $10 additional monthly wages; with land and cow, from which he derives products worth $70 during the year. What is the value of the foregoing for a year? 352 WALSH'S BUSINESS ARITHMETIC 2. His wages are increased $25, the following year, he is given corn to the value of $25, and he sells $25 worth of vegetables. What is his income the second year, including the use of the house and the value of the other products obtained from the land, cow, etc., which this year were worth $80? ONE AND ONE-HALF ACRES IN TEN HOURS 3. During the next year he receives an additional $25 in cash, and 50 bushels of corn worth $1 a bushel. What is his income for the third year, including the use of the house, and $120 as the value of vegetables, milk, etc., sold and used? 4. During the fourth year he receives, in addition to other items given in the third year, 30 bushels of wheat worth $1.50 a bushel. What is his income for the fourth year? PRODUCTION AND CONSUMPTION 353 5. Find the cost of plowing an acre of land when one man at $2 a day, and 4 horses at $1.25 each a day, plow (a) 2 acres in a day; (6) 3 acres. 6. If it requires 80 hours of a man's work, and 320 hours of a horse's work to plow 40 acres, (a) how many horses are used to the plow? At 10 hours a TWENTY ACRES IN SIXTEEN HOURS day, how many days are required (6) to plow 40 acres? (c) To plow 5 acres? 7. Assuming that a man and a team can do work as follows, find (I) the number of days of labor re- quired to do each of the following for 40 acres; and (II) the cost of each at the rate of $2 a day for a man, and $2.50 for a team: a Plowing, 1% acres a day b Disking, 6% " " " 354 WALSH'S BUSINESS ARITHMETIC c Harrowing, twice, 10 acres a day each time d Rolling, 13% acres a day e Seeding, 10 / Spreading manure, X acre a day g Cultivating three times, 673 acres a day each time h Harvesting, 6% acres a day i Tying and shocking, no horses, 3^ acres per man j Husking, % acre a day, per man, no horses 8. (a) How many men and teams would be required to do the plowing in 5 days? (6) How many men would be required to do the husking in 8 days? WRITTEN PROBLEMS 1. What are the average yearly receipts of James Reed for wages, when he is paid during four years $200, $275, $350 and $385 respectively? 2. (a) Find his average yearly receipts from the sale of vegetables, milk, etc., which, for the four years, are $25, $45, $70, and $95 respectively. 3. Find his average yearly income. 4. His cash expenditures for food average $70 per year, the remainder being supplied by the farm. Mrs. Reed boards the temporary help, the profits on which supply the family clothing. How much is left during the four years for expenses other than rent, food, and clothing? 5. Each of Mrs. Bruen's permanent hands works 2% hours on Sundays caring for the stock, 3% hours on each of six holidays, 5% hours on Saturdays, and 10 PRODUCTION AND CONSUMPTION 355 hours on the other days. How many hours a year does each work? 6. In calculating the labor cost per man-hour, Mrs. Bruen determines the annual expenditures for a man's yearly work from the following data: Wages, supplies, etc., $385; 6% on $50 for use of cow; 6% on $250 for land for vegetables and pasture; 6% on $1000, the cost of the house, as rent; and $2 for insur- ance, etc. Find (a) the labor cost of a man a year. (6) Find the cost per man-hour based on the number of hours of work in example 5. 7. Find the total expense of a horse for a year, covering 6% interest on $275, its cost; feed, 365 days, at 30 cents a day; shoeing, etc., $9. 8. (a) If the horse works 1080 hours in a year, what is the expense an hour? (6) What is the ex- pense an hour if the horse works only 1000 hours a year? 9. Arthur Gravely bought a tractor for $2080. What is the yearly interest at 6 % on its cost? 10. If the life of the tractor is 6% years, what is the average yearly loss by depreciation? 11. Find the total of the yearly interest, depreci- ation, and repairs amounting to $75.20. 12. The tractor is used for 104 days at an average of 12% hours a day. How many hours of work does it furnish a year? 13. What is the expense an hour of work for in- terest, depreciation, and repairs? SECTION V FROM THE PRODUCER TO THE CONSUMER CHAPTER ONE BUYING AND SELLING AGENCIES SIGHT EXERCISES 1. From the following data (a) give the price paid for a barrel of apples by the consumer: Farmer receives $2.50 Cartage to jobber .15 Local buyer's profit .25 Jobber's profit .25 Freight and refrigeration .35 Cartage to retailer .25 Receiver's profit .15 Retailer's profit 1.10 (6) What per cent of the price paid by the consumer is received by the farmer? (c) What is the total of the gross profits of the four dealers? (d) What per cent does each receive of the price paid by the consumer? (e) What per cent of this price goes for freight and refrigeration? (/) What per cent for the two cartage items? 2. When a farmer receives $1.10 per 100 pounds for onions that cost the consumer $2.50, what per cent of this selling price does the farmer receive? 3. A lot of cabbage is subject to the following charges from the farm to the retailer. 856 FROM PRODUCER TO CONSUMER 357 Farmer receives $5 per ton Jobber's profit $3 per ton Freight charges 10 " " Commission 1 " " Refrigerating 5 ." " Cartage 2 " " Barrels and handling 2 " " Wholesaler's profit 2 (( " (a) Give the total of the foregoing. (6) How much a ton does the retailer receive, at the rate of 3 a pound? What per cent of the cost to the customer does the farmer receive? COMMISSION Compensation received by one person for buying or selling goods for another, for collecting money, for selling real estate, etc., is called a commission. The person doing this work is called the agent; the person for whom it is done is called the principal. An agent receiving eggs, butter, vegetables, berries, etc., to be sold for the account of a distant principal is called a commission merchant. A shipment of this kind is called a consignment, the principal being the consignor and the agent the consignee. A CONSIGNMENT OF PRODUCE A. T. Weekes, of Marquette, Kansas, ships to Sulli- van and Conroy, commission merchants, Kansas City, 60 cases of eggs and 150 barrels of potatoes, to be sold for his account. The shipper (consigner) delivers the goods at Mar- quette to the Missouri Pacific R.R. agent, from whom he receives a bill of lading (receipt), which sets forth that the railroad company has received from A. T. 358 WALSH'S BUSINESS ARITHMETIC Weekes the above-mentioned items, to be delivered to Sullivan and Conroy upon surrender of the bill of lading and payment of the amount due for freight. The consignees (Sullivan and Conroy) present the bill of lading, pay the freight bill, and transfer the goods to their store. When all the articles are sold, they send an account of sales to Mr. Weekes with a check for the sum due him. ACCOUNT OF SALES KANSAS CITY Mo., Aug. 25, 1919 SULLIVAN & CONROY Sold for account of A. T. WEEKES, Marquette, Kansas. 60 cases Eggs. 150 bbl. Potatoes. 1919 Aug. 18 40 cases Eggs, 1200 doz. .32 (a) 20 80 bbl. Potatoes 3 . 20 (b) 23 20 cases Eggs, 600 doz. .31 14 24 70 bbl. Potatoes 3.15 (d) () Charges , Aug. 17 Freight and drayage 123 75 25 Commission, 4 % Cf) (*) Net proceeds by check in- closed (A) WRITTEN EXERCISES 1. Copy and complete the foregoing account. Insert the extensions (a) to (c?) and the footing at (e). Find (/), which is 4% of (e). Insert at (g) the total charges. Find (h) by deducting (g) from (e). 2. Make out a check on the First National Bank for the sum due Mr. Weekes. FROM PRODUCER TO CONSUMER 359 3. Find the weight (a) of a case of 30 dozen eggs at 22 ounces per dozen eggs and adding 8% pounds for the weight of the package. (6) Of the shipment of 30 cases. 4. Find the weight of a barrel containing 2% bushels of potatoes at 60 pounds to the bushel, adding 21 pounds as the weight of the barrel. 5. How much less than a minimum car load of 36,000 pounds is there in the total shipment? 6. (a) What is the commission at 2}% for 'collect- ing a debt of $240.75? (6) How much does the agent remit to his principal? 7. Find the commission on the sale of a house for $9750 at 5% on $1000, 2%% on $4000, and 1% on the remainder. 8. How much should a salesman sell in a year to yield him a commission of $5000 at 3%% on his sales? 9. An agent bought for his principal 60,000 feet of lumber at $42 per 1000 ft. How much did the lumber cost the latter after he had paid freight amount- ing to $275 and the agent's commission of 2%%? 10. A commission merchant received a consign- ment of 60 crates of blackberries. He sold 20 crates at $2.40 each, 15 crates at $2.60, and the remainder at $2.50. Find the net proceeds after the deduction of charges amounting to $12.75 and commission at 5%. THE LOCAL BUYER The individual producer generally disposes of his goods in the neighborhood. His surplus eggs he exchanges for groceries at the nearest store. His 360 WALSH'S BUSINESS ARITHMETIC milk he sells to the creamery, his grain to the owner of the elevator at the railroad station, his cotton to the warehouse man, his cattle to a traveling buyer, etc. WRITTEN EXERCISES 1. A farmer delivered 12 loads of wheat to an ele- vator. The gross weights and the tares were as follows : Gross Tare Gross Tare Gross Tare 3150 ' 1061 3216 1070 3168 1069 3210 1062 3420 1072 3056 1073 3095 1064 3175 1073 3384 1067 Find (a) the total gross weight, (b) the total tare, (c) the total net weight, (d) the sum received for the wheat at $2.10 a bushel (60 lb.). 2. How much does a planter receive for 12 bales of cotton, weighing, respectively, 523 lb., 519 lb., 532 lb., 527 lb., 518 lb., 516 lb., 517 lb., 523 lb., 518 lb., 525 lb., 516 lb., 525 lb., when the deduction for tare is 22 pounds a bale, and the rate is 23% cents a pound? 3. A local buyer pays pickers of wild huckleberries 12 cents a quart for picking, and he delivers the berries to a local shipper at an advance of 2 cents a quart. The latter supplies crates holding 32 quart-cups and consigns the berries to a commission merchant. Find the shipper's profit on a crate when the berries bring 20 cents a quart less 10% commission; 50 cents is deducted for expressage, and 30 cents for the cups and the deterioration of the crate. 4. Copy and complete the following statement rendered by the commission merchant: FROM PRODUCER TO CONSUMER 361 WILMINGTON, N. C., Aug. 1, 1919 E. K. WILSON Fruit and Produce Commission Merchants Sold for account of Mr. F. T. O'ROURKE, Hamlet, N. C. 12/32 Hbs. 6/32 " (soft) Express Commisson .20 .18 Check herewith (a) (b) (d) (a) NOTE: (a) 12/32 means 12 crates of 32 quarts each, which bring 20 cents per quart. (6) Six crates of 32 quarts each bring 18 cents per quart, being overripe. Insert at c the total receipts. At (d) insert expressage on 18 crates at 45 cents per crate; at (e) the commission at 10% on the receipts (c); at (/), the total of (d) and (e); at (0) the difference between (c) and (/). Observe the abbreviations used in expressing 12 crates of huckleberries, each containing 32 quarts. 5. Find the weight of a loaded crate, when the crate weighs 8 pounds, each quart-cup 1 ounce, and the berries 1% pounds a quart. SELLING THROUGH A BROKER Tormey and Ryan are local grain buyers, at Fair- view, near Marquette, Kansas. Wishing to sell three car loads of No. 2 wheat in Kansas City, they load it on cars numbered 18790, 24360, and 9411 of the Missouri Pacific Railroad, consigned to their broker, George Smith, notifying the latter by the following telegram: Have shipped 1800 bu. 2 wheat, M. P., 18790, 24360, 29411. Have drawn for $3000. The last sentence notifies the broker that they have made a sight draft on him for $3000, which he is to 362 WALSH'S BUSINESS ARITHMETIC pay to their credit at a bank in Kansas City, and receive the bill of lading. The draft is in this form: $3000 %o Marquette, Kan., July 30, 1919 At sight, pay to the order of Ourselves Three Thousand 00/100 -Dollars value received, and charge to account of To George Smith 1 v r*' ir I lormey & Ryan Kansas City, Mo. J They deposit this draft in The Farmers Bank of Marquette, for collection after indorsing it as follows: Pay to the order of The Farmers Bank for collection only. Tormey & Ryan. This draft they attach to the bill of lading. The Farmers Bank indorses it over to its Kansas City correspondent as follows : Pay to the order of The First National Bank, Kansas City, Mo. for collection only The Farmers Bank, Marquette, Kansas A. T. Sullivan, Cashier. sending it and the attached bill of lading with instructions to deliver the latter to George Smith when he "takes up" the draft. When the draft with the bill of lading reaches The First National Bank, it immediately notifies George FROM PRODUCER TO CONSUMER 363 Smith. The latter pays $3000 to the bank, receiving the draft and the bill of lading. The First National Bank transmits the $3000 less collection charges to The Marquette Bank, which places the proceeds to the credit of Tormey & Ryan. As soon as Mr. Smith had learned by telegraph of the consignment, he offered the wheat to Chas. Scott & Co., who agreed to take it, on arrival, at $2.15, provided it proved, upon inspection, to be of No. 2 grade. When the wheat reached Kansas City on Aug. 5, Chas. Scott & Co. accepted it, giving a check for its value at its arrival weight of 107,160 pounds. George Smith rendered Tormey & Ryan the follow- ing account of sale: KANSAS CITY, No., Aug. 6, 1919 GEORGE SMITH Grain Receiver Sold for account of MESSRS. TORMEY & RYAN Marquette, Kan. 1919 Aug. 5 107,160 # Wheat #2 2.15 Cars M. P. 18790, 24360, 29411 Charges Freight 2^ 36. Interest 4 da. @ 6 % (6) Weighing .40 Inspection . 35 Commission (c) Net proceeds to your credit Draft Balance due you George Smith perK. (a) GO W 3000 (/) 364 WALSH'S BUSINESS ARITHMETIC WRITTEN EXERCISES 1 . (a) How many bushels are there in 107,160 pounds of wheat? (b) Find its value at $2.15 a bushel. 2. George Smith charges a commission of \ a bushel, also interest at 6 % for 4 days on $3000. What is (a) his commission? (b) The interest? 3. At 2 cents a bushel, for freight, what is the rate per 100 pounds? 4. Copy and complete the foregoing statement, from data given above: Observe that (d) is the total of the charges, that (e) is (a) less (d), and that (/) is (e) less $3000. 5. Write George Smith's check on The First Na- tional Bank in settlement of his account with Tormey & Ryan. BUYING THROUGH A BROKER A broker acts as purchasing agent as well as selling agent. George Smith having received an order from Burton & Billings, Milwaukee millers, to buy 6000 bushels of wheat for their account, made an agreement with Robert Black for the delivery of the wheat at $2.17%, in Kansas City on cars "routed" for Mil- waukee. When the cars were loaded, Robert Black received a bill of lading consigning the shipment to Burton & Billings, Milwaukee. This bill he attached to a sight draft for the cost of the wheat, which he de- posited for collection in the Commercial National Bank. FROM PRODUCER TO CONSUMER 365 George Smith notified his principals by telegraph of the purchase, and mailed his bill of $60 for com- mission. In this transaction the broker did not handle the money paid for the wheat. He gave the millers' order to Robert Black, and received his commission from them. Mr. Black collected the value of the wheat from the consignees by means of a draft. WRITTEN EXERCISES 1. Find (a) the cost of 6000 bushels of wheat at $2.17%. (6) The freight at 6 cents per 100 pounds, (c) The total cost in Milwaukee including freight and commission. 2. (a) Make out the sight draft drawn by Robert Black on Burton & Billings, (b) Write the indorse- ments transferring it to The Commercial Bank for collection, and the latter 's indorsement, for collection, to the Wisconsin Trust Co., of Milwaukee. 3. Ryan & Co., brokers of Savannah, bought for a Lowell mill 800 bales of cotton weighing 394,000 pounds at 23J^ delivered to a steamer. Find the cost of the cotton and the commission of $5 per 100 bales. STORAGE Railroad companies require the removal of goods from their cars within, say, 48 hours after arrival at terminus. If such merchandise is not intended for immediate sale, it is stored in a warehouse. Butter, eggs, poultry, etc., are bought by dealers at low rates and placed in cold storage until higher prices enable the dealers to withdraw them for sale at a profit. 366 WALSH'S BUSINESS ARITHMETIC WRITTEN EXERCISES 1. A dealer stored 175 cases of eggs for 5 months at the following rates : For the first 25 cases, 20 cents a month " " next 25 " 18 " " " " third 25 " 16 " " For each additional 25 cases 2 cents less a month than the rate for the previous 25. What was the cost of storage? 2. Find the cost of storing 1875 pounds of poultry for 3 months, at % a pound for the first month and Kj a pound thereafter. 3. (a) Find the cost of storing 40,000 bushels of wheat for 40 days at % a bushel for receiving, weighing, and storing for 10 days; and Y$ a bushel for each succeeding 5 days. (6) Find the cost of screen- ing and blowing it at % a bushel, and delivering it to an ocean vessel at % a bushel. 4. What is the difference in the expense of the stor- age in the last example, and the rate in another ware- house of 1^ a bushel for 20 days and Mo a bushel for each subsequent day? CHAPTER TWO TRANSPORTATION PROBLEMS SIGHT EXERCISES 1. Assuming 1000 pounds, including wagon, as the reasonable load for a mule to draw for 10 hours on a level dirt road, (a) how many pounds can 2 mules draw on a wagon weighing 1000 pounds? (6) 4 mules, on a wagon weighing 1500 pounds? (c) 6 mules, on a wagon weighing 2000 pounds? 2. Find the rate per ton-mile (1 ton for 1 mile) when it costs $1 to transport 1 ton (a) for 4 miles by horse and wagon; (6) for 125 miles by rail; (c) 333K miles by canal; (d) 1500 miles on the Great Lakes. 3. A team that can haul a load of 3000 pounds, including a 1000-pound wagon, on a level dirt road, can haul 5000 pounds on the same road after it is macadamized. What part of the expense of trans- portation is saved by the improvement of the road, assuming that the same wagon is used? 4. Find the cost (a) of 9 pounds of oats at 80 cents a bushel of 32 pounds, (b) Of 12 pounds of oats. (c) Of 14 pounds of hay at $1.25 per 100 pounds. 367 368 WALSH'S BUSINESS ARITHMETIC 6. Find the cost of hauling wheat when the time required to make the round trip was 10 hours, at the cost of 30 cents per man-hour for the driver and 6 cents per mule-hour for each of a pair of mules. 6. When the load consisted of 20 bushels and the distance to the station is 10 miles, give (a) the number of ton -miles; (b) the cost per ton-mile; (c) the cost per bushel. NOTE: In estimating the number of ton-miles ignore the weight of the wagon; also the length of the return trip with the empty wagon. 7. How many pounds does a mule draw on rails when his load consists of 3 cars each weighing 4000 pounds and con taming 3000 pounds of coal? 8. How many tons are there in a canal boat load of 8000 bushels of wheat? 9. How many ton-miles are represented by a canal boat containing 240 tons of freight and going 2 miles an hour for 24 hours? If 4 mules are used, how many ton-miles are obtained a mule? 10. At 2 miles an hour (a) how many hours would it require a mule-drawn boat to travel 288 miles? (b) How many days? ANIMAL TRANSPORTATION WRITTEN EXERCISES 1. An army mule's daily ration is 9 pounds of oats and 14 pounds of hay. (a) Find the daily cost at 80 FROM PRODUCER TO CONSUMER 369 cents a bushel of 32 pounds for oats, and $1.25 per hundred pounds for hay. (b) Find the cost for 365 days, including 100 pounds of straw monthly for bedding at 80 cents per hundred pounds. 2. Find the yearly cost of keeping a horse whose daily ration is 12 pounds of oats and 14 pounds of hay. Use the foregoing prices, and include the cost of bedding as above. 3. A planter's figures show that it cost 44 cents a day for a mule's feed for 210 days, and 12 cents a day for pasture, etc., for 155 days, (a) Find the cost for the mule's keep a year after adding $1 a month for interest, depreciation, etc. (6) Find the cost a mule-hour when it works 2000 hours a year. 4. (a) Find the cost of transporting 20 bushels of wheat to the railroad station when it requires 10 hours to make the round trip at 30 cents an hour for the driver and 12 cents an hour for the team. (6) What is the cost a bushel? (c) If the farm is 10 miles from the station, how many ton-miles are represented by a load of 1200 pounds hauled 10 miles? (d) What is the cost per ton-mile? 5. A mule travels 3 miles an hour for 8 hours a day, drawing 3 car loads of coal from the vein to the shaft and returning with the empty cars. If each loaded car contains 1% tons of coal (a) how many ton-miles are represented by the loads drawn in 4 hours? (b) Give the cost a ton-mile, if the boy driver receives $2 a day and the mule's work is con- sidered to be worth 70 cents a day. 370 WALSH'S BUSINESS ARITHMETIC IMPROVED ROADS 6. Mr. Wilson hauls on an average 64 tons a year a distance of 5% miles, (a) How many ton- miles does this represent? (6) What is his annual saving in the cost of hauling, by the reduction of 18% cents a ton-mile by the improvement of his road? His share of the cost of the improvement was $375. (c) What per cent of this amount is the an- nual saving? 7. The year following the improvement of the roads of Bagnell County 100,000 tons of freight were hauled an average distance of 7% miles at a reduction of 17% cents a ton-mile in the cost of transportation, (a) What was the saving? The improvement of the 120 miles of roads cost $1750 a mile. The value of the property in the county was $18,000,000. (6) What per cent of the value of the property did the improvement cost? (c) What was Mr. Bradford's share of the cost, if his farm of 160 acres was valued at $112.50 an acre? 8. (a) How many square yards are there in the surface of a road a mile (1760 yards) long and 15 feet wide? (b) If a ton of broken stone will cover 3% square yards to the proper depth, how many tons will be required for a mile of road? RAILROAD TRANSPORTATION The freight rates between Missoula and Portland, Oregon, are as follows: FROM PRODUCER TO CONSUMER 371 1st class $1.60 a 100 Ib. Furniture, Dry Goods, etc. 2d . " 1.36 " " " Hardware, Copper, etc. 3d " 1.12 " " " Paint, Plow Points, etc. 4th " .96 " " " Canned Vegetables, etc. 5th " .80 " " " Wrapping Paper, etc. There are four other classes, A, B, C, and D, the rates being 64^, 48^, 40^, and 32 j, respectively. 9. Find the cost a ton-mile at each of the fore- going rates from Missoula to Portland, 634 miles. * 10. Find the freight from Missoula to Portland, for an automobile weighing 2750 pounds, when the rate is double the 1st class one. 11. The freight rates from Denver to Salt Lake City, 745.5 miles, are as follows a 100 pounds: 1st class, $1.54; 2d class, $1.31; 3d class, $1.15; 4th class, $ .96; 5th class, $ .79%. Find the rate a ton-mile for each class. 12. The rate on fruit for less than car loads (L.C.L.) is $1.54 a 100 pounds; for car-load lots (C.L.), it is $1 a 100 pounds. What per cent of the former rate is the latter? 13. How much will a shipper of 18,690 pounds of fruit (and packages) save by paying $1 a 100 pounds for a car load of 24,000 pounds, instead of the L.C.L. rate of $1.54 a 100 pounds on the actual weight of the shipment? COMMODITY RATES In addition to the 100-lb. rate for ordinary freight, there is frequently a "commodity " rate for such articles 372 WALSH'S BUSINESS ARITHMETIC as grain, which pays by the bushel; coal, by the ton; milk, by the 40-quart can, etc. WATER TRANSPORTATION 1. (a) How many tons are there in a Lake steamer load of 400,000 bushels of wheat? (6) How many freight cars containing 36,000 pounds each are needed to transport this quantity of wheat? (c) How many such steamer loads will be required to fill a tow of 48 barges, each having a capacity of 1000 short tons? 2. Find the cost of transferring 400,000 bushels of wheat from canal boats to an ocean steamer as fol- lows: Harbor towing, $4 a boat of 8,000 bushels Transportation of floating elevator, }$ a bushel Weighing and transferring, % a bushel Trimming on canal boat, $1.50 a 1000 bushels Trimming on steamer, $2. a 1000 bushels 3. (a) When the rail freight rate was 16 cents a 100 pounds from Chicago to New York, what was the rate a bushel? (b) How much less a bushel would it cost at 1.2^ a bushel by lake from Chicago to Buffalo, Kj a bushel for transferring from steamer to canal boat; and 5^ a bushel by canal boat from Buffalo to New York? 4. At 9.6 cents for the freight on a bushel of wheat for 960 miles, what is the rate a ton-mile? 5. Find (a) the canal (and river) rate a ton-mile when the cost for transporting a bushel of wheat was .44^ for 440 miles, (b) The ocean rate a ton-mile when the cost was 6 for a bushel 1800 miles. FROM PRODUCER TO CONSUMER 373 6. When the steamboat rate on eggs is 47^ a 100 pounds between Cincinnati and Memphis, find the ton-mile cost, taking (a) the distance by water, 750 miles; (b) the land distance of 500 miles by road. (c) Find the ton-mile rate by rail at 60 cents a 100 pounds for 494 miles. 7. How much more would it cost to ship 5400 dozen eggs in cases containing 30 dozen each than in cases containing 36 dozen each, when the freight is 23 cents a case regardless of its weight? SHIPMENTS BY EXPRESS The minimum freight on a package is the rate per 100 pounds, while express rates cover all weights from a pound up. The Union Express Company, which covers nearly every section of the United States, has nearly 300 "scales." The "scale" for any office gives the rate to every other office in the country. Express packages are divided into three classes, according to their bulk, value, etc. Most of the pack- ages are of the first class. They are carried on a car forming part of a passenger train, which insures rapid transit. They are delivered to the stores or residences of city consignees. SPECIMEN RATE SCALES The cost of the expressage on a first-class package to New York from certain specified cities is as follows for certain weights up to 100 pounds. 374 WALSH'S BUSINESS ARITHMETIC RATES TO NEW YORK FROM Weights Chicago St. Louis Dallas Denver Butte San Francisco lib. $0.30 $.30 $.33 $.33 $.36 $.38 2 .32 .33 .38 .40 .44 .49 3 .34 .35 .44 .45 .53 .60 4 .37 .37 .49 .52 .60 .73 5 .40 .41 .55 .57 .69 ' .84 6 .42 .43 .60 .64 .77 .95 7 .44 .45 .65 .69 .86 1.06 8 .47 .48 .71 .76 .93 1.17 9 .49 .51 .77 .81 1.02 1.28 10 .51 .53 .81 .87 1.10 1.39 20 Ib. .75 .79 1.36 1.47 1.94 2.51 30 Ib. .98 1.04 1.90 2.07 2.76 3.62 50 Ib. 1.45 1.56 2.99 3.27 4.42 5.85 100 Ib. 2.64 2.86 5.72 6.27 8.58 11.44 A fraction of a pound is taken as abound. WRITTEN EXERCISES 1. Find the expressage to New York on packages from Chicago as follows: a 24 weighing 4% pounds each. b 47 weighing 6)4 pounds each. c 36 weighing 8% pounds each. 2. Find the expressage to New York on packages from St. Louis as follows: a 137 weighing 3 Ib. 5 oz. each. b 294 weighing 19 Ib. 7 oz. each. c 178 weighing 7 Ib. 5 oz. each. 3. Find the expressage to New York on the follow- ing packages: FROM PRODUCER TO CONSUMER 375 a 168 from Dallas, each weighing 3^ pounds. b 209 from Denver, each weighing 9 Ib. 14 oz. c 329 from Butte, each weighing 29% pounds. d 415 from San Francisco, each weighing 49 Ib. 9 oz. 4. A merchant shipped from New York packages as follows, each weighing 99 Ib. 1 oz.: 153 to Chicago, 217 to St. Louis, 98 to Dallas, 369 to Denver, 54 to Butte, and 147 to San Francisco. Find the total charge for expressage. MAIL MATTER Domestic United States and Possessions Domestic mail matter is divided into four classes: First Letters, postal cards, sealed packages. Second Periodical publications. Third Miscellaneous printed matter weighing four pounds or less Fourth (Parcel Post) All mailable matter not included in previous classes. RATES OF POSTAGE First-class Matter Postal cards, 1 cent each. Letters and sealed pack- ages 2 cents an ounce or fraction thereof. Mail carried by aeroplane, 6 cents for the first ounce or fraction thereof, and 6 cents for each additional ounce. SIGHT EXERCISES 1. Give the cost of postage (a) on 246 letters each weighing less than 1 ounce, (b) On 122 similar letters weighing over 1 ounce, but less than 2 ounces. 376 WALSH'S BUSINESS ARITHMETIC 2. What postage should you pay on a sealed package weighing 10 ounces? 3. Give the cost of mailing 25 letters by aeroplane post, each weighing three quarters of an ounce. Second-class Matter The rate of postage on newspapers and periodicals bearing notice of entry as . second-class matter and sent unsealed by the public, is 1 cent for each 4 ounces or fraction thereof. 4. Give the postage on a newspaper weighing a 1 oz. b 2% oz. c 3% oz. d 8% oz. e 11 oz. 5. Give the postage on a package of magazines weighing a 18 oz. b % Ib. 3 oz. c 3 Ib. 1 oz. d 5 Ib. 10 oz. Third-class Matter The rate of postage on circulars, newspapers, and periodicals not entered as second-class, and other printed matter (not books), is 1 cent for 2 ounces or fraction thereof. Limit of weight is 4 pounds. 6. Give the postage on a map weighing a 5 oz. b 3 oz. c 7 oz. d 4% oz. e 6% oz. / 8 oz. 7. Give the postage on a package of pictures weigh- ing a 12 oz. b 1 Ib. 10 oz. c 3 Ib. 4 oz. d 2 Ib. 9 oz. e 21 oz. Fourth-class Matter Parcels weighing 4 ounces or less, except books, seeds, plants, etc., pay 1 cent for each ounce or fraction thereof. Parcels weighing 8 ounces or less, con- FROM PRODUCER TO CONSUMER 377 taining books, catalogues, seeds, plants, etc., pay 1 cent for each 2 ounces or fraction thereof. Larger parcels of books, seeds, plants, and other mailable articles pay the parcel post rates given on another page. These are based on the weight of a parcel and the distance to which it is to be carried. 8. Give the postage on a package of seeds weighing a 1 oz. b 7 oz. c 3 oz. d 8 oz. e 5 oz. / 4 oz. PARCEL POST RATES Weight Local Rates 1st and 2nd zones 50 to 150 mi. 3d zone 150 to 300 mi. 4th zone 300 to 600 mi. 5th zone 600 to 1000 mi. 6th zone 1000 to 1400 mi. 7th zone 1400 to 1800 mi. 8th zone over 1800 mi. lib. $0.05 $0.05 $0.06 $0.07 $0.08 $0.09 $0.11 $0.12 2 .06 .06 .08 .11 .14 .17 .21 .24 3 .06 .07 .10 .15 .20 .25 .31 .36 4 .07 .08 .12 .19 .26 .33 .41 .48 5 .07 .09 .14 .23 .32 .41 .51 .60 6 .08 .10 .16 .27 .38 .49 .61 .72 7 .08 .11 .18 .31 .44 .57 .71 .84 8 .09 .12 .20 .35 .50 .65 .81 .96 9 .09 .13 .22 .39 .56 .73 .91 1.08 10 .10 .14 .24 .43 .62 .81 1.01 1.20 etc. etc. etc. etc. etc. etc. etc. etc. etc. 20 Ib. .15 .24 .44 .83 1.22 1.61 etc. etc. etc. etc. etc. etc. etc. 50 Ib. *. _ .30 JL_ .54 1.04 2.03 3.02 4.01 etc. 70 Ib. etc. .40 etc. .74 Maximum weight 50 Ib. Maximum weight 70 Ib. 9. Give the postage on each packages mailed in Kansas City: of the following Place Zone Weight Any P. 0. Zone Weiqht a Pierre, S. D. 4 9 Ib. 13 oz. b In Alaska 8 22 Ib. 3 oz. c Topeka, Kans. 1 69 Ib. d Nevada 6 9 oz. e Peoria, 111. 3 17 Ib. 4oz. f S. C. 5 16 11). 7 oz. 80 80^ 30.01 to 40 40j 80.01 to 90 90^ 40.01 to 50 50j 90.01 to 100 $1.00 English Money 12 pence (d.) 1 shilling (s.) 20 shillings 1 pound sterling () A farthing is one fourth of a penny. It is generally written as a fraction. The coin value of l in U. S. gold is $4.8665. WRITTEN EXERCISES 1. (a) Taking the value of l as $4.87 what sum in U. S. money will pay a bill in Liverpool amounting to 9 5s.? (6) How much U. S. money will pay for a money order (including fee) to settle the bill? 2. Find the sum required to pay for a money order and fee to settle the following accounts and pay the money order fee: a Paris, 273.50 francs, at 19.4 cents b Brussels, 378.65 francs, at 19.4 cents c Madrid, 135.90 pesetas, at 19.4 cents FINANCING BUSINESS 413 d Rome, 463.75 lire, at 19.4 cents e Geneva, 312.60 francs, at 19.4 cents / Athens, 295.30 drachmas, at 19.4 cents NOTE: The coin value of each of these units is 19.3 cents, the extra mill being charged to cover the rate of exchange. Bills of Exchange Chas. E. Teale & Company of Peoria wish to pay in London for an invoice of cloth purchased of John M. Stafford amounting to 384 14s. 6d. They purchase the following sight bill of exchange from their bank. 384 14s. 6d. Peoria, 111., Dec. 9, 1920 At sight of this original bill of exchange (duplicate unpaid) pay to the order of John M. Stafford Three Hundred Eighty-four pounds, fourteen shillings, six pence Value received, and charge to account of To Strachan & Rector 1 First National Bank London Peoria, 111., U. S. A. England ) per Chas. W. Lyon Cashier The bank gives Teale & Company two bills, an original and a duplicate, marked 1 and 2, respectively. They send the former to Mr. Stafford, and retain the other as a receipt, sending it later if the first is lost by a disaster to the vessel carrying the mail. The cost of the draft depends on the rate of exchange, which varies from time to time. The daily quotations give the cost of cable transfers, sight bills, and sixty- day bills. WRITTEN EXERCISES 1. Chas. E. Teale & Company pay for this bill of exchange by means of their check drawn on the First 414 WALSH'S BUSINESS ARITHMETIC National Bank. Find the face of the check at the rate of $4.88^ a . ONE METHOD Value of 250 $1221.25 % of $4885.- 125 610.625 % of 250 9 9 times $4.885 10s. X of $4.885 2s. 6d. K of 10s. 2s. Xo of $4.885 Value of 384 14s. 6d. Test by multiplying $4.885 by 384.725 changing 14s 6d. to the decimal of a pound. Do this by subtracting .115 times 384.725 from 5 times 384.725. 2. Find the cost (a) of a cable transfer to Liverpool of 178 16s. 9d. at $4.90 per and an additional charge of $3.75 for the cable message, (b) Of a 60- day bill for 236 9s. 4d. at $4.86% a sterling. A Documentary Bill of Exchange Arthur Brown, a cutlery manufacturer of Sheffield, England, sells Franklin Bros, of Chicago an invoice of goods amounting to 265 7s. 8d. including in- surance on the goods for 60 days. He consigns the goods to the buyers, and obtains a through bill of lading to Chicago, the freight charges to be paid by Franklin Bros. He draws a sight bill on Franklin Bros, for the equivalent of the foregoing amount in U. S. money, FINANCING BUSINESS 415 to which bill he attaches the policy of insurance and the bill of lading. These combined documents con- stitute a documentary bill. Mr. Brown sells this documentary bill to Hatton & Hatton, Sheffield dealers in foreign exchange. The following is the bill itself: Sheffield, England, May 3, 1920 At sight of this original bill of exchange, second unpaid, pay to the order of Hatton & Hatton Dollars Value received, and charge to the account of To Franklin Bros. Arthur Brown Chicago, 111., U. S. A. He assigns to Hatton & Hatton the bill of lading and the policy of insurance. They indorse the bill of exchange and the other documents to their Chicago correspondent, and send to the latter, for collection, the bill with the other papers. 4. (a) How much does Arthur Brown insert in the foregoing bill for the sum to be collected in U. S. money, at the rate of $4.85% a ? (6) How much does he receive from Hatton & Hatton for the bill of exchange, at the rate of $4.84% a ? The quotations for French exchange give the number of francs for $1. The following are specimen rates charged in St. Louis for Paris transfers: Cable Transfers Sight Bills 60-day Bills 5.18% @ 5.17% 5.18% @ 5.18% 5.20% @ 5.20% 5. What is the cost a franc (a) when 5.18% francs is obtained for a dollar? (6) When 5.20% francs is obtained for a dollar? 416 WALSH'S BUSINESS ARITHMETIC 6. A Paris merchant draws a 60-day bill on Oct. 5, 1919, on a Denver creditor. It catches a mail steamer sailing 4 days later, which makes the voyage in 6 days. Three days thereafter it reaches the drawee who then accepts it. The latter pays it on maturity. If the proceeds of the bill require the same time for their return to Paris as was consumed in reaching Denver, on what day was the sum received by the drawer of the bill? The quotations for German exchange give the value in U. S. money of 4 marks. The following are recent quotations : Cable Transfers Sight Bills 60-day Bills 93% @ 94% 93% @ 93% 93% @ 93% 7. What is the cost of a cable transfer to Hamburg of 1870.65 marks at 94% cents for 4 marks, and a 15- word message at 35 cents a word? 8. A Berlin merchant sent to a Seattle purchaser an invoice amounting to 2784.60 marks, less 7%, 5, and 2% %. The seller added the freight on 215 kilos to Bremen at 5.20 marks a kilo, and insurance at 1 % on the net cost of the goods and the freight charge. How much must the purchaser pay for a sight bill at 93% cents for 4 marks to cover the cost of the goods deliv- ered on the steamer at Bremen, and the insurance? CHAPTER TWO BANKS AND BANKING BANKS OF DEPOSIT AND DISCOUNT The following is a statement of the condition of the Fairfax National Bank at the close of business June 30, 1920: RESOURCES Bonds and Mortgages $14,597. Public Securities 380,218.56 Other securities Loans Real Estate Accrued interest Due on acceptances Cash on hand and in bank 438,906.68 Total 250,708.91 1,411,007.25 50,534.90 14,501.14 39,599.70 (a) LIABILITIES Capital stock $125,000 Surplus 150,000. Undivided profits (ft) Deposits 2,257,933.56 Reserved for taxes 4,626. Accrued interest 8,946. Cashier's checks 3,938.57 Acceptances 39,599.70 Total (a) WRITTEN EXERCISES 1. Find the total resources (a). Insert this as the total of the liabilities and find (6), the undivided profits. 2. Rewrite the foregoing statement of resources and liabilities, expressing the items in thousands of dollars. First write the totals as even thousands. Next, add the thousands' column of the resources to ascertain how much must be carried to this column to make the new total. Then, rewrite the items as thousands, in- creasing by 1 thousand the necessary number of items, selecting those having the largest excess, and rejecting the remaining figures of the others. Thus, write "Bonds and Mortgages, $15,000; Public Securities, $380,000; Other Securities, $251,000; etc. A savings bank depositor desiring to withdraw any portion of his funds may be required by the bank to wait 60 days for his money. The check of a depositor 417 418 WALSH'S BUSINESS ARITHMETIC in a bank of deposit (state bank, national bank, or trust company) must be paid on proper presentation. Experience has shown that under ordinary conditions less than 5 % of a bank's deposits are demanded on any one day. When it is evident that larger calls for money are likely to be made, a bank can withdraw some of its deposits in other banks, sell some securities, rediscount in the Federal Reserve Bank some accept- ances, collect some of its demand loans, etc. The following is -a condensed form of a collateral time note: $24,000 %, Butte, Montana, May 14, 1920 On Sep. 14, 1920, for value received we promise to pay to Merchants & Miners Bank or order, at its banking house Twenty-four Thousand 00/100 Dollars with interest at six (6) per cent having deposited with said Bank, as collateral security for the payment of this liability, the following property: Two hundred fifty shares of stock of the Pennsylvania Railroad Company with this condition that the Merchants & Miners Bank has the right to call for such additional security as it may deem proper, and, on failure to respond forthwith to such call, this obligation shall immediately thereupon become due and payable, and the said Bank is hereby given full authority to sell and deliver the whole or any part of said securities, and upon such sale the said Merchants & Miners Bank after deducting all legal costs and expenses may apply the residue to pay this liability, returning the over- plus to the undersigned. And the undersigned agrees to pay the holder hereof any deficiency upon demand. Wilcox & Wilcox LOANS ON COLLATERAL A bank is always willing to lend money to the extent of at least 80% of the value of acceptable property deposited with it as security. To be accept- able, the property must be such as can be sold by the bank at once, in case the conditions of the loan are FINANCING BUSINESS 419 not observed, one of them being the promise of the borrower to deposit additional security at the call of the bank. Bonds or stocks are generally employed in some sections; in others, warehouse receipts show- ing the ownership of grain, cotton, etc. SIGHT EXERCISES 1. (a) Give the value of 250 shares of stock at $132 per share. (6) What is 80% of this value? 2. When a bank is willing to lend 80% of the value of the collateral, how much of the latter will secure a loan of $24,000? 3. For how many days is the foregoing collateral note drawn? 4. Give the discount on the note at 6 %. 6. Give the interest at 6 % (a) on $3000 for 30 days. (6) On $90,000 for 1 day. (c) On $1 for 90,000 days. 6. Give the interest at 6% on $1 for a 18,000 days b 21,000 days c 36,000 days d 144 days 7. John Martin has 200 shares of stock worth $150 a share. How much can he borrow on the security of this stock if a bank will loan him 80 % of the value? 8. (a) To borrow $30,000, what should be the market value of the security? (b) How many bales of cotton at $125 a bale would equal this sum? (c) When corn is selling at $1.50 a bushel, a warehouse receipt for how many bushels would be required as security for the same loan? INTEREST PAYMENTS At large trade centers brokers every few days borrow money payable on demand with interest. At 420 WALSH'S BUSINESS ARITHMETIC the end of each month the bank renders a statement of the interest due to date by the depositor, and noti- fies him that his account is debited with the total in- terest items due. INTEREST STATEMENT Minneapolis, Minn., Dec. 31, 1920 THE FLOUR CITY NATIONAL BANK To Jones & Cooke, Dr. Your account has been debited with the following interest charges to date: 1920 Loans Days 1 Day Rate Interest Dec. 1 $3000 30 $90,000 6% 5 5000 26 130,000 8 7500 23 etc. 12 6000 19 etc. 22 12000 9 etc. 27 8000 5 etc. Totals (a) 0) () WRITTEN EXERCISES 1. Find the interest due for December, 1920. METHOD The interest on $3000 for 30 days is the same as the interest on $90,000 for 1 day; on $5000 for 26 days, it is the same as that on $130,000 for 1 day. In the column headed "1 day" write the product of the face of the loan by the number of days for which interest is due. Obtain (6) the sum of this column, which gives the number of dollars on which 1 day's interest is due. (b) X 1 (da.) X .06 FINANCING BUSINESS 421 2. (a) Find the total amount, principal, and interest, due by Jones & Cooke to the Flour City National Bank on Dec. 31, 1920. (b) Find the total of the interest if the rate had been 5 %. CHANGE IN RATE OF INTEREST As the demand for loans increases, the interest rate advances, and a bank may "call" a demand loan un- less the borrower agrees to pay a higher rate. The following example shows several increases during a month. 3. Find the interest charged on Oct. 31, on a demand loan of $20,000, the rate being 5% from Oct. 1 to Oct. 5, inclusive; 5%% from Oct. 6 to Oct. 10, inclusive; 5^% from Oct. 11 to Oct. 20, inclusive, and 5%% from Oct. 21 to Oct. 31, inclusive. BANK TABLES The large amount of work an interest clerk is called upon to do, requires the employment of tables to facilitate his calculations. The following is a portion of a table used to determine the number of days between any two dates in a year of 365 days. An extra day must be added when Feb. 29 (leap year) falls between the dates. To find the time between any day in January and the corresponding day in another month, use the January line. The time between Jan. 13, 1921, and Aug. 13, 1921, is 212 days, found in the January line and the August column. 422 WALSH'S BUSINESS ARITHMETIC DATE TABLE Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. Jan. 365 31 59 90 120 151 181 212 243 273 304 334 Feb. 334 365 28 59 89 120 150 181 212 242 273 Mar. 306 337 365 31 61 92 122 153 184 214 Apr. 275 306 334 365 30 61 91 122 153 May 245 276 304 335 365 31 61 92 Jun. 214 245 273 304 334 365 30 Jul. 184 215 243 274 304 335 Aug. 153 184 212 243 273 Sep. 122 153 181 212 Oct. 92 123 151 Nov. 61 92 Dec. 31 The time between Jan. 1 and Aug. 13 is 224 days, 12 days more; between Jan. 13 and Aug. 1 it is 200 days, 12 days less; between Jan. 5, 1924, and Aug. 5, 1924 (leap year), it is 213 days. ORAL EXERCISES 1. Find the time between the following dates : a Jan. 5, 1921 and Sep. 5, 1921 c Mar. 7, 1922 and Jan. 8, 1923 e May 9, 1923 and Mar. 9, 1924 g Aug. 8, 1924 and May 1, 1925 i Oct. 6, 1925 and Mar. 2, 1926 k Jul. 2, 1926 and Jun. 7, 1927 6 Feb. 13, 1922 and Oct. 13, 1922 d Apr. 20, 1923 and Sep. 15, 1923 / Jun. 25, 1924 and Jan. 31, 1925 h Sep. 28, 1925 and Apr. 20, 1926 j Nov. 30, 1926 and Feb. 28, 1927 / Dec. 16, 1927 and Jan. 31, 1928 2. Give the number required to complete (a) the February line; (b) the February column in the Date Table. 3. (a) How many days does each number in the February column exceed the number in the correspond- ing line in the January column? (b) How many days is each number in the February line less than the corresponding number in the January line? FINANCING BUSINESS 423 4. Give the numbers required to complete (a) the successive lines; (b) the successive columns. INTEREST TABLES To make it possible for a clerk to determine the interest on as large as possible a number of accounts, banks supply books showing the interest for 1, 2, 3, 4, etc., to 360 days; on sums of $10,000, $11,000, $12,000, etc., to $990,000; at each of the customary rates. The following is an extract from the pages showing the interest for 196 days, on a small number of prin- cipals, at a few rates: 196 days Year of 360 days Principal 4% 5% 6% 7% $1000 2000 3000 $21.77,8 43.55,6 >^54.44,4 $27.22,2 54.44,4 81.66,7 $32.66,7 65.33,3 98. $38.11,1 76.22,2 114.33,3 4000 5000 6000 87.11,1 108.88,9 130 . 66,7 108.88,9 136.11,1 163.33,3 130.66,7 163.33,3 196. 152.44,4 190.55,6 228.66,7 7000 8000 9000 152.44,4 172.44,2 196. 190.55,6 217.77,8 245. 228.66,7 261.33,3 294. 266.77,8 304.88,9 343. SIGHT EXERCISES 1. Give to the nearest cent the interest on each of the following for 196 days: a $10,000 at 4% e 20,000 at 5 % i 30,000 at 6% m 40,000 at 7 % 6 $5000 at 6 % / 6000 at 7 % j 7000 at 5 % n 8000 at 4 % c $900 at 4% g 800 at 5% k 700 at 6 % o 600 at 7 % d $50 at 7% h 40 at 6 % / 30 at 5 % p 20 at 4 % 424 WALSH'S BUSINESS ARITHMETIC 2. From the table, give the interest for 196 days, to the nearest cent on a $1000 at 2 % b $2000 at 1% % c $3000 at 3 % d $4000 at 3# % NOTE: The bank clerk obtains these four results directly from his book which gives interest at the foregoing rates: 2^%, 3}%, etc. WRITTEN EXERCISES 1. Find the interest for 196 days, to nearest cent, on $1234 at 4 %. METHOD Take from the book the following items, at 4 % : Interest at 4 % on $1000 $21.778 200 4.3556 (& of $2000) 30 .5444 (Xoo of $3000) " " " 4 .0871 (Mooo of $4000) " " " $1234 ? Ans. NOTE: In practice, write only the four interest items. Check by finding the interest for $617 and multiplying the result by 2. The table used by the clerk requires but two items, that for $1200, and that for $34. 2. Find the interest for 196 days on a $2345 at 4 % b $3456 at 5 % c $4567 at 6 % d $4567 at 7% e 9876 at 4% / 8765 at 5% g 7654 at 6% h 6543 at 7% Check each result. ACCURATE INTEREST In England, all interest is calculated on the basis of 365 days to the year. The United States Govern- ment uses the same basis, as do banks in making in- terest payments. FINANCING BUSINESS 425 The following extract shows the exact interest for 264 days on a few sums, at specified rates : 264 days Year of 365 Days Principal 4% 5% 6% 7% $1000 $36.16,4 $43.39,7 $50 . 63,0 2000 72 . 32,9 86.79,5 101.26,0 3000 108 . 49,3 130.19,2 151.89,0 4000 144 . 65,8 173.58,9 202.52, 5000 180 . 82,3 216.98,6 253.15, 6000 216.98,6 260 . 38,4 303.78, 7000 253.15,1 303.78,1 354.41, 8000 289.31,5 347.17,8 405.04, 9000 325.47,9 390 . 57,5 455.67,1 WRITTEN EXERCISES 1. Fill out the 4 % column. Int. on $1000 METHOD 200 X 264 X .04 m 73 $2112 73 Carry out the quotient to five decimal places. Mul- tiply this successively by 2, 3, etc., to 9. Write the results to the nearest mill. Check the interest on $6000 and $9000, respectively, by comparing each with the interest on $3000; etc. 2. Find the interest for 264 davs on : a $1234 at 5 % 6 5678 at 6 % b $2345 at 6 % / 6789 at 7% c $3456 at 7% g 9876 at 5% d $4567 at 5 % h 8765 at 6% 426 WALSH'S BUSINESS ARITHMETIC CERTIFICATE OF DEPOSIT A bank that pays 2 % interest on a customer's daily balances will pay 3 %, for instance, on money left with it for 3 months or more on a special deposit. John T. Collins having in the Mechanics Bank a balance of $3,800, for which he has no use for three months or more, withdraws $2500 from his account and obtains from the bank the following: Certificate of Deposit $2500%o Woodrow, Mont., fan. 25, MECHANICS BANK This certifies that fc>fw, &. &Mim* has deposited with this bank v& Awyidi&d 00 / fOO .............. Dollars payable on or after Apr. 25, 1920 to the order of 3 with interest at 3 per cent upon the return of this certificate property indorsed. faefih tftzwoAt /i/. c&o*t6U' l&e&k&i, Asst. Cashier Vice Pres. 3. Find the exact (accurate) interest on the fore- going certificate from Jan. 25, 1920, to Apr. 25, 1920. METHOD $2500 X .03 X 91 Find the interest on 91 days, taking 365 days to the year. Cancel two ciphers in $2500, and the decimal point in .03. Cancel 25 and 365. FINANCING BUSINESS 427 4. Mr. Collins, finding he needs money on March 25, returns the certificate on this date. The bank allows him but 2 % interest for the time it has had the money. How much does it pay Mr. Collins, principal and exact interest at 2 %? INTEREST ON DAILY BALANCES Some banks and trust companies pay interest on daily balances when these are in excess of a certain sum. An account that has less than an average balance of $200 is probably carried by a bank at a loss. The following table shows the interest for 1 day, taking 365 days to the year: Interest for 1 day Year of 365 days Principal 2% 2#% 3% 3^% $100,000 200,000 300,000 $5.47,9 10.95,9 16.43,8 $6.84,9 13.69,9 20.54,8 $8.21,9 16.43,8 24.65,8 $9.58,9 19.17,8 28.76,7 400,000 500,000 600,000 21.91,8 27.39,7 32.97,7 27.39,7 34.24,7 41.09,6 32.87,7 41.09,6 49.31,5 .38.35,6 47.94,5 57.53,4 700,000 800,000 900,000 38.35,6 43.83,6 49.31,5 47.94,5 54.79,5 61.64,4 57.53,4 65.75,3 73.97,3 67.12,3 76.71,2 86.30,1 5. A depositor's balance for 20 days is $900; for the next 12 days it is $1200; for the next 15 days it is $1600. Find the interest at 2% for the 47 days. 428 WALSH'S BUSINESS ARITHMETIC METHOD $900 for 20 days = $18,000 for 1 da. 1200 " 12 " = 14,400 " 1 " 1600 " 15 " = 24,000 " 1 " = $56,400 for 1 da- To find the interest use the table 6. Find the exact interest on the following: a $12,000 for 75 da. at 2% b $3000 for 235 da. at c $14,000 for 61 da. at 3 % d $4000 for 186 da. at 3% % e $16,000 for 39 da. at 2% / 5000 for 127 da. at g $18,000 for 47 da. at 3% h 6000 for 206 da. at SAVINGS ACCOUNTS Postal Savings Certificates In a place remote from banks, a person ten years of age or over can obtain interest on his savings by means of postal savings certificates, obtained through any post office. These certificates are issued in denominations of $1, $2, $5, $10, $20, $50, $100, $200, and $500, each bearing the name of the depositor, the number of his account, the date of issue, the name of the depository office, and the date on which interest begins (the first day of the month next following the day on which the deposit is made). Interest is paid at the end of a full year; if not collected, it accrues annually. No interest is paid on accrued interest. If a certificate is lost or destroyed, the depositor may obtain a new one. FINANCING BUSINESS 429 Postal Savings Bonds A depositor may exchange certificates into U. S. postal savings bonds on Jan. 1 or Jul. 1 by making application one month previously. These bonds are issued in denominations of $20, $100, and $500. They bear interest at 2%%, payable semi- annually. SAVINGS BANKS H. M. Devoe's account in the savings department of the Mississippi Valley Trust Company shows deposits and withdrawals as follows: Date Deposits Interest Withdrawals Balances 1921 Jan. 1 327 49 Apr. May 9 8 250 75 577 502 49 49 Jul. Sep. 1 10 6 54 50 509 459 03 03 Nov. 4 100 559 03 1922 Jan. 1 (a) (&) Mar. 13 75 to May 24 150 (d) Jul. 1 () (/) This company allows interest semiannual ly on January 1 and July 1, on even dollars of deposits that have been in the bank for 6 months at the interest date. On July 1, 1921, 2% was allowed on $327 (rejecting the cents), the interest being added to the balance. On January 1, 1922, 2% of $509 was allowed (a); on July 1, 1922, 2% of $559 was allowed (e). 430 WALSH'S BUSINESS ARITHMETIC WRITTEN EXERCISES 1. Write from the book the answers (a) to (/). 2. Copy and complete . the foregoing account by allowing 1 % quarterly. Insert two other interest dates, April 1 and October 1. At each date insert 1 % of the smallest sum in the bank during the quarter. Other banks, while allowing interest on April 1 and October 1, do not enter interest at these dates, but add it to the interest due on January 1 and July 1, respectively. 3. Copy and complete the foregoing account by calculating the interest due on April 1 and October 1 as in Example 2. Do not credit these interest items to the account until the following July 1 and January 1, respectively. Calculate the interest due on April 1, but do not enter it until July 1, combining it then with the interest from April 1 to July 1. This makes a slight difference in some of the "balances" and, therefore, in the interest. 4. Copy and complete the foregoing account by allowing interest on January 1 and July 1, at the rate of 4 % annually on all sums three months in the bank at those dates. Check up the interest allowance in your bank book or in those of your parents. Read carefully the in- terest rules printed on one of the cover pages. CHAPTER THREE STOCKS AND BONDS FORMING A CORPORATION Wishing to provide employment for residents of Accotink, some of the progressive citizens determined to establish a cannery. They interested the farmers in the vicinity, who agreed to furnish a portion of the funds, and to supply fruits and vegetables at a fair price. It was found that a beginning could be made with $50,000, and a charter was obtained from the Legis- lature, authorizing the establishment of the Accotink Canning Company, with a capital of $50,000. Capital Stock 500 Shares of $50,000 $100 each THE ACCOTINK CANNING COMPANY Incorporated 1918 Stock Certificate No. ## This certifices that is entitled to 25 shares of $100 each of the stock of THE ACCOTINK CANNING COMPANY fully paid and non-assessable, transferable on the books of this corporation only by the holder hereof in person or by attorney upon the surrender of this certificate. In witness whereof this corporation has caused this certi- ficate to be signed by its duly authorized officers and to be sealed with the seal of the Corporation, this ft/Ml day of Luoi Secretary and Treasurer President 431 432 WALSH'S BUSINESS ARITHMETIC This capital stock of $50,000 was divided into shares of $100 each, the purchaser of one or more shares receiving a stock certificate in the preceding form. DIRECTORS AND OFFICERS The stockholders elected twelve (12) directors to serve for a year from March 1, 1918. To this Board of Directors, given the general management of the corporation and the selection of officers to take charge of the details. PREPARATORY EXERCISES 1. At the end of a year, the profits of the Accotink Canning Company were found to be $5510.85. About what per cent of $50,000 does this represent? 2. The directors decided to distribute $6 per share among the stockholders, (a) How much was thus distributed? (b) How much of the profits remained for working capital, etc.? 3. How much of the profits did Mr. Laplace receive, who owned 45 shares? 4. Mr. Laplace sold 15 of his shares to Mr. Beattys at $140 a share. How much did the latter pay for them? 6. At the end of the next year, the directors dis- tributed $7 a share. What per cent of $140 did Mr. Beattys receive? PAR VALUE OF STOCK By the par value of a stock is generally meant its cost to the original contributors to the capital. This is generally fixed at $100 a share. The par value of a share of the Pennsylvania Railroad is $50 a share. FINANCING BUSINESS 433 When the stock sells below its par value ($100 in the case of most stocks), it is said to be sold at a discount; when it sells above its par value, it is said to be sold at a premium. DIVIDENDS At stated times the directors meet to declare a dividend. This means that they determine the sum per share to be paid as a dividend to the stockholders. In the case of the Accotink Canning Company for example, the books showed earnings for the year of $5510.85. Of this amount $1000 had been spent for new machinery, and $750 more was needed for the purpose. To have funds in hand for emergencies, same it was agreedto distribute $3000 among the stock- holders. This made the dividend $6 a share. To each stockholder of record was mailed a check for the amount of his dividend at the rate of $6 for each share owned by him according to the Company's books. PRICES OF STOCKS The daily papers give the prices at which stocks are bought and sold at the Stock Exchange. The following were the rates for a few stocks : Adams Express Co. 51% American Beet Sugar 70% Baltimore & Ohio 57% Delaware & Hudson 104% General Electric 148% Illinois Central 96% Louisville & Nashville 116% Union Pacific 128% United States Steel 110% Western Union These prices mean that on a certain day, stock of 434 WALSH'S BUSINESS ARITHMETIC Adams Express Co. sold at $51.25 a share, of U. S. Steel, $110.1% a share, etc. THE STOCK BROKER A person desiring to buy or tp sell stock generally finds it advisable to do so through a stock broker, who charges for his services %% of the par value of $100 a share. When the broker buys Baltimore & Ohio Railroad stock for $57.75 a share, he charges his client $57.87%, adding 12% cents a share as his commission. When he sells stock of the General Electric Co. for $148.37% a share, he remits to his client $148.25 a share, deducting his commission of 12% cents a share. NOTE: In all examples in stocks take as the par value $100 unless another value is given. SIGHT EXERCISES 1. A broker bought for a client stocks for which he paid the following prices: a 70% b 83% c 97% d 101% e 93 / 56% g 64% h 73% i 174% j 86% Give the cost of each per share to the client, after he pays the broker's commission of % %. 2. Stock was sold through a broker at the following rates : a 68 b 75% c 86% d 97% e 118% / 57% g 82% h 95% i 88% j 129 Give the price per share received by the seller in each case, after the deduction of the broker's commission FINANCING BUSINESS 435 3. A broker filled orders for stocks, buying the following quantities at the prices specified: a 25 shares at 83% b 4 shares at 71% c 88 shares at 99% d 6 shares at 60% e 50 shares at 80% / 8 shares at 87% Give the cost of each lot when %% commission is added to each purchase. 4. Give the price received by the seller of each of the following lots, after the deduction of the broker's commission of % % : a 25 shares at 127% b 4 shares at 81% c 96 shares at 100 d 6 shares at 70% e 50 shares at 144% / 8 shares at 62% 6. How much commission does a broker receive who sells 25 shares at 127%, and 96 shares at 100? Ignore the prices, since a broker's commission is the same whether he sells a $100 share for $27% or for $127%. WRITTEN EXERCISES 1. A broker bought for a customer 176 shares of General Electric at 148%. How much did the stock cost the latter including the broker's commission? METHOD The stock cost the cus- 100 sh. $14,862.50 tomer $148.62% a share, in- 50 " 7,431.25 eluding commission. Find 25 ' 3,715.625 the product of 176 times 1 " 148.625 $148.62% by aliquot parts. Ans. $16,158. Test by multiplying 176 by 148%. 436 WALSH'S BUSINESS ARITHMETIC 2. Find the amount a purchaser should pay for each of the following blocks of stock, adding a com- mission of %% to the given rates: a 125 shares at 163% b 75 shares at 57% c 287 shares at 148% d 63 shares at 64% e 144 shares at 126% / 98 shares at 76% 3. A broker sold for Mr. Jenkins 275 shares of Illinois Central at 96%. How much should Mr. Jenkins receive after the deduction of the commission? METHOD Mr. Jenkins receives 250 shares @ $96.75 $24187.50 $96% - $% a share, _25 2418.75 or $96.75. Test 75 " Ans. $26606.25 4. Find the sum due each seller of the following blocks of stock after deduction of the broker's commis- sion, the respective quantities and selling prices being a 216 shares at 112% 6 86 shares at 76% c 154 shares at 106% d 79 shares at 59% e 375 shares at 184% / 38 shares at 64% 5. M. E. Kelley sent his broker $10,000 with in- structions to buy stock of the Pacific Lumber Co. How many shares at 86% could be bought, and how much money should the broker return his principal after deducting his commission at %%? 6. Find the maximum number of shares at each of the following rates that can be bought for $10,000, and the balance remaining after paying for the shares and the commission of % %. a 94% b 86% c 74% d 116% e 127 FINANCING BUSINESS 437 7. Mr. Guiry ordered his broker to sell a sufficient number of shares of Midvale Trolley Co. to realize $10,000 after the deduction of the usual commission. How many shares at 114% must be sold? METHOD $10,000 -i- $114% = 40,000 -T- 459 = 87 Ans. 88 shares. 8. Find the number of shares of each of the following that must be sold to realize $10,000. a 96^ b 87% c 64% d 109% e 137% PREFERRED STOCK In 1921, needing more money to extend the business of the Accotink Canning Company, its stockholders authorized the issue of 500 shares of preferred stock, on which an annual dividend of $6 a share was to be paid before any dividend payment was made to holders of the original (common) stock. Each stockholder was permitted to buy for $100 each the same number of shares as he held of the common stock. Owners of the latter unable or unwilling to buy preferred stock could sell their rights. SIGHT EXERCISES 1. (a) How much should an outsider pay for 6 % pre- ferred stock to enable him to obtain 5% annually on his investment? -v- ?=5% 438 WALSH'S BUSINESS ARITHMETIC (6) How much a share could he afford to pay for the right to purchase the preferred stock? 2. If the company's profits the next year were $9000, how much would be left after paying the holders of 500 shares of preferred stock $6 a share and the holders of 500 shares of common stock $7 a share? 3. The folio whig year the amount available for the payment of dividends was only $5750. (a) How much would remain for the holders of common stock after the payment of $6 a share to the holders of the pre- ferred stock? (6) How many dollars a share could be paid the former? BONDS Finding that it could use to advantage a large sum of money, the Accotink Canning Company offered for sale bonds maturing in 20 years, to the amount of $50,000, bearing interest at 5 % a year, payable semi- annually. As security the company mortgaged its property, worth $80,000, to the Old Dominion Trust Company for the benefit of the bondholders. The bonds were issued in denominations of $100, $500, and $1000. SIGHT EXERCISES 1. How much will be required annually to pay 6% on bonds amounting to $50,000, C% dividends on preferred stock of $50,000, and 7% dividends on common stock of $50,000? 2. In order to pay the principal of $50,000 in 20 years, how much must a company set aside semi- annually out of its gross profits? FINANCING BUSINESS 439 3. How much must it set aside semiannually to allow for 2 % annual depreciation on equipment valued at $43,750? PUBLIC SECURITIES Bonds are issued to raise money to build schools, improve roads, install water systems, etc., etc. Investors can be certain that the interest on these bonds will be paid as it becomes due, and the principal at the time the bond matures. As the benefits from the foregoing improvements will continue for some time it is only fair that the payment of the cost thereof should be spread over a series of years. INTEREST PAYMENTS An examination of a Liberty Bond will show that it specifies the principal, the rate of interest, the time of each interest payment, and the date when the principal is payable. Bonds are issued in two forms, registered and coupon. The registered bond shows the name of the owner. His address is kept by the Treasury Depart- ment, and the check for the interest is mailed to him. If he wishes to sell the bond he transfers it by assign- ment, which must be recorded by the Washington authorities, so that they may send interest checks to the new owner. One advantage of the registered bond is that the owner suffers no financial loss if it is destroyed or stolen. A disadvantage to a person desiring to obtain cash at once, is the necessity of waiting a few days for the intending purchaser to obtain title. 440 WALSH'S BUSINESS ARITHMETIC COUPON BONDS A coupon bond is generally payable to the holder, making it possible to sell it by handing it over to the purchaser. A 20-year bond with interest payable semiannually contains as a part of it 40 interest coupons, one of which is detached each half year. They are numbered from 1 to 40; each shows the amount of the half-yearly interest and the date when it is due. When this day arrives the holder of the bond detaches the current coupon and cashes it through his bank. DENOMINATIONS Bonds, registered and coupon, are issued in various denominations: $50, $100, $500, $1000, $5000, $10,000, etc. BOND QUOTATIONS Wlien the price of a bond is given as 115, this means 115% of the face of the bond. If bought or sold through a broker, there is a charge of %%. A bond quotation gives the rate payable for a bond bought on an interest day. If bought thereafter, the buyer pays the "accrued" interest; that is, the interest earned by a bond from the day the last interest was paid until the day of purchase. ACCRUED INTEREST When a person on Aug. 15 sells a bond paying in- terest on Jan. 1 and Jul. 1, he is entitled to the interest it has earned during these 45 days between Jul. 1 and FINANCING BUSINESS 441 Aug. 15. He turns the bond over to the buyer with the coupon covering six months' interest from Jul. 1. If the bond purchased is a 4 % one for $1000 and the price is 115, the purchaser pays $1151.25+45 days' interest on $1000 at 4 %. In the following examples take the interest for the accrued time, at the rate paid by the bond, on the basis of 360 days to the year. The pupil should, however, know that in large transactions the buyer may insist upon actual interest, 365 days to the year. The most equitable way is to take the number of days in the interest period and to calculate the accrued interest on the basis of the number of days in this period. WRITTEN EXERCISES 1. At 112% plus brokerage, find the cost of bonds to the amount of $15,000, bearing interest at the rate of 5%, payable semiannually on March 1 and Sep- tember 1, when the purchase is made (a) June 20, (6) September 6. METHOD (a) Accrued interest on $15,000, Mar. 1 to Jun. 20, 111 da. at 5% is $231.25 (b) For 5 da. at 5 %, it is $10.42. The cost of the bonds on Mar. 1 or on Sep. 1 after the removal of the proper coupon, would be times $15,000 or $16,837.50 Total cost (a) $16,837.50 + $231.25 = Ans. Total cost (b) 16,837.50 + 10.42 = Ans. 2. Find the amount paid for each of the following purchases of bonds. Add brokerage to the given price. 442 WALSH'S BUSINESS ARITHMETIC Bought Price Face Val. Int. rate Int. payable a Jun. 28 112^ $15,000 6% Jan. 1 6 Sep. 20 97% 12,000 3% Jul. 1 c Nov. 19 104K 20,000 5% Oct. 1 d Dec. 13 96% 18,000 3% Dec. 1 e May 12 101% 24,000 4 % Mar. 1 INCOME RATE ON INVESTMENTS When a person buys a 3% bond for 90, including brokerage, and holds it until its maturity, 5 years later, his total income from a $100 bond would be $15 for 5 years' interest plus $10, the difference between $90, the cost of the bond, and the $100 he received for it when it was paid off. This total income of $25 in 5 years represents an average of $5 a year, which was obtained from an investment of $90, making the annual rate 5% %. These figures ignore the interest obtained by the reinvestment of each interest item as it is collected. Large investors take this into account, also the fact that the interest is payable quarterly, semiannually, or annually. They ascertain the income rates from bond tables, which involve calculations that can be made only by experts. SIGHT EXERCISES 1. Ignoring the matte? of interest on interest, how much less than $100 must a buyer pay for a 3% bond to receive $4 profit a year when the bond matures in (a) 1 year; (b) 2 years; (c) 3 years? 2. How much more than $100 can a buyer pay for a 5% bond maturing in (a) 1 year; (6) 2 years; (c) 3 years? CHAPTER FOUR FINANCING THE GOVERNMENT THE TAXPAYER Everybody contributes to the expenses of running the government. He may not receive a bill, but he pays taxes when he buys anything the price of which includes a tax paid by someone else. If he is not the owner of a house, a portion of his rent is used by his landlord to pay the tax. Everybody, therefore, should be interested in the proper use of government receipts. THE BUDGET The residents of a rural school district meet annually to determine the sum to be raised for educational purposes. The legislative department of a county, a city, or a state fixes the sums to be raised for its special pur- poses. Each body receives estimates from the officers in charge of the various activities, and finally deter- mines the sum to be raised by taxation. % STATE REVENUES WRITTEN EXERCISES 1. Using the following data, write from the book the total of a state's revenues. 443 444 WALSH'S BUSINESS ARITHMETIC Direct Taxes $45,510.43 Indirect Taxes Excise 114,787.50 Corporations 5,894,051.60 Inheritance 1,280,660.49 Stock transfers 985,902.38 Secured debt 635,902.53 Mortgages 745,132.12 Motor vehicles 262,747. Other revenue receipts 643,982.05 Total $ 2. The direct taxes are collected from the counties. What per cent of the revenue is obtained in this way? 3. Write the total of the following yearly EXPENDITURES OF A STATE Executive $18,798.80 Defensive $108,490.76 Administrative 250,244.41 Penal 111,178.29 Legislative 153,004.94 Curative 687,904.95 Judicial 200,755.71 Charitable 322,434.56 Regulative 382,962.83 Protective 160,371.90 Educational 250,249.90 Constructive 201,494.44 Agricultural 224,516.88 General 78,596.88 THE CITY BUDGET The following are the approximate appropriations made by the city of Belle Haven for the year 1921 : Department of Finance $43,420 Department of Water and Sewers 39,380 Department of Public Works 42,450 Department of Buildings 10,800 Department of Charities and Correction 32,650 Department of Police 35,400 Fire Department 31,250 FINANCING BUSINESS 445 Department of Parks 24,000 Department of Health 12,250 Judicial Purposes 10,000 Department of Street Cleaning 11,350 Interest on City Debt 44,500 Sinking Fund 24,000 Expenses of Administration 48,000 Department of Education 90,450 Sundry Expenses 8,450 4. Write the total appropriations for the year. 5. Find the per cent of the total appropriation allowed for (a) Educational purposes, (b) Charities and Correction, (c) Fire department, (d) Police purposes, (e) Parks. (/) Health, (g) Interest and Sinking Fund. VALUATIONS For purposes of taxation, the value of the property in the city is fixed by officials called assessors. They visit each parcel once a year; they are furnished with maps of every block, showing the character of the improvements; and they endeavor in every way to keep acquainted with the changes in the value of the real property during the year. They then fix the assessed value, which is sometimes as low as one half its actual value. Personal property is also assessed, and its valuation is added to that of the real estate, the sum of both repre- senting the total valuation for purposes of taxation. SIGHT EXERCISES 1. (a) When property worth 400 millions of dollars is valued by the assessors at 300 millions, what per cent 446 WALSH'S BUSINESS ARITHMETIC of the actual value is the assessed value? (6) What would be the assessed value of Mr. Ritchie's house, at this rate, if its actual value is $4000? 2. (a) If the sum to be raised by taxation is 3 mil- lions, give the tax rate when the valuation is 300 millions. What would be (6) Mr. Ritchie's valuation? (c) His tax bill? 3. If the valuation were made 200 millions, what would be (a) the tax rate? (b) Mr. Ritchie's valu- ation? (c) His taxes? 4. Why would there be no difference in his taxes when there was a change in the valuation of his property? EQUALIZATION Whether property is assessed at its full value or at any per cent of it, the tax payment on any parcel is the same. All that an owner can desire is that all the parcels should be assessed at the same per cent of their value. If he feels that his valuation is propor- tionately greater than that of his neighbors, he can appeal to the Board of Assessors. WRITTEN EXERCISES 1. The budget requirements for city purposes are $2,973,468; for county purposes, $387,596; and for state purposes $294,810. The city will receive from revenues $843,495. How much remains to be derived from taxation? 2. If the assessed valuation of the real and personal property to be taxed is $275,483,500, (a) what must FINANCING BUSINESS 447 be the tax on each $100 to raise the amount needed as shown in the preceding example? (Give the result correct to five decimal places.) Find the tax to the nearest cent on property assessed (6) at $2000, (c) at $30,000, (d) at $400,000, (e) at $5,000,000. 3. Find H. DeW. Slater's tax at $1.80 per $100 on personal property, as follows: furniture, $500; clock, $10; watch, $25; vehicle, $100; horse, $175. 4. For the guidance of county assessors, the State Board of Equalization established the following classi- fications and valuation of an acre for land acreages in Nevada for the following year: Cultivated 1st class 3d 50 2d class $65 4th " 35 Meadow 1st class (1 ton or more to the acre) $30 2d " (less than 1 ton to the acre) 18 Pasture 1st class $30 2d class $20 3d 11 4th 7 5. The classification of cultivated land is deter- mined by the production from an acre as follows: 1st class 2d class 3d class 4th class Alfalfa Hay Grain 5 tons IK tons 1 ton 3 to 5 tons under 1% tons 1400 to 2000 Ib. 2 to 3 tons 800 to 1400 Ib. under 2 tons under 800 Ib. 448 WALSH'S BUSINESS ARITHMETIC (a) Find the assessed value of 160 acres of land owned by Stephen Luken, 40 acres of which produced 180 tons of alfalfa; 40 acres, 70 tons of hay; 40 acres, 1200 bushels of wheat; and 40 acres of first-class pasture. (6) Find the average valuation per acre. 6. Neville Hart had 156 sheep which were assessed at $9 each; 68 hogs at $12; 42 pigs at $4; 35 cattle at $38; 6 horses at $275; and 3 mules at $195. What was the total valuation of the foregoing? Find the amount of the following tax bill: To the Treasurer of Fairfax County, Dr. Mt. Vernon District State Taxes 35 on $100 1921 County Taxes. .Levy, 30^; Pensions, 5^; County Schools, 20& District Schools, 15{; Road Tax, 25jf. Total 95{ on $100. SUBJECTS OF TAXATION State Taxes County Taxes Total STATE CAPITATION TAX Personal Property \ B Val. $3620 ;c " eoo (/) (j) 07) (*) 1 CW (*) (0 50 Total Valuation $ (a) Dog tax, 2 at 50^ each 160 A. val. $40 $6400 40" " 30 (6) 20" " 25 (c) 20" " 18 (rf) Total Valuation (e) Total Add tax 5% (w) (n) (o) Received payment in full . (ody<&n, Treasurer FINANCING BUSINESS 449 NOTE: Enter the capitation tax and the dog tax only; in the "Total" column. Insert at (a) the total value of the personal property, at (/) the tax at 35 at (0) the tax at 95 i, and at (K) the sum of $) and (g). Do the same with the tax on the real estate. To (ra) add 5 % of itself for delay in payment. UNITED STATES REVENUES WRITTEN EXERCISES 1. During the year preceding the war the receipts of the United States Government from all sources were $1,153,044,639.10. The total disbursements dur- ing the same period were $1,072,894,093.23. Find the balance. 2. Among the items of revenue were: Customs $213,185,845.63 Internal Revenue (a) Ordinary $303,486,474.94 Emergency 84,278,302.13 Income tax Corporation 56,993,657.98 Individual 67,943,594.63 Sales of public lands 1,887,661.80 Consular fees 1,466,572.72 Profits and coinage 4,354,613.12 Tax on bank circulation 3,838.034.25 Sale of two battleships 12,535,275.96 Patent fees 2,329,510.36 Forest reserve fund 2,883,783.73 Receipts, Dist. of Columbia 9,132,976.52 Items not enumerated (6) Insert at (a) the total of the four items of internal revenue receipts. Write at (c) the total receipts as given in the preceding example. Insert at (6) the difference between (c) and the sum of the other items, adding the latter and subtracting then* total from (c) in one operation. 450 WALSH'S BUSINESS ARITHMETIC DUTIES In ordinary times about one fourth of the total receipts of the Government are obtained from duties. These are the taxes paid on imported goods. The rates of duty are fixed by the tariff. This is an act of Congress specifying the duty to be paid on each class of imports. THE TARIFF On some articles the tariff fixes an ad valorem duty. This is a certain per cent on the foreign cost. Bicycles and motorcycles pay 25%, for instance; breech- loading shot guns and rifles, 35%; silk ribbons, 40%; pen knives, 35 %. On other articles there is a specific duty of so much a square yard, pound, ton, etc. The rate on window glass, for instance, ranges from %j to 2fi a pound, according to its size, the lowest being for that not exceeding 150 square inches in surface. On sugar, the rate is 71/100f a pound with higher rates for the better grades. Grapes are charged 25 cents a cubic foot; lemons and oranges 15 cents a package not exceeding 1% cu. ft., 25 cents a package not exceeding 2% cu. ft., etc., and % a pound in packages containing over 5 cu. ft. DOUBLE DUTIES A few articles pay both a specific and an ad valorem duty. Perfumery which contains alcohol is charged 40^f a pound and 60%; that without alcohol pays only 60%. Lead pencils are charged 36^ a gross and 25%; sweet chocolate, 2^ a pound and 25 %. FINANCING BUSINESS 451 THE FREE LIST Many articles are admitted free of duty; among them are agricultural implements, blooded cattle, bagging, binding twine, books, plants, trees, tea, coffee, wool, etc. A DUTCH INVOICE B. E. McAveney & Co. import two cases of dry goods. They receive the following invoice from the sellers : ROTTERDAM, Mar. 20, 1920 Invoice of two (2) cases of dry goods marked Sold to Messrs. A. W. Ross & Co., Omaha By Bergen & Van Brunt and shipped Mar. 23, 1920, from Amsterdam per S.S. Victory. 1609 1610 840 m Dress Goods fl 1 . 80 360 " Laces 1.85 180 " Embroideries 2.10 1200 " Sateens 1.97% Less 5 % The first column shows the mark on both cases; the second gives the number on each. No. 1609 contains three kinds of goods, and No. 1610 one kind. The length of each kind is given in meters (ra) and the price in florins (//) WRITTEN EXERCISES 1. Copy the foregoing invoice, inserting the exten- sion for each item. From the footing deduct 5 %, and insert the net amount due in florins. 452 WALSH'S BUSINESS ARITHMETIC 2. Find the equivalent value in U. S. money at the gold value of the florin, 40.2 cents. 3. At 39.37 inches to the meter find the number of yards (a) of dress goods. (6) Of laces, (c) Of embroi- deries, (d) Of sateens. 4. (a) Find the cost of each of the four items in the foregoing invoice after the deduction of the discount of 5 %. (b) Express the net cost in U. S. money to the nearest dollar. PAYING DUTIES The goods imported by B. E. McAveney & Co. were landed in New York and sent in bond in a sealed car to Omaha. Upon their arrival, the importers filed at the custom house their bill of lading and the foregoing invoice with the following entry: OMAHA, NEBR., Apr. 15, 1920 Entry of Merchandise imported by B. E. McAveney & Co. Invoice dated Rotterdam, Mar. 20, 1920 Arrived at New York, Mar. 31, 1920 Marks Nos. Contents 35% 60% 15% 40% Total * I60 /,o Dress Goods Laces Embroideries Sateens () (*) (c) (<0 w (/) (*) (*) (0 (;) ) 35% (*) j) 60% (0 (h) 15% (m) (0 40% (n) (o) 6. Copy the foregoing entry. Insert (a to d), the net cost of the various items, and at (e) the total. FINANCING BUSINESS 453 Insert (/ to j) the value in TJ. S. money, omitting cents. Calculate the duty on each item (k to ri) at the given rates. Find the total amount (o). Two copies of this entry, when complete, are handed to the entry clerk, who verifies the calculations, affixes his initials at (o), and passes one copy along to the cashier. He also designates the package to be sent to the appraiser's stores with the invoice. Here the package is opened, the goods measured, their char- acter determined, and the rate of duty noted on the invoice. The latter is returned to the custom house. If the figures on the entry are correct, a liquidating clerk certifies thereto by affixing his initials in red. If the appraiser changes the values or the rates, the liquidating clerk makes out a new duty statement in red ink, and the difference to be collected from the importer or to be returned to him. 6. Find the duty on each of the following: Classification of goods Cost at place of purchase U. S. coin value of foreign money Rate of duty a Opera glasses b Watches c Pickled fish d Vases 1463. 90 francs 183 16s. 10 d. 1237. 85 kroner 2460. 50 lire 19.3?f $4.8665 26.8^ 19.3{ 35% 30% 25% 45% 7. What is the duty on 48,648 pounds of sugar testing 87, the rate being 71/100^ a pound for sugar testing 75, and 26/lOOOc' additional for each degree above 75? CHAPTER FIVE PROTECTING THE INDIVIDUAL A fire loss of $1000. or $100,000, which might greatly embarrass an individual, is easily shared by a multitude. For some such sum as $2.50 in one case or $250 in the other, an insurance company will provide for the pay- ment of the loss if it happens during the year. FIRE INSURANCE The contract is evidenced by a policy. This sets forth that the specified insurance company (the under- writer) in consideration of a certain sum (the premium) agrees to insure John Doe (the insured) for a specified term, from - - to - , against all Direct Loss and Damage by Fire and by removal from premises en- dangered by fire to an amount not exceeding - Dollars to the following property: INSURANCE RATES The rates for a given locality are generally fixed by a Board of Underwriters, who take into consideration all the conditions. The following shows those for $100 of insurance for 1 year on certain types of houses in a given section, also on their contents : Occupied as Residence Apartment Store and Dwelling Construction Brick Frame 16* Brick 15* Frame Brick Frame Building 10* 20* 20* 40* Household goods 16 20 20 24 24 40 454 FINANCING BUSINESS 455 FACTORS DETERMINING RATES A rate is provided for every type of building and for all varieties of goods. The size of a building, the nature of the roof, the water supply of the vicinity, the character of the business carried on, the proximity to other buildings all are considered. An extra per cent is sometimes added to the regular rates when the water supply is decreased; a per cent is deducted when the insured installs fire-fighting equipment; hose, fire-extinguishers, sprinklers, etc. WRITTEN EXERCISES 1. Find the premium for insuring a house for $7000 and household goods for $5000 for 3 years at 2% times the annual rate of 24 cents for the former and 32 cents for the latter. 2. A manufacturer paid 75 cents insurance on a building and 90 cents on stock, the former being insured for $20,000 and the latter for $80,000. a What was the insurance per year? He installed a sprinkler equip- ment at a cost of $6000. If his insurance was reduced 75% thereby, (6) how much did he save a year in excess of 6 % interest on the cost of the equipment and 6% additional allowed for its depreciation? 3. A dealer in dry goods occupied the 7th, 8th, and 9th floors of a loft building. He insured goods to the amount of $48,000 on the 7th floor, at 75 ff; to the amount of $45,000 on the 8th floor, at 80^; and to the amount of $65,000 on the 9th floor, at 85^. Find (a) the total cost of the insurance, (b) The average rate paid on the total amount insured. 456 WALSH'S BUSINESS ARITHMETIC 4. A merchant insures his goods while in a ware- house for 25 days at 19 % of the yearly rate of 72 cents. What is the premium for insurance to the amount of $25,000? 250 X .19 X $.72 Represent the number of $100 in $25,000 as 250; 19% as .19; and 72 ff as the decimal of a dollar. Write the answer. Rates for less than a year are fixed for a locality by the Board of Underwriters. The following table gives the rates for one section. Insurance generally begins at 12 M and terminates at the same hour. SHORT-TERM RATES Time % Time % Time % Time % Time % 1 da. 2 8 da. 9 15 da. 13 1 mo. 20 6 mo. 70 2 " 4 9 10 16 " 14 45 da. 27 7 " 75 3 " 5 10 10 17 " 15 2 mo. 30 8 " 80 4 " 6 11 11 18 " 16 75 da. 37 9 " 85 5 " 7 12 11 19 " 16 3 mo. 40 10 ' 90 6 " 8 13 12 20 " 17 4 mo. 50 11 " 95 7 " 9 14 13 25 " 19 5 mo. 60 12 " 100 5. A person who has taken out insurance for a year from March 3, surrenders his policy of $10,000 on the morning of April 17. If the rate was 54 cents per year, what should the insurance company return? The rate for 45 days (March 3 to April 17) being 27 % of that for a year, the company would refund 73 % of 100 times 54 cents. If the policy were surrendered on the afternoon of April 17, the company would retain 30%, the next higher rate, returning 70%. Periods other than those specified are not considered by in- surance companies using the foregoing short-term rates. FINANCING BUSINESS 457 7. An insurance company canceled policies as follows : Issued Face Term Rate Canceled a Jan. 4. 1921 $16,000 75 da. 55 1 Feb. 16, 1921 b Feb. 5. 1922 20,000 3 mo. 70ff Apr. 10, 1922 c Mar. 9, 1921 25,000 25 da. 26? Mar. 20, 1921 d Apr. (>, 1922 12,000 1 y. 32^ Sep. 30, 1922 e May 8, 1921 15,000 10 mo. 90 ji Jul. 15, 1921 Find (I) the premium originally paid on each; (II) the premium retained by the company; (III) the sum returned to the insured upon the surrender of his policy. Since the great majority of fires cause only a partial loss, most insurers take out a policy for a sum less than the value of the property insured. A man, for instance, may insure for $5000 property worth $10,000. If the policy contains no provision to the contrary, he will be reimbursed in full for any loss not exceeding $5000. CO-INSURANCE The laws of many states require that a provision similar to the following be inserted in every policy issued in these states: "This company shall not be liable for a greater pro- portion of any loss or damage to the property described herein than the sum hereby insured bears to eighty per centum (80%) of the actual cash value of said property at the time such loss shall happen. ..." This means that the holder of policy of $5000 on property worth $10,000 will receive only % of any loss he incurs not exceeding the face of the policy. To secure payment in full up to the amount of his insurance he must insure for $8000. SECTION VII BUSINESS MEASUREMENTS CHAPTER ONE COMMON TABLES A housekeeper buys milk by the quart; a dealer, by the 100 pounds. While a miller pays for wheat at a given price a bushel, the quantity is determined by the weight of the grain. Small dealers now sell by weight such vegetables as potatoes, onions, tomatoes, etc. In some states the use of dry measures in selling goods is forbidden by law. The following tables include the weights and meas- ures in common use. MEASURES OF LENGTH 12 inches (in. or ") = 1 foot (ft. or ') 3 feet = 1 yard (yd.) 5% yards = 1 rod (rd.) 320 rods = 1 mile (mi.) MEASURES OF SURFACE 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq. yd.) 30% square yards = 1 square rod (sq. rd.) 160 square rods = 1 acre (A.) 640 acres = 1 square mile (sq. mi.) 458 BUSINESS MEASUREMENTS 459 MEASURES OF VOLUME 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd) 128 cubic feet = 1 cord AVOIRDUPOIS WEIGHT 16 ounces (oz.) = 1 pound (Ib.) 2000 pounds = 1 ton (T.) 2240 pounds = 1 long ton DRY MEASURE 2 pints (pt.) = 1 quart (qt.) 8 quarts = 1 peck (pk.) 4 pecks = 1 bushel (bu.) LIQUID MEASURE 2 pints (pt.) = 1 quart (qt.) 4 quarts = 1 gallon (gal.) SIGHT EXERCISES 1. At 60 pounds of potatoes to the bushel, what should be the weight of a peck? 2. There are 231 cubic inches in a gallon. How many cubic inches are there in a quart, liquid measure? 3. A cubic foot of water weighs 1000 ounces. (a) How many pounds does it weigh? (6) Give the weight of a gallon of water, assuming that there are 7% gallons to the cubic foot. 4. A section of land is a square mile. How many acres are there in a quarter section? 5. How do two panes of glass compare in area when the dimensions of one are 6" X 8" and those of the other are each 1% times as great? 460 WALSH'S BUSINESS ARITHMETIC 6. How long does it take a soldier to travel 2% miles at the rate of 3 miles an hour? 7. When soldiers march 88 yards a minute, (a) how many minutes do they take to march a mile (1760 yd.)? (b) How many miles an hour do they march? 8. A carrier pigeon flew from Rheims to Paris, 81 miles, in 4% hours. How many miles an hour did it fly? WRITTEN EXERCISES 1. At 2150.42 cubic inches to the bushel (a) how many cubic feet are there in a bushel? (Give answer to two decimal places.) (b) How much does this differ from the approximate rate of 1.25 cubic feet? 2. Find the difference in cubic inches between IJi cubic feet and 2150.42 cubic inches. 3. At $4.8665 to the pound, find the value of 247 17s. 6d. 4. Express 4.835 miles in miles, rods, and yards. 5. Find the average height of forty boys four of whom measure 5 ft. 5 in. each; eight, 5 ft. 6 in. each; twelve, 5 ft. 7 in. each; and sixteen, 5 ft. 8 in. each. 6. A regiment made a forced march, starting at 8 A.M. It rested from 8:50 to 9, from 9:45 to 10, from 10:40 to 11, from 11:30 to 11:40, from 12:10 to 1, from 1:50 to 2, from 2:45 to 3, from 3:40 to 4, from 4:30 to 4:40, and reached its journey's end at 5:10, covering a dis- tance of 19% miles, (a) How many hours elapsed between the start and finish? (b) How much time was spent in rest? (c) Find the average rate of travel an hour while on the march. BUSINESS MEASUREMENTS 461 1 barrack bag lib. 1 mosquito bar 14 oz. 1 canvas basin 7 " 1 bedding roll 11" 12" 1 blanket 5 " 2" 1 canvas bucket 2" 1 bedsack 1 " U" 1 mosquito headnet 14" 1 lantern 2" 4" 1 pack carrier 8" 1 comb 2" 1 pkg. paper 15" 1 cake soap 6" 3 face towels 1" 7. Find the total weight of the following items of an officer's baggage in a summer campaign: 1 pr. woolen breeches 1 Ib. 9 oz. 2 " cotton drawers 1 " 11 " 1 flannel shirt 15 " 1 pr. marching shoes 2 " 10 " 5 " stockings 10 " 3 cotton undershirts 1 " 8 *' 1 clothing roll 3 " 14 " 3 handkerchiefs 2 " 1 sweater 2 " 1 poncho 3 " 13 " 1 housewife 4 " 1 mirror 6 " 1 shaving outfit 1 " 4 " 1 toothbrush and dentrifice 4 " 8. When a soldier's pace is 30 inches, (a) how many paces does he take in going a mile? (6) When he goes 3 miles in an hour, how many paces does he take in a minute? 9. How many miles does a horse walk in an hour (a) when it walks a mile in 16 minutes? (6) When it takes 120 steps of 33 inches each in a minute? METRIC MEASURES AND WEIGHTS The basis of the metric system is the meter, which is one forty -millionth of the earth's circumference pass- ing through the poles. LONG MEASURE 10 millimeters (' 10 centimeters 10 decimeters 10 meters 10 decameters 10 hectometers 1 centimeter ( cm ) 1 decimeter (***) 1 meter ( m ) 1 decameter ( dftm ) 1 hectometer (*"*) 1 kilometer ( km ) 462 WALSH'S BUSINESS ARITHMETIC The subdivisions of each metric unit are denoted by the Latin prefixes, deci, centi, milli, which indicate tenths, hundredths, thousandths, respectively. The multiples are denoted by the Greek prefixes, deca, hecto, kilo which indicate ten, hundred, thousand, respectively. The denominations in common use are the millimeter, to express the thickness of wire, for instance; the centimeter, to express the width of ribbon; the meter, to express ordinary lengths; and the kilometer to express long distances. WRITING METRIC NUMBERS To express 84 centimeters, write either 84 cm or O. m 84, just as you would write either 84 j or $0.84 to express 84 cents. To indicate 3 meters, 8 decimeters, write 3 m .80, expressing the deci- meters as centimeters; just as you would use $3.80 to express 3 dollars 8 dimes. SIGHT EXERCISES 1. The meter is 39.37 inches. Taking 40 inches as its length, how long is (a) the deci- meter? (6) The centimeter? The accompanying strip is 1 decimeter long, divided into 10 centimeters, the first of which is subdivided into ten millimeters, the others showing sub- division of 5 millimeters each. 2. Give the approximate number of centimeters to the inch. 3. About what size collar in centimeters should be BUSINESS MEASUREMENTS 463 bought in Paris by an American soldier who wears 16- inch collars? 4. About what is the bore of a 77 millimeter gun? 5. Taking the kilometer as % mile, how many miles are equal to (a) 40 kilometers, (6) 200 kilometers? 6. When the bore of a cannon measures 155 milli- meters, what is it approximately in inches? WRITTEN EXERCISES 1. An importer bought 1879 meters of silk; how many yards did he buy? 2. How many centimeters is it in width if it is 27 inches wide? 3. Find the difference between a kilometer and % mile (a) in inches. (6) In feet. 4. A merchant bought 7200 meters of silk at 12 fr. 50 a meter and sold it at $2.50 a yard. Find his profit. 5. How far does a cavalry squad travel from 7 :45 A.M. to 11:15 A.M. if it travels 2 hectometers in 2 min. 30 sec? DRY AND LIQUID MEASURE The unit for measuring liquids, grain, etc. in small quantities is the liter ( ] ). Its multiples and its sub- divisions are indicated by the prefixes used with the meter: deci, centi, deca, etc The liter may be con- sidered as a hollow cube 1 decimeter long, 1 decimeter wide, and 1 decimeter high. Grain in large quantities is sold by the hectoliter. SIGHT EXERCISES 1. There are 231 cubic inches in a gallon, (a) How many cubic inches are there in a quart? (b) How many 464 WALSH'S BUSINESS ARITHMETIC cubic inches are there in a cube 4 inches long, 4 inches wide, 4 inches high? Taking the latter as the equiva- lent of a liter, how many more cubic inches does this contain than the liquid measure quart? 2. A liter is equivalent to .908 dry quart, (a) How many quarts are there in a hectoliter? (6) About how many bushels? 3. About how many gallons are there in a hectoliter at .9463 liquid quarts to the liter? METRIC WEIGHTS The unit of weight is the gram, used in one or the other of its denominations for weighing everything from diamonds to iron ore. The prefixes are the same as in the other tables. A kilogram is the weight of a liter of water. The most commonly used denomination is the Idlo- gram (generally called a kilo). This is equivalent to 2.2046 pounds. The metric ton of 1000 kilos (the tonneau) is used in selling articles we sell by the ton. The druggist weighs some drugs in milligrams. SIGHT EXERCISED Give the difference between the long ton of 2240 pounds and the metric ton of 1000 kilos of 2.2046 pounds each. WRITTEN EXERCISE Find the weight (a) of a gallon of water (231 cu. in.) at 62.5 pounds to the cubic foot. (6) Of a quart of BUSINESS MEASUREMENTS 465 water, (c) Of a liter of water, taking 1.0567 quarts as the equivalent of a liter. SQUARE MEASURE PREPARATORY EXERCISES 1. What is the area (a) of a piece of land 12 meters long, 12 meters wide? (6) Of a piece of leather l m 2 long, l m 2 wide? (c) Of a piece 12 dm long, 12 dm wide? 2. (a) How many square decimeters are there in a square meter? (ft) How many square centimeters are there in a square decimeter? 100 square centimeters ( emq ) = 1 square decimeter ( dmq ) 100 square decimeters = 1 square meter ( mq ) 100 square meters = 1 square decameter ( dam< i) Observe that in the table of square measure there are 100 divisions of one denomination to 1 of the next higher. FARM AREAS In giving the area of a field, the term are ( a ) is used, which is equivalent to 100 square meters. The are has one multiple, the hectare ( ha ), and one subdivision, the centiare ( ca ). WRITTEN EXERCISES 1. What is the duty on 1000 tiles measuring 75 cm square at \%i per square foot. (1 sq. meter = 1.196 sq. yd.) 2. How many square yards are there in a roll of cloth 48 m long 105 cm wide? 466 WALSH'S BUSINESS ARITHMETIC 3. Find the number of pounds in a barrel of oil con- taining 45 gallons when I 1 weighs .8 kg . 4. Find the number of square yards in a square meter. 5. How many square meters are there in an acre (4840 sq. yd.)? 6. Find the number of acres (a) in an are. (6) In a hectare. CUBIC MEASURE Table 1000 cubic centimeters ( cmc ) = 1 cubic decimeter ( dmc ) 1000 cubic decimeters = 1 cubic meter ( mc ) 1000 cubic meters = 1 cubic decameter ( damc ) etc. etc. Observe in the table of cubic measure that there are 1000 divisions of one denomination to 1 of the next higher. In some countries the abbreviation for cubic meter is ( cbm ). In others, exponents are used for the. square meter ( m *) and the cubic meter ( mS ) . MEASURING FIREWOOD Firewood is sold by the stere ( 8t ), which is a cubic meter. This has one multiple, the decastere ( dast ); and one subdivision, the dedstere ( dat ). The practice of selling wood by weight is increasing. The buyer of wood by the stere or by the cord cunnot be sure of the amount of space occupied by the "voids." When he buys by weight, he requires that the wood be dry. BUSINESS MEASUREMENTS 467 WRITTEN EXERCISES 1. Find the contents in cubic meters of a tank 3. m 75 long, 2 m wide, l m .50 deep. 2. How many liters of water would this tank con- tain? 3. What would be the weight of the water in kilo- grams? 4. How many decaliters of grain would a bin of the foregoing dimensions contain? 5. Find the weight (a) of a stere of white pine as- suming that the wood occupies only 75 % of the space, and that the weight of the wood is 38 % of the weight of the same volume of water. (6) Of a stere of white oak with the same per cent of "voids," when its weight is 80 % of that of the same volume of water. 6. What is the weight of a cubic foot of each of the foregoing at the rate of 1000 ounces of water to the cubic foot? CHAPTER TWO AREAS AND VOLUMES LINES AND ANGLES A straight line (Fig. 1) keeps the same direction throughout its length. A broken line (Fig. 2) is made FIG. 1 FIG. 2 FIG. 3 up of two or more straight lines. A curved line (Fig. 3) changes its direction continually. When two straight lines meet at a point, they are said to form an angle (Fig. 4). In Fig. 5 are shown two angles formed by two lines. These are called supplementary angles. When these supplementary FIG. 4 FIG. 5 l-'Ii!. C angles are equal, each is said to be a right angle (Fig. 6). The angle in Fig. 5 that is smaller than a right angle is called an acute angle; the larger one is called an obtuse angle. The term oblique angles is used to denote those llmt are not right angles; the one in Fig. 4 and the two in Fig. 5 are oblique angles. 468 BUSINESS MEASUREMENTS 469 The size of an angle is expressed in degrees (and subdivisions). The lines forming the four equal angles in Fig. 7 at the center of the circle divide the circumference into four equal parts. As a circle con- tains 360, each portion contains 90, and eachangle is said to contain 90. FIG 7 CIRCULAR MEASURE 60 seconds (") = 1 minute ('); 60 minutes = 1 degree () ; 360 degrees = 1 circle. ORAL EXERCISES 1. How many degrees are there in the angle made by the hands of a clock (a) at 3 o'clock? (6) At 9 o'clock? 2. (a) How many degrees does the minute hand move in going from XII to III? (6) How many degrees beyond III does the hour hand move in 15 minutes? (c) How many degrees are there in the angle made by the hands of a clock at 3:15? (d) How many degrees are made by the hands of a watch at the same hour? (e) By the hands of the town-clock? DETERMINING DIMENSIONS A person that wishes to ascertain an area must know what lines to measure and how to measure. Some practice can be had about the class-room, the school building, and the grounds. A yard stick or a two-foot rule will do for the first, a steel tapeline for 470 WALSH'S BUSINESS ARITHMETIC the others. A 4-rod chain composed of 100 links is used to some extent. Some longer distances may be approximated by pacing. Each pupil should determine the length of his ordinary step: (a) by measuring a single one; and (6), by measuring the distance covered by 20 or more, and finding the average, doing this several times and comparing results. AREA OF RECTANGLE A rectangle is a quadrilateral (figure of four sides) having four right angles. By drawing a rectangle 4 inches by 3 inches and dividing it into 1 inch squares, you will see that there are 3 rows of squares, each containing 4 squares, a total of 12 squares. Since each is 1 square inch, the rectangle contains 12 square inches.. This is called its area. To find the area of a rectangle in square units, multiply its length in the linear unit by its width in the same unit. This may be stated as follows: FIG. 8 Area of rectangle = Length X Width SIGHT EXERCISES 1. Give the areas of rectangles having dimensions as follows : a 25 ft. by 96 ft. 6 88' X 99' c 64 yd. X 12% yd. d 44 rd. by 25 rd. e 98" x 32" / 66 ft. x 16% ft. BUSINESS MEASUREMENTS 471 2. What is the area, in square feet, of a rectangle (a) 12 feet long, 9 inches wide? (b) 3 yards long, 18 inches wide? Change (a) to 12 ft. X % ft. (b) 36 ft. X 1% ft. 3. Give the areas in square feet. (a) 25 ft. by 32 yd. (6) 33 yd. X 88 ft. (c) 22 yd. X 33% ft. WRITTEN EXERCISES 1. (a) How many square feet will 1416 bricks cover when each is laid on its side, which measures 4" X 2K"? (b) How many square yards will 1296 tiles cover, when each is 7 inches square? METHOD 1416 X 1 X 5 W 3 X 24 = ? (s 1296 X 7 X 7 (6) 36X36 " ? (sq ' yd ' } In (a) change 4" to K ft. and <%" to & ft. In (b) change 1" to & yd. 2. Find the area, in square yards, of a piece of carpet 89 yards long 27 inches wide. 3. How many square feet will be covered by 68 boards 18 feet long 8 inches wide? 4. Find the number of acres in a field (a) 144 rods long, 32 rods wide. (b) 320 yards long, 186 yards wide. 472 WALSH'S BUSINESS ARITHMETIC METHOD 144 X 32 320 X 186 Since there is no linear unit corresponding to the acre, indicate the area of (a) in square rods (144 X 32) and the division of this product by 160, the number of square rods in an acre. In (6) divide the product in square yards by 4840, the number of square yards in an acre. Cancel in each example. 5. A field is 924 yards long by 792 yards wide. (a) How many acres does it contain? (6) How many rods of barbed wire, 4 wires high, will be needed to inclose it? (c) How many posts 6 feet apart will be required? (d) If boards are used, how many would it take when the boards are 12 ft. long and the fence is 3 boards high? PARALLELOGRAMS A quadrilateral having its opposite sides and oppo- . y site angles, respectively equal, each \ \ to each, is called a parallelogram \ \ (FiR. 9). The area of any parallelogram is equal to that of a rectangle having the same length and width. This may be seen in Fig. 10, which shows a right triangle A(x)D out from the left side of the parallelogram and transferred to B(y)C at the right, forming the rectangle AByx. The area BUSINESS MEASUREMENTS 47S of the latter is the length of the parallelogram (AB) multiplied by its width (Ax). The width of a parallelogram is generally called its altitude, and is the perpendicular distance between the sides constituting its length. Either of the latter sides is called the base. Area of parallelogram = Length X Width This is generally stated as the product of the base by the altitude. NOTE: The line that measures the width must be perpendicular to the length. For this reason it is sometimes called the perpendicular. NAMES OF QUADRILATERALS While a rectangle is a parallelogram, a parallelogram is not always a rectangle. To distinguish between them, a rectangle is sometimes called an oblong, while the term rhomboid is used to denote a parallelogram con- taining oblique angles. An equi- lateral rectangle is called a square; an equilateral rhomboid is called a rhombus. A quadrilateral that has two parallel sides is called a tra- pezoid; one that has no sides paral- lel, a trapezium. In Fig. 11, the broken line half- way between the parallel sides represents the "average length" of the trapezoid, and the broken line perpendicular to 474 WALSH'S BUSINESS ARITHMETIC it represents the width. The average length is one- half the sum of the lengths of the two parallel sides. Area of trapezoid = l / 2 (Sum of Parallel sides x Per- pendicular) NOTE: The words "perpendicular," "altitude," and "width" have the .same meaning in these examples. DIMENSIONS OF A PARALLELOGRAM If a person desires to obtain the area of ABCD, (Fig. 13) which has opposite sides equal, and is, there- fore, a parallelogram, he may measure any convenient side as a base, say DC. In this case he will measure Bx as the perpendicular. To do this, he must locate x, the point at which a perpendicular from B will intersect the base DC. This he can approxi- mate by the use of a mounted T-- square having pins F and G, near the extremities of one arm, and N and S near the extremities of the other. Keeping on the line DC at each end of which a stake is placed, he locates the point x, by sighting B through S F and N. If he can then see D through G and F 9 and C through F and G, the hole made by the staff supporting his T-square will mark the point x. FIG. 13 t s FIG. 14 BUSINESS MEASUREMENTS 475 THE TRAPEZOID In Fig. 15, vw, one half the sum of AB and DC (the parallel sides), is multiplied by Ay (the length) or Bx to find the area of the trapezoid. Since y must be located to measure Ay, the per- pendicular between the parallel lines AB and DC, it will be unnecessary to locate v and w in field work. To check the result, x may be located and Bx measured. If these two lines are parallel, the length of vw may be determined by taking the half sum D of the parallel sides, AB and DC. In this case the length Ay is multiplied by the aver- age width, vw. TRIANGLES The accompanying figures show three triangles, ABC, DEF, and GIH, with broken lines drawn parallel FIG. 15 FIG. 18 to two sides of each triangle to form a parallelogram that has twice the area of its corresponding triangle. 476 WALSH'S BUSINESS ARITHMETIC Taking CB, FE, and HI as the respective bases of the triangles, their altitudes will be AB, Dm, and Hn, respectively. Since the area of each triangle is one-half that of the corresponding parallelogram, the area of a triangle may be thus expressed : Area of triangle = % (Base X Altitude) The triangle ABC, having a right angle at B, is called a right triangle; the other two are called oblique- angled triangles. DEF, having three angles acute, is called an acute-angled triangle; GIH, containing an obtuse angle, is called an obtuse-angled triangle. The line AC, DF, or FD, connecting the opposite angles of a parallelogram (Figs. 16-18), is called its diagonal. POWERS AND ROOTS PREPARATORY EXERCISES 1. Give the area of a square whose base measures a 5 in. b 6 ft. c 7 rd. d 9 yd. e 12 mi. / 20 m - 2. Give products : a 13 X 13 b 21 x 21 c 30 X 30 d 25 X 25 e 99 X 99 To indicate that a number is to be multiplied by itself, write above it to the right a small 2, called an exponent. The result is called the square of the number. 3. Give squares as follows: a 13 2 b 21 2 c 30 2 d 32 2 e 40 2 / 41 2 g 80 2 BUSINESS MEASUREMENTS 477 To indicate that a number is to be used three times as a factor, use 3 as an exponent. The result is called the cube of the number. 4. Give cubes as follows: a 2 3 6 3 3 c 4 3 d 5 3 e 6 3 / 7 3 g 8 3 h 9 3 i 10 3 When a number is taken 4 times, 5 times, etc., as a factor, the result is called the 4th power, 5th power, etc. SQUARE ROOT 6. Give the base of a square whose area contains a 144 sq. in. b 100 sq. ft. c 81 sq. yd. d 64 sq. mi. e 49 sq. rd. The answer to each of the foregoing requires the finding of one of the two equal factors that make the given number. This factor is called the square root of the number. The sign of square root is \/ 6. Give square roots as follows: a V25 b A/100 c \/144 d V400 e V169 / V^OO y/ indicates the cube root, V the 4th root, etc. WRITTEN EXERCISES 1. What is the side of a square plot that contains 2304 square feet? Draw a square. Since it is evident that the square root of 2304 is between 40 and 50, lay off a 1600 sq.ft.' W portion measuring 40 ft. square, K in one corner. This contains 2304 1600 sq.ft. The remainder of 1600 (4 O 2 ) the plot may be considered to OQ , yfnl comprise two rectangles each x ttvtu ft. wide, one of them being 40 ft. long and the other 40 ft. + x ft. long. The two combined form a single rectangle FIG. 19 x ft. wide and 80 ft. + x ft. long, containing 704 478 WALSH'S BUSINESS ARITHMETIC sq. ft. Since 704 contains 80 more than 8 times, try 8 as the value of x taking 88 ft. for the length of the combined rectangles and 8 ft. for the width. The product of 88 and 8 being 704, 8 is the value of x and 40 -f 8, or 48, is the length in feet of a side of the square. METHOD Divide 2304 into periods of two figures each, beginning at the Ans. 4 8 (ft) right. Write 16, the largest square 23'04 in 23, under the latter, and 4, 16 its square root, over 23. Deduct 88 704 16 from 23. To 7, the remainder, 704 annex 04. To the right of 704 write 8, twice the tens' figure of the root. Taking this as a trial divisor, divide it into 70 for the ones' figure. Try 8, writing it after the trial divisor and also after the 4 tens of the root. Multiply 88 by 8, writing the product under 704. Since the product agrees with the latter, 8 is correct, and the root is, therefore, 48. Write ft. in a parenthesis. Test by multiplying 48 by 48. 2. Find roots: a A/8281 b V5184 c 3. (a) Multiply 7. 9 by 7. 9. How many decimal places are there in the product? (b) Find the square of .29. How many decimal places does it contain? 4. Extract the square root of each of the following: a V5^29 b V.0841 c Vl3J59 d \/34ltt 6. Extract the square root of 136,161. BUSINESS MEASUREMENTS 479 METHOD Proceed as in the previous 369 Ans. example. Separate 136161 into 13'61'61 periods of two figures each. 9 Write 3 in the root and 9 under QQ 13. Subtract. Bring down 61. Take twice 3 for the first figure fi of the first trial divisor. Di- vide 46 by 6 for the second figure of the root. Note, however, that 7 times 67 would be greater than 461, and try 6, writing it in the root and annexing it to the other 6. Multiply 66 by 6, subtract. Bring down. For the second trial divisor, take twice 36, the portion already obtained, which gives 72 as the first two figures. Divide 65 by 7 for the third figure of the root. Write 9 in the root and annex 9 to 72. Multiply 729 by 9. 6. Find the root of each of the following: a V103041 b V178929 c V88804 d \/443556 THE RIGHT TRIANGLE PREPARATORY EXERCISES NOTE: In making graphs, drawing to scale, etc., the use of cross-ruled paper is very helpful and saves much time. 1. Draw three right triangles as follows: a On a scale of %" to 1', having base and perpen- dicular of 3 ft. and 4 ft., respectively. b On a scale of }{" to 1', having base and perpen- dicular of 5 ft. and 12 ft., respectively. 480 WALSH'S BUSINESS ARITHMETIC c On a scale of %" to 1', having base and perpendic- ular of 8 ft. and 15 ft., respectively. 2. Measure the hypotenuse of each triangle. The results will show that the hypotenuse in (a) will be 5 ft.; in (6), 13 ft.; and in (c), 17 ft. 3. Give the length of each in the scale drawing. Observe the following : 3 2 = 9 5 2 = 25 8 2 = 64 4 2 = 16 12 2 = 144 15 2 = 125 5 2 = 25 13 2 = 169 17 2 = 189 that is, the square of the hypotenuse is equal to the sum of the squares of the other sides. Hypotenuse 2 = Base 2 -f- Perpendicular APPLICATION OF SQUARE ROOT 1. Find the length of the missing side in each of the following triangles: . a Perpendicular, 45; base, 24; hypotenuse, ? b Perpendicular, 70; base, ?; hypotenuse, 74 c Perpendicular, ?; base, 30; hypotenuse, 78 d Perpendicular, 40; base, 42; hypotenuse, ? 2. How many rods of fence will be needed to enclose a field in the form of a right triangle having a base of 48 rods and a perpendicular of 64 rods? 3. How far from the foot of a building is the foot of a ladder 50 feet long that reaches a window 48 feet above the ground? 4. Find the diagonal of a rectangular field (Fig. 16) 165 yards long, 144 yards wide. BUSINESS MEASUREMENTS 481 AREAS OF OBLIQUE-ANGLED TRIANGLES Owing to the difficulty, at times, of measuring the altitude of a triangle, it becomes necessary, in finding its area, to use the lengths of its sides. 5. Find the area of a triangle whose sides are, respectively, 21 rods, 24 rods, and 27 rods. METHOD A/36 X (36-21) X (36-24) X 36-27 24 / 27 V 36 X 15 X 12 X 9 = A/58320 = 241.4953 36 Ans. 241.5 (sq. rd.) Take the square root of the continued product of the half sum of the three sides (36) by the difference between this half sum and each of the respective sides. 6. The following is a right triangle. Find its area by the foregoing method. Test the result by finding the half product of its base and altitude. The sides are 63 ft., 65 ft., and 16 ft. 7. The following is an isosceles triangle; that is, one having two equal sides. The sides are 29 yd., 29 yd., 40 yd. Find its area. 8. In an isosceles triangle, the unequal side is called the base. A perpendicular let fall from the opposite angle bisects the base. Find the perpendicular (alti- tude) of the triangle in the last example, and obtain its area by the use of the base and the altitude as the dimensions. 482 WALSH'S BUSINESS ARITHMETIC 9. A triangle having three equal sides is called an equilateral triangle, (a) Find the area of an equilateral triangle with sides of 100 yards. (6) Find the altitude. 10. Find the square root of the following: b Vl.6 c V.225 NOTE: In finding the square root of a decimal the latter must have an even number of decimal places. Change the foregoing to (a) \/-50; (b) \/l .60; (c) \/-2250. In pointing off a mixed decimal whose root is to be found, begin at the decimal point, and point off in two directions. AREAS OF POLYGONS A polygon of three sides is called a triangle; of four sides, a quadrilateral; of five sides, a pentagon; of six sides a hexagon; of eight sides, an octagon; etc. In the case of a regular polygon, the sides are all equal, as well as the angles. Give the name of a regular triangle. Of a regular quadrilateral. A regular polygon may be divided by lines into as many equal triangles as the polygon has sides each triangle having its apex at the center. Com- puters' tables give the number to be multiplied by the square of the length of the side to give the area. This number is .4330 for the equilateral tri- angle; 1, for the square, 2.5980, for the regular hexagon; 4.8284 for the regular octagon. To find the area of an irregular polygon, divide it into triangles, two less than the number of sides. WRITTEN EXERCISES 1. Find the area (a) of an equilateral triangle having sides of 17 feet, (b) Of a regular octagon having 6- inch sides, (c) Of a regular hexagon having sides of 11 inches. BUSINESS MEASUREMENTS 483 2. ABCD is a trapezium. To find its area, the line AC has been measured and found to be 42 rods long. The perpendiculars Bx and Dy meas- ure, respectively, 24 rods and 32 rods. Find the area of the trapezium, which is in square rods, % of (42 X 32) + K of (42 X 24). Shorten the work by multiplying Y 2 of (24 + 32) by 42. " 3. Find the sum of the areas of the two triangles in the foregoing trapezium by determining the area of each triangle from the following: In ABC: AB 34 rods, BC 20 rods, AC 42 rods " ADC: AD 40 rods, DC 26 rods, AC 42 rods Compare the two results. 4. A room is 18 feet wide, 24 feet long, and 9 feet high, (a) How many square yards are there in the ceil- ing? (b) How many square feet are there in the floor? (c) Find the number of square yards in one side wall (18' X 9 r ) . (d) In the opposite wall after the deduction of the space occupied by a door (6' 9" X 4'). (e) Find the number of square yards in an end wall, deducting for two windows, each 6' X 3'. (/) In the opposite wall, deducting for a door of the size given above. (g) Find the number of running feet of baseboard in the room, deducting the space occupied by the doors. (It) Find the number of square feet, when the base- board is 9" high. 5. Determine, by making the necessary measure- ments, (a) the number of square yards of plastering required for your classroom, (b) The number of cubic 484 WALSH'S BUSINESS ARITHMETIC feet of air space, (c) The number of square feet of floor space, (d) The area of the exposed window glass. 6. A box of window glass contains 50 square feet as nearly as possible. Find the number of panes in a box for each of the following sizes: a 6"x 8" 6 8"xlO" c 8"xl2" d 9"xl2" e 9"xl6" / 10"xl5" g 10"xl6" h 12"xl2" i 12"xl5" j 12"xl8" BOARD MEASURE Lumber is sold by the board foot. A board foot is 1 foot wide, 1 foot long, and 1 inch thick. When the thickness is less than an inch, it is taken as 1 inch. A board 12 ft. long, 1 foot wide, and 1 inch thick contains 12 board feet; if of the same length and thickness and 8 inches wide, it contains 8 board feet; 16 feet long, 6 inches wide, and 1 inch thick, 8 board feet; etc. Board feet = Feet long X feet wide X inches thick SIGHT EXERCISES 1. Give the number of board feet in planks, scant- lings, etc., having dimensions as follows: Length Width Thickness Length W'idth Thickness a 12' %' r b 16' %' 2" c 18' %' 2" d 12' %' I" DEALERS' TABLES In a dealer's tables, the number of board feet in a board, scantling, plank, joist is given, for various lengths in feet and widths and thicknesses in inches. BUSINESS MEASUREMENTS 485 Length in ft. Width and thickness in inches xi 2X6 2x9 2^X6 2^X8 3X3 3x6 4x7 4x10 8 10 12 14 16 18 2% 8 12 10 1SK 6 12 18% 26ft 2. From the foregoing dimensions give the number of board feet (a) by lines. (6) By columns. WRITTEN EXERCISES 1. Find the number of board feet in each of the following : a 2 sills, 4" X 4" X 10' 62 plates, 2" X 4" X 10' c 2 " 4" X 4" x 14' d 2 " 2" X 4" X 14' e 16 pieces, 2" X 4" X 12' for studs, rafters, roosts. 2. Draw to a convenient scale the end view of a shed 13 feet high in front, 8 feet high in the back, and 12 feet deep. Find (a) the area of the end. (6) The length of the edge of the roof, if it projects 6 inches beyond the front and the back of the shed, (c) Find the area of the roof if the length of the shed is 18 feet and the roof projects 6 inches beyond each side also. SHINGLES Shingles vary in width. A bundle of 250 shingles contains a total width of 250 times 4 inches, or 1000 inches. When shingles are laid to form a roof, each row so overlaps the under one as to leave only a 486 WALSH'S BUSINESS ARITHMETIC portion of the length of the latter exposed to the weather, generally 4 inches. Since a shingle is con- sidered as 4 inches wide, the space covered by each is 4" X 4". 3. (a) How many shingles with 4" X 4" exposed, will cover a square foot? (6) How many bundles of 250 shingles will be required for a roof 14' X 19'? (c) Find the cost of the shingles at $30 a 1000 (4 bundles of 250 each). A whole bundle must be bought for any excess. 4. How many gallons of paint will be required to paint the sides and the back of the shed in Ex. 2 at the rate of a gallon to 45 square yards for the first coat, to 50 square yards for the second coat, and to 55 square yards for the third coat? (Give results to the nearest K gallon). 5. How many hours of work will a painter require for three coats, if he takes an 8 hour day for each 100 square yards in the first coat and for each 80 square yards in the second and third coats? (Give result to nearest % day.) THE CIRCLE The circle is a plane surface bounded by a curved line called the circumference. Every point on the latter is equi-distant from a point (C) called the cento-. The line mn passing through the center of a circle and beginning and terminating in its circumference, is called a diameter. Each of the semi- diameters Co, Cm, and Cn, is called a radius. A portion BUSINESS MEASUREMENTS 487 of the circumference, om or on, is called an arc. A portion, oCm, or oCn, of the area of a circle, bounded by an arc and two radii is called a sector. The circumference of a circle whose diameter is 1 inch has been found to be 3.1416 inches. This ratio of the circumference to the diameter is expressed by the Greek letter w (pronounced pi) . Circumference = TT x Diameter You can find this ratio approximately by measuring the circumference of a cylindrical tumbler with a tape line and comparing this length with that of the diameter of the tumbler. DIAMETER AND CIRCUMFERENCE NOTE: In the following exercises take 3% as the value of TT. SIGHT EXERCISES 1. Give the diameter of the trunk of a tree when its circumference is 22 inches. 22 in. -h 3# 2. A bicycle wheel has a diameter of 28 inches. How far will the bicycle travel during one revolution of the wheel? 3. Give the circumference of a circle whose diameter is 1% inches. 4. How long will be the circumference of a circle drawn by a compass when the points are % inch apart? 5. What is the circumference of the bottom of a tent when its diameter is 7 feet? 6. Give the circumference described by the minute hand of a clock if the hand is 8 feet long. 488 WALSH'S BUSINESS ARITHMETIC WRITTEN EXERCISES 1. How many revolutions are made by a bicycle wheel in going a mile (5280 ft.) when the radius of the wheel is 28 inches? 2. What is the diameter of a circle whose circum- ference is 1 mile? 3. A circular running track is 16% feet wide, and its interior circumference is l / 2 mile. Find the length of the circumference of the outer side of the track. 4. Find the difference between the length of the circumference of a circular pond 375 yards in diameter when TT is taken as 3% and when it is taken as 3.1416. AREA OF CIRCLE WTien a circle (Fig. 22) is divided into a large num- ber of equal parts, and these are arranged as is shown // R FIG. 22 no. .in Fig. 23, they form a parallelogram whose altitude is Rj the radius of the circle, and whose base measures TT R, its semi-circumference. The area is, therefore, Area of Circle = * x Square of Radius BUSINESS MEASUREMENTS 489 WRITTEN EXERCISES 1. Taking 3% as the value of TT, find the areas of circles, as follows: a Diameter, 14 ft. 6 Radius, 21 in. c Diameter, 35 yd. 2. (a) Find the area in square yards inclosed by a circular running track having a circumference of % mile. (6) Find the area inclosed by the outer circum- ference of the track, when the width of the track is 16K feet, (c) Find the area of the track, which is the difference between (a) and (b). RECTANGULAR SOLIDS A solid having six faces, the opposite ones of which are equal and parallel, is called a parallelopipedon. When the faces are rectangles, it is called a right parallelopipedon. When the faces are equal, it is called a cube. The term solid is applied to bodies that are hollow. The volume of a solid may mean the quantity it will hold. FIG. 24. VOLUMES The number of cubic units in the volume of a rec- tangular solid is equal to the combined product of its three linear units of the corresponding kind. Volume of Rectangular Solid Length x Breadth x Height 490 WALSH'S BUSINESS ARITHMETIC SIGHT EXERCISES 1. Give the number of cubic units in the volume of each of the following rectangular solids, their dimen- sions in linear units being a 1% X 17 X 8 b 12 X 19 X 33% c 16 X 41 X 25 d 66% X 11 X 6 e 12 X 37 X 16% / 12 X 31 x 75 2. How many cubic inches will a canteloupe crate hold, when its dimensions are 12" X 12" X 22"? An orange crate measures 12" X 12" X 24"; how many cubic feet does it contain? WRITTEN EXERCISES 1. Find the number of gallons that can be contained in a tank 17 ft. 6 in. long, 12 ft. 3 in. wide, and 4 ft. 7 in. deep. Express each dimension in inches. -j^. .j , . ~ ., . \ .1 Divide by 231 (cu. in.) the contents ^ ^Av w X IT! X of a gallon. 2. Give the capacity, in bushels, of a bin measuring 24' X 16' X 14'. Take 2150.4 cubic inches to the bushel. 24 X 12 X 16 X 12 X 14 X 12 . Mu v ltip ^ eadl sion by 12 to express it 2150 ' 4 in inches. 3. How many cubic feet are there in a bale of cotton whose dimensions are 54" X 27" X 45". Give answer to nearest cubic foot. 4. How long a piece of bagging, 54 inches wide, will be required (a) to wrap the four sides of the bale? (b) To cover the two ends? (c) How much bagging BUSINESS MEASUREMENTS 491 will be saved by compressing the bale to one measuring 54" x 27" x 22}"? 5. At 55 pounds to the cubic foot, how many pounds of anthracite coal are there in a bin 6 ft. 8 in. wide, 10 ft. 6 in. long, when the depth of the coal is 4 ft. 6 in.? THE PRISM A solid having two equal and parallel faces and the remaining faces parallelograms is called a prism. One of these parallel faces is called the base of the prism. When the other faces are rectangles, the prism is said to be a right prism. A prism is designated as triangu- lar, quadrilateral, hexa- gonal, according to the number of sides in the base. THE CYLINDER The cylinder has two parallel circular bases and a curved lateral surface. The lateral surface of a prism or a cylinder, that is, the surface exclusive of that of the bases, is also called its convex surface. LATERAL SURFACE OF PRISM OR CYLINDER PREPARATORY EXERCISES A factory is making a number of hollow prisms and cylinders 20 inches high. For the lateral surface of each a strip of sheet iron is taken, 20 inches wide. FIG - FIG. 26 492 WALSH'S BUSINESS ARITHMETIC 1. Give the length of the strip required for the lateral surface of each of the following regular prisms when the length of each side of the base is 7 inches, making no allowance for overlapping: a Triangular b Square c Hexagonal 2. What is the area of the strip in each case? 3. How long must be the strip for a cylinder 14 inches in diameter? Lateral Surface of Prism (Cylinder) = Perimeter (Circumference) of Base x Height WRITTEN EXERCISES 1. How many square yards of painting are required to give three coats to the outside of a cylindrical silo 28 feet in diameter and 36 feet high? 2. Find the convex surface of a marble octagonal shaft 6 ft. 8 in. high, when each side of the base meas- ures 4 inches. VOLUME OF PRISM; OF CYLINDER Volume of Prism (Cylinder) = Area of Base x Height WRITTEN EXERCISES 1. Find the volume in cubic feet of a silo 28 feet in diameter and 35 feet high. 2. At 231 cubic inches to the gallon, find the capacity of a standpipe 42 feet high and 14 feet in diameter. BUSINESS MEASUREMENTS 493 PYRAMID AND CONE Surface The lateral faces of a right pyramid are isosceles triangles, the base of each being a side of the base of the pyramid, and the ver- tices of the triangles meet- ing at a common point called the apex. Pyramids are triangular, square, etc. The area of ABC is one-half the product of AB by BC. To make a hollow paper cone take a sector, HlyJ (Fig. 28), bring together the radii HI and H J, which , makes the arc lyJ the circumference of the base of the cone (Fig. 29). The area of the sector is one-half FIG. 27 FIG. 28 FIG. 29 the product of the arc lyJ by the radius HI. In Fig. 27 the line Ax represents the slant height of the pyramid; in the cone, Fig. 29, any straight line 494 WALSH'S BUSINESS ARITHMETIC drawn from the vertex to the circumference of the base is its slant height. SIGHT EXERCISES 1. Give the area of a lateral face of a square pyramid when a side of its base measures 24 inches and its slant height 99 inches. NOTE: Remember that the slant height of the pyramid is the altitude of a triangular face. 2. When the base is a square 50 feet on a side, and the slant height is 47% feet, give the surface of the four lateral faces. 3. WTiat is the lateral surface of a cone, the circum- ference of the base being 49 feet and its slant height 50 feet? Lateral Surface of Regular Pyramid (Cone) = % Per- imeter (Circumference) of Base x Slant Height WRITTEN EXERCISES 1. Find the lateral surface of a triangular pyramid, having a slant height of 37 yards and each side of the base 23 yards. 2. Find the entire surface of a square pyramid (including the base) when its slant height is 16^ feet, and each side of the base is 7 feet 3 inches. 3. Find the lateral surface of a cone having a base 14 feet in diameter and a slant height of 22 feet. 4. Draw a rectangle 3" X 1%". On two adjacent sides construct isosceles triangles having sides of 3%". Measure the altitude of each triangle. BUSINESS MEASUREMENTS 495 Take these sides as the scale drawing of two of the lateral faces of a rectangular pyramid having a base 24 inches by 14 inches, with edges measuring 25 inches each. Calculate the slant height of each of these faces. (a) Find the lateral surface of the pyramid, (b) Its entire surface. Volume of Pyramid. Of Cone By making a hollow pyramid of any height (alti- tude), and a prism having the same base and altitude, respectively, as the pyramid, it will be found that the prism will contain the contents of the pyramid three times. Volume of Pyramid (Cone) = % (Area of Base x Altitude) WRITTEN EXERCISES 1. Find the volume (a) of a square pyramid, each side of the base measuring 23 inches and the altitude 45 inches, (b) Of a rectangular pyramid of the same height when the sides of the base are 12 inches and 14 inches, respectively. 2. Find the volume of a cone 15 feet high, with a base 7 feet in diameter. 3. How many bushels of wheat are there in a freight car 40 feet long and 8% feet high when the depth of the grain is 5% feet? 4. How many square yards of canvas are required for a conical tent 14 feet in diameter at the base and having a slant height of 12 feet? 496 WALSH'S BUSINESS ARITHMETIC 5. (a) How many square feet of boards will be re- quired to inclose a rectangular plot 174 yards long and 126 yards wide with a rectangular fence 6 feet high? (6) How many boards 12 feet long 8 inches wide will be needed? (c) How many board feet, if the boards are 1 inch thick? 6. (a) How many square feet are there in the fore- going plot? (6) A walk 4 feet wide is made inside the fence; what is the area of the plot inside the walk? (c) How many square feet does the walk contain? (d) How many square feet are there in a 4-foot walk along the fence on the outside? 7. (a) How many square yards are there in the space covered by a wall 3 feet wide inclosing a cellar 24 feet wide and 48 feet long? (6) How many cubic yards of material are there in the wall, if the latter is 9 feet high? (c) What is the outside perimeter of the wall? (d) The inner perimeter? (e) The average of the two? 8. How many cubic feet of material are there in a sewer pipe 4 feet long whose inner diameter is 13 inches and the outer diameter 15 inches? 9. In framing a diploma that measures 18" X 12", a girl uses a cardboard "mat" that covers one inch of each side of the diploma and shows 3 inches. One inch of each side of the mat is covered by the frame, which is 2 inches wide. Find (a) the outer dimensions of the framed picture; (b) the dimensions of the mat; (c) the area of the opening; and (d) the number of running feet of frame needed, making allowance for the waste at the corners. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW Books not returned on time are subject to a fine of 50c Der volume after the third day overdue, increasing to $1.00 per volume after the sixth day. Books not in demand may be renewed if application is made before expiration of loan period. SEP . 21 1.*. SEP 4 1920 NOV 2 1920 0261 81 AO NOV 18 1920 APft 18 1921 JUN 30 1921 FEB 28 1846; /#%$. UNIVERSITY OF CALIFORNIA LIBRARY