University of California • Berkeley The Theodore P. Hill Collection of Early American Mathematics Books 1 THE PEIMAEY ARITHMETIC. DESIGNED AS A.N" INTEODUCTION TO MENTAL AND WRITTEN ARITHMETIC. BY PHILOTUS DEAK A.M. PITTSBURGH: PUBLISHED BY A. II. ENGLISH & CO. 98 FOURTH STREET. -« Entered according to Act of Congress, in the year 1860, by A. H. ENGLISH & CO., in the Clerk's Office of the District Court of the United States for the Western District of Pennsylvania. STEREOTYPED BY L. JOHNSON AND CO. PHILADELPHIA. CAXTON PRESS OF SHERMAN & CO., PHILADELPHIA. 9 PREFACE. This work is designed for those who are acquiring their first ideas of the science of Arithmetic. In its stjde and material, it is strictly elementary, and thus adapted to the capacities of children beginning the study of numbers. In its arrangement, it is strictly progressive. Commencing with the idea of natural unity, it first aims to represent to the eye the smallest assemblages of those units, to give just conceptions of such numbers as a whole, while teach- ing the art of counting, by which we gain a knowledge of those numbers. After explaining the symbols of number, called figures^ it takes the pupil, by easy steps, through the tables and exercises of the four fundamental rules. Then follow corresponding explanations and exercises in the same part of Written Arithmetic, in which he is taught to read, write, add, subtract, multiply, and divide with simple numbers, of sufficient magnitude to give him knowledge and skill in small operations. Next come Fractions, only developed enough to give the pupil their elementary ideas, and familiarity with their simple processes. Finally, he is taught and exercised upon the usual statistical tables, to give him information upon the common matters of money, weight, and measure. It is believed that the scope of this book is sufficient to prepare the pupil for easy and rapid advancement through Mental and Written Arithmetic, which should follow the study of this, in the order in which they are named. If the cause of Public Education is promoted by this little work, it will fulfill the design of its composition, and gratify the highest wishes of The Author. SUGGESTIONS TO TEACHERS. 1. It should always be borne in mind that this is the child's first book of Arithmetic, and that the work of education, if well done now, will have its greatest ef- ficiency. 2. Aim always to secure the pupil's clear comprehension of every point as he advances. Do not think repetition useless, till his answers are perfectly prompt and clear. 3. Drill the memory on the sections of the tables, in every possible order of saying them, till every statement in them is at perfect and instantaneous command. 4. Assign every task a sufficiently long time before reci- tation to have it thoroughly acquired. 5. Do not allow the pupils to use the book in recitation. 6. Use the blackboard often for explanation, as well as for the written processes of the lessons. 7. Manage the recitations of large classes so that every pupil in the class may have his interest excited in every question and process. 8. Kequire a full analysis with the answer to every question, generally following some definite form of words. 9. After the mental solution of a question, require the pupil to perform the written process, and explain it. -a PRIMARY ARITHMETIC. LESSON I. One tree and one tree are two trees. Two trees and one tree are three trees. Three houses and one house are four houses. Six balls and and and one man five men. one ball one ball are are six balls. are seven balls. Seven marks and one mark are eight marks. I I I I I I I I I I I I I I I I Eight cents and one cent are nine cents. oooooooo o ooooooooo 1* COUNTING. Nine cents and one cent are ten cents. OOOOOOOOO O OOOOOOOOOO When we count things, we notice them one by one, and think how many each one makes with those noticed before it. In counting ten things we say, one two three four five six seven eight nine ten. Note to Teachers. — Let the pupil be now exercised by counting ten visible things, such as marks on the blackboard, books, schoolmates, panes of glass in the window, &c., till he is perfect in the exercise LESSON II. Ten and one are eleven ; one more makes twelve ; one more thirteen; one more fourteen ; one more fifteen; one more sixteen; one more seventeen; one more eighteen; one more nineteen; and one more makes twenty. Now count this row of balls. One, two, &c. Note. — Let the pupil be exercised in counting twenty things, of various kinds, till perfect in his knowledge as far as twenty. Twenty and one are twenty -one ; one more makes twenty 'two ; one more twenty-three; one more twenty- four; one more twenty-five; one more tioenty-six ; one more twenty-seven; one more tw enty -eight ; one more twenty-nine ; and one more makes thirty. Now count the balls in the row above, and then keep on in th^-S row. Twenty-one, &c. From this we see that the word twenty^ with the name of a number less than ten, makes the name of a number between twenty and thirty. & COUNTING. LESSON III. Count the balls in these rows, making the names of numbers as you did from twenty to thirty. Thirty, thirty-one Forty, forty-one Fifty, fifty-one Sixty Seventy Eighty Ninety One hundred. If you count in this way as far as one hundred and ninety-nine, the next one makes two hundred. After two hundred and ninety -nine comes three hun- dred ; after three hundred and ninety-nine comes /our hundred ; and so on till you come to nine hundred and ninety-nine, when the next one makes one thousand, which is the same as ten hundred. Note to Teacheks. — Now let the pupil be exercised upon the sections of this lesson, one by one, and compare them. NOTATION. LESSON IV. When we write numbers, it is too much trouble to write them out in words. We make marks which have the same meaning as the words. These marks are called figures. NUMBERS ARABIC Printed. FIGURES. Written, ROMAN. Naught, nothing, or cipher One .... 1 4 I. Two - 2 2 II. Three - - 3 3 Ill Four - 4 A IV. Five . 6 5 V. Six - 6 6 YI. Seven . 7 7 YII. Eight Nine - 8 - 9 9 VIII. IX. Ten . 10 40 X. Eleven - - 11 44 XI. Twelve - . 12 42 XII. Thirteen - 13 43 XIII. Fourteen - 14 4j^ XTV. Fifteen - - 15 45 XV. Sixteen . 16 46 XVI. Seventeen - 17 47 XVII. Eighteen . 18 4^ XVIII. Nineteen - 19 49 XIX. Twenty - - - - 20 SO XX. What figures has twelve ? Sixteen */ Fourteen ? Seventeen? Twenty? Thirteen? Eighteen? Nineteen? The Roman figures are only used for heads of chap- ters, for the faces of clocks, &c. R ■ NOTATION. 9 LESSON V. Twenty-one - 21 S4 XXI. Twenty-two - 22 22 XXII. Twenty-three 23 23 XXIII. Twenty-four 24 Si XXIV. Twenty-five - 25 25 XXV. Twenty-six - 26 26 XXVI. Twenty-seven 27 27 XXVII. Twenty-eight 28 2^ XXVIII. Twenty-nine 29 29 XXIX. Thirty 30 30 XXX. Forty 40 iO XL. Fifty 50 50 L. Sixty 60 60 LX. Seventy 70 70 LXX. Eighty 80 ^0 LXXX. Ninety 90 90 xc. One hundred 100 400 c. Two hundred 200 200 cc. Two hundred an d six - 206 206 CCVI. Three hundred . 300 300 ccc. Four hundred . 400 MO CCCCorCD. Five hundred • 500 500 D. Six hundred . 600 600 DC. Six hundred and twelve 612 642 DCXII. Seven hundred - - 700 700 DCC. Eight hundred - . 800 ioo DCCC. Nine hundred - . 900 900 DCCCC. One thousand . . 1000 4000 M. Two thousand . . 2000 2000 MM. e 10 NOTATION AND NUMERATION. LESSOI^ [ VI. Pronounce the numbers meant by these figures. 1 16 39 55 68 71 607 5 14 31 95 86 91 706 9 27 37 79 67 73 831 6 28 30 59 76 82 138 7 28 33 89 66 80 852 4 22 35 49 98 92 258 8 29 54 99 88 90 528 3 21 44 69 96 91 582 2 26 64 47 52 97 285 15 20 94 51 77 100 963 19 24 74 40 78 105 369 11 25 84 48 87 207 639 18 38 45 50 60 212 936 12 34 75 57 61 321 1000 17 36 85 58 70 400 2016 13 32 65 56 72 505 3478 LE SSON VII. Write in figures the following numbers : — Twenty-four. Forty-two. Thirty-five. Fifty-three. Forty-seven. Seventy-four. Fifty-six. Sixty-five. Sixty-seven. Seventy-six. Seventy-eight. Eighty-seven. Eighty-nine. Ninety-eight. Twenty-five. Fifty. Fifty-two. Thirty-six. Sixty-three. Seventy. Seventy-one. Seventeen. Eighty-one. Eighteen. Forty-one. Fourteen. Fifty-one. Fifteen. Ninety-one. Nineteen. Thirty-one. Thirteen. Twenty-one. Twelve. Twenty-two. Forty-four. Thirty-three. Ninety-nine. Seventy-seven. Fifty-five. Eighty-eight. Sixty-six. Thirty-four. Forty-three. Fifty-seven. Seventy-five. Eighty. Sixty-eight. Eighty-six. One hundred and sixty. Two hundred and two. Seven hundred and four. One thousand two hundred and thirty-four. ADDITION. 11 ADDITION. LESSON I. Adding numbers is finding how much they all make when reckoned as one number. The sum of two or more numbers is that number which they all make when reckoned as one number. When we count things, one at a time, it is adding one every time to the numbers we have counted before. If we had to find the sum of several large numbers, by counting the single things one by one, it would take a long time. Hence it is best to learn and remember the sums of all small numbers, so as to help us with the large ones. Two cents and two cents are four cents. OO OO OOOO Three hats and two hats are five hats. Three cows and three cows are how many cows ? Four combs and five combs are how many combs ? Note to Teachers. — At the foot of the following pages are exercises showing the written way of working the examples. The teaclier should exercise the pupil in these processes when the lesson above them is recited. The pupil thus learns the simple methods of Written Arithmetic, while acquiring the first ideas of the science. » 12 ADDITION LESSON II. and are 1 1 and are 1 1 and are 2 1 and 1 are 2 2 and are 3 1 and 2 are 3 3 and are 4 1 and 3 are 4 4 and are 5 1 and 4 are 5 6 and are 6 1 and 5 are 6 6 and are 7 1 and 6 are 7 7 and are 8 1 and 7 are 8 8 and are 9 1 and 8 are 9 9 and are 10 1 and 9 are 10 10 and are 11 1 and 10 are 11 a 1. Frank had 1 cent, and his father gave him 1 cent more ; how many cents had Frank then ? Answer. — Two; because 1 and 1 are 2. 2. Mary gave 2 cents for an orange, and 1 cent for candy; how many cents did she spend? 3. John had 7 marbles, and his brother gave him 1 more; how many had he then ? 4. James caught 1 fish in the mill-dam, and 5 below it ; how many did he catch ? 5. While 10 birds were on a tree, another joined them; how many were there then ? 6. If you give 8 cents for a slate, and 1 cent for a pencil, how much do you give for both ? 7. If you spell 3 words wrong one day, and 1 word the next day, how many do you miss in both days ? 8. John found 9 eggs in the barn, and Jane found 1; how many did both find ? 9. How many persons are 6 girls and 1 boy? FOR THE SLATE OE BLACKBOARD. 1 2 7 1 10 Ill 6 4 1 1 1 5 1 8 3 9 1 1 ■^ ADDITION. 13 LESSON III. and 2 are 2 2 and are 2 1 and 2 are 3 2 and 1 are 3 2 and 2 are 4 2 and 2 are 4 3 and 2 are 5 2 and 3 are 5 4 and 2 are 6 2 and 4 are 6 5 and 2 are 7 2 and 5 are 7 6 and 2 are 8 2 and 6 are 8 7 and 2 are 9 2 and 7 are 9 8 and 2 are 10 2 and 8 are 10 9 and 2 are 11 2 and 9 are 11 10 and 2 are 12 2 and 10 are 12 1. In one lot are 5 cows, and in another 2 cows; how many cows are in both lots ? 2. How many children has a man who has 3 sons and 2 daughters ? 3. Ellen is 7 years old, and Horace is 2 years older; how old is Horace ? 4. There are 6 trees in the garden, and 2 in the front yard ; how many are in both places ? 5. I own 9 ducks, and Mary 2 ; how many have we? 6. David gathered 2 quarts of chestnuts, and Horace 8 ; how many did both gather ? 7. Harriet bought tape for 2 cents, and thread for 2 cents ; how much did both cost ? 8. Henry sold 4 dollars' worth of produce, and Edward 2 dollars* worth ; how much did both sell ? 9. How many are 3 apple-trees and 2 pear-trees ? 10. How many animals are 2 cows and 7 sheep? 11. What 12 things are 10 carp and 2 trout? FOR THE SLATE OR BLACKBOARD. 5 2 7 2 9 2 2 4 2 7 10 2 3 2 6 2 8 2 2 3 2 2 14 ADDITION • -» LESSON IV. and 3 are 3 3 and are 3 1 and 3 are 4 3 and 1 are 4 2 and 3 are 5 3 and 2 are 5 3 and 3 are 6 3 and 3 are 6 4 and 3 are 7 3 and 4 are 7 5 and 3 are 8 3 and 5 are 8 6 and 3 are 9 3 and 6 are 9 7 and 3 are 10 3 and 7 are 10 8 and 3 are 11 3 and 8 are 11 9 and 3 are 12 3 and 9 are 12 10 and 3 are 13 3 and 10 are 13 1. Martha visited 2 weeks at Uncle John's, and 3 at Uncle Greorge's ; how long were both visits ? 2. Julia counted 4 rooms on the first floor, and 3 on the second ; how many were on both floors ? 3. There are 6 chairs in the parlor, and 3 in the kitchen; how many chairs are in both rooms ? 4. There are 8 steps in the lower stairs, and 3 in the upper ; how many steps are in the stairs ? 5. Sarah owned 7 chickens, and David 3 chickens; how many did both own ? 6. If you earn at one time 10 cents, and at another 3 cents, how many cents do you earn in all ? 7. Harvey and Peter bought a ball; Harvey gave 5 cents and Peter 3 ; what did the ball cost ? 8. After Robert had given away 3 apples, he had 3 left ; how many had he at first ? 9. Charles traveled 9 miles by steamboat and 3 by stage ; how far did he travel ? FOB THE SLATE OR BLACKBOARD. 2 3 3 4 6 3 3 8 7 3 3 5 3 10 3 3 9 3 3 1 ADDITION. 15 LESSON V. and 4 are 4 4 and are 4 1 and 4 are 5 4 and 1 are 5 2 and 4 are 6 4 and 2 are 6 3 and 4 are 7 4 and 3 are 7 4 and 4 are 8 4 and 4 are 8 5 and 4 are 9 4 and 5 are 9 6 and 4 are 10 4 and 6 are 10 7 and 4 are 11 4 and 7 are 11 8 and 4 are 12 4 and 8 are 12 9 and 4 are 13 4 and 9 are 13 10 and 4 are 14 4 and 10 are 14 1. There are 5 houses on one side of the park, and 4 on the other ; how many are on both sides ? 2. There were 7 boys skating and 4 girls sliding on the ice ; how many were in the company ? 3. There were 10 turkeys in one flock, and 4 in an- other ; how many were in both flocks ? 4. Ann saw, from the window, 6 men in one group, and 4 in another ; how many were in both ? 5. I saw 3 doves alight on the roof, and 4 on the ground ; how many were there in all ? 6. Laura had 8 pins on the cushion, and stuck on it 4 more ; how many were on it then ? 7. Alfred gave 9 cents for a line, and 4 for a hook; how many cents did he give for both ? 8. A farmer had 4 cows in a lot, and put in 2 more; how many cows were then in the lot ? 9. If the right hand has 4 fingers, and the left 4 fingers, how many fingers have both hands ? FOR THE SLATE OR BLACKBOARD. 5 4 4 7 10 4 3 4 4 8 9 4 4 4 2 4 4 1 4 16 ADDITION. LESSON VI. and 5 are 5 5 and are 5 1 and 5 are 6 5 and 1 are 6 2 and 5 are 7 5 and 2 are 7 3 and 5 are 8 5 and 3 are 8 4 and 5 are 9 5 and 4 are 9 5 and 5 are 10 5 and 5 are 10 6 and 5 are 11 5 and 6 are 11 7 and 5 are 12 5 and 7 are 12 8 and 5 are 13 5 and 8 are 13 9 and 5 are 14 5 and 9 are 14 10 and 5 are 15 5 and 10 are 15 1. How many are 3 fingers of one hand, and the fingers and thumb of the other ? 2. How many are 4 fingers of one hand, and the fingers and thumb of the other ? 3. How many are all the fingers and thumb of one hand, and all of the other ? 4. How many are 2 fingers of one hand, and all of the other, including the thumb ? 5. How many are 1 finger of one hand, and all of the other, including the thumb ? 6. There are 7 tumblers in the cupboard, and 5 on the table ; how many are there in all ? 7. Frank counted 10 freight-cars and 5 passenger-cars in a train ; how many in all ? 8. In an omnibus, 6 persons were on one side, and 5 on the other ; how many were in the omnibus ? 9. I saw 9 barrels standing on their ends, and 5 lying on their sides ; how many in all ? FOR THE SLATE OR BLACKBOARD. 5 3 4 5 5 2 5 5 5 7 10 5 9 15 5 6 5 ADDITION. 17 LESSON VII. and 6 are 6 6 and are 6 1 and 6 are 7 6 and 1 are 7 2 and 6 are 8 6 and 2 are 8 3 and 6 are 9 6 and 3 are 9 4 and 6 are 10 6 and 4 are 10 5 and 6 are 11 6 and 5 are 11 6 and 6 are 12 6 and 6 are 12 7 and 6 are 13 6 and 7 are 13 8 and 6 are 14 6 and 8 are 14 9 and 6 are 15 6 and 9 are 15 and 6 are 16 6 and 10 are 16 1. The white cow gives 4 quarts of milk, and the red cow 6 quarts ; how much do both give ? 2. Mr. Jones had 8 trees before his house, and he planted 6 more 3 how many were there then ? 3. Sarah's mother had 6 cups and saucers, and she bought 6 more ; how many had she then ? 4. She bought 3 brooms at one time, and 6 at another ; how many in all did she buy ? 5. Carrie counted 7 large plates on the table, and 6 small ones ; how many did she count ? 6. George caught in his traps 2 mice one day, and the next day 6 more ; how many did he catch ? 7. Susan baked at one time 5 cakes and 6 pies; how many things did she bake at that time ? 8. Oscar went a fishing, and caught 9 trout and 6 perch ; how many fishes did he catch ? 9. Daniel gave 10 cents for a bottle of ink, and 6 cents for pens ; what did both cost ? FOB THE SLATE OR BLACKBOARD. 46667656 10 66 68636269 610 &- 18 ADDITION. LESSON VIII. and 7 are 7 7 and are 7 1 and 7 are 8 7 and 1 are 8 2 and 7 are 9 7 and 2 are 9 3 and 7 are 10 7 and 3 are 10 4 and 7 are 11 7 and 4 are 11 6 and 7 are 12 7 and 5 are 12 6 and 7 are 13 7 and 6 are 13 7 and 7 are 14 7 and 7 are 14 8 and 7 are 15 7 and 8 are 15 9 and 7 are 16 7 and 9 are 16 10 and 7 are 17 7 and 10 are 17 1. Oliver had 5 marbles, and bought 7 more; how many had he then ? 2. Martin saw on the wharf 9 barrels of molasses, and 7 of oil } how many barrels did he see ? 3. Ada saw at a drug-store 6 bottles in one window, and 7 in another; how many did she see? 4. John drives 3 cows to pasture, and James 7; how many cows do both drive ? 5. Anna picked 7 red apples and 7 yellow ones; how many apples did she pick ? 6. Jacob saw in a lot 10 sheep lying down, and 7 stand- ing ; how many sheep did he see ? 7. In the next lot he saw 4 cows standing, and 7 lying down ; how many cows did he see ? 8. He saw 7 swallows fly out of a barn, and 2 others fly in ; how many did he see ? 9. Mary made 8 sheets and 7 pillow-cases; how many pieces were these ? FOR THE SLATE OR BLACKBOARD. 5 7 6 7 7 10 7 2 7 1 7 7 9 7 3 7 7 4 7 8 7 ADDITION. 19 LESSON IX. and 8 are 8 8 and are 8 1 and 8 are 9 8 and 1 are 9 2 and 8 are 10 8 and 2 are 10 3 and 8 are 11 8 and 3 are 11 4 and 8 are 12 8 and 4 are 12 5 and 8 are 13 8 and 5 are 13 6 and 8 are 14 8 and 6 are 14 7 and 8 are 15 8 and 7 are 15 8 and 8 are 16 8 and 8 are 16 9 and 8 are 17 8 and 9 are 17 10 and 8 are 18 8 and 10 are 18 1. Andrew's school has 4 weeks' vacation in winter, and 8 in summer ; how many has it in a year ? 2. How many fingers are 8 fingers and 2 thumbs ? 3. Edwin dug 5 potatoes from one hill, and 8 from another ; how many did he dig from both ? 4. Seven rolls papered the dining-room, and 8 the parlor ; how many rolls did both rooms take ? 5. Mrs. Hill made 6 pounds of butter one week, and 8 the next ; how many pounds in both weeks ? 6. The family ate, in a week, 9 pounds of beef, and 8 of mutton ; how much meat was that ? 7. They ate 10 loaves of bread in one week, and 8 in another ; how many did they eat in both weeks ? 8. How many cents are 8 cents and 1 cent ? 9. John's coat has 8 buttons on the right side, and 8 on the left ; how many are on both sides ? 10. Harry brought in 3 bucketfuls of water, and Richard 8 ; how many did both bring in ? 20 ADDITION. LESSON X. and 9 are 9 9 and are 9 1 and 9 are 10 9 and 1 are 10 2 and 9 are 11 9 and 2 are 11 3 and 9 are 12 9 and 3 are 12 4 and 9 are 13 9 and 4 are 13 5 and 9 are 14 9 and 5 are 14 6 and 9 are 15 9 and 6 are 15 7 and 9 are 16 9 and 7 are 16 8 and 9 are 17 9 and 8 are 17 9 and 9 are 18 9 and 9 are 18 10 and 9 are 19 9 and 10 are 19 1. Joseph Henderson has 6 letters in the first name, and 9 in the second ; how many in both ? 2. In Elm Street are 8 gas-lights on one side, and 9 on the other; how many are on both sides ? 3. Herman planted 5 rows of beets, and 9 rows of onions; how many rows in all did he plant? 4. In the hall there are 10 hat-hooks on one side, and 9 on the other; how many are on both sides? 5. Willie learned 4 letters one day, and 9 the next; how many did he learn in both days ? 6. If you give 7 cents for a top, and 9 cents for fire- crackers, how much do both cost you? 7. Some boys, " playing soldier,'^ had 3 officers, and 9 not officers ; how many boys were playing ? 8. Nine girls were swinging, and 9 jumping the rope; how many girls were playing ? 9. Emily's father brought home 2 pounds of tea, and 9 of sugar; how much weight were both ? FOR THE SLATE OR BLACKBOARD. 6 9 5 9 4 9 3 9 2 9 9 9 8 9 10 9 7 9 9 9 1 ADDITION. 21 LESSON XI. and 10 are 10 10 and are 10 1 and 10 are 11 10 and 1 are 11 2 and 10 are 12 10 and 2 are 12 3 and 10 are 13 10 and 3 are 13 4 and 10 are 14 10 and 4 are 14 5 and 10 are 15 10 and 5 are 15 6 and 10 are 16 10 and 6 are 16 7 and 10 are 17 10 and 7 are 17 8 and 10 are 18 10 and 8 are 18 9 and 10 are 19 10 and 9 are 19 and 10 are 20 10 and 10 are 20 1. If you had 3 cents, and your father gave you a 10-cent-piece, how much would you have? 2. If you had a 5-cent-piece, and a man gave you a 10-cent-piece, how much would you have ? 3. If you had a 10-cent-piece, and earned another, how much money would you have ? 4. On New-Year's Day Ernest spent 8 cents, and Frances 10 cents; how much did both spend? 5. Christmas morning, Frank's stocking had 9 sugar- kisses, and Ada's 10; how many had both? 6. In the spring one hen came cut with 6 chickens, and another with 10; how many had both? 7. Edwin built a little oven of 10 bricks, and its chimney of 4 bricks ; how many did he use ? 8. He baked in it 2 pears and 10 apples at a time; how many things did he bake at a time ? 9. Lucius had 7 dollars, and sold his colt for 10 dol- lars ; how much money had he then ? FOR THE SLATE OR BLACKBOARD. 3 10 10 8 10 6 10 2 10 10 10 5 10 10 9 10 4 10 7 1 22 ADDITION. » LESSON XII. REVIEW '. 1. How many are 2 and 3? 3 and 2? 4 and 2? 2. How many are 2 and 4? 5 and 2? 6 and 3? 3. How many are 2 and 5? 3 and 6? 8 and 2? 4. How many are 2 and 7? 2 and 8? 7 and 2? 5. How many are 2 and 10? 9 and 2? 10 and 2? 6. How many are 2 and 9? 4 and 6? 6 and 2? 7. How many are 2 and 6? 6 and 4? 3 and 5? 8. How many are 7 and 3? 5 and 3? 3 and 7? 9. How many are 4 and 3? 3 and 8? 3 and 4? 10. How many are 8 and 3? 3 and 9? 10 and 3? 11. How many are 9 and 3? 3 and 10? 5 and 4? 12. How many are 4 and 10? 4 and 5? 10 and 4? 13. How many are 7 and 4? 9 and 4? 4 and 9? 14. How many are 4 and 7? 4 and 4? 8 and 4? 15. How many are 3 and 3? 4 and 8? 2 and 2? 16. How many are 5 and 5? 6 and 5? 5 and 6? 17. How many are 10 and 5? 5 and 8? 5 and 10? 1 18. How many are 8 and 5? 5 and 7? 9 and 5? 19. How many are 5 and 9? 7 and 5? 6 and 6? 20. How many are 10 and 6? 6 and 10? 7 and 6? 21. How many are 6 and 7? 8 and 6? 6 and 8? 22. How many are 6 and 9? 9 and 6? 7 and 7? 23. How many are 9 and 7? 7 and 9? 10 and 7? 24. How many are 8 and 7? 7 and 10? 7 and 8? 25. How many are 8 and 8? 10 and 8? 8 and 9? 26. How many are 9 and 8? 9 and 9? 10 and 9? 27. How many are 1 and 2 and 3? 28. How many are 2 and 3 and 4 ? 29. How many are 3 and 4 and 5 ? 30 How many are 4 and 5 and 6 ? 31. How many are 4 and 6 and 7 ? 32. How many are 1 and 3 and 7 and 8 ? 33. How many are 2 and 7 and 8 and 9 ? 34. How many are 10 and 10 and 5 and 3 ? » — c — a I ADDITION. 23 LESSON XIII. PROMISCUOUS EXERCISES. 1. If you give 3 cents for tape, 3 for thread, and 4 for needles, how much do you give for all ? 2. If you sell eggs for 6 cents, a cabbage for 5 cents, and currants for 5 cents, how many cents do you get for all? 3. John's hat cost 2 dollars, his shoes 2 dollars, and the rest of his suit 7 dollars; what did his whole suit cost? 4. I gave 4 dimes for spice, 2 dimes for salt, and 1 dime for pepper; how much did I give for all ? 5. Jane saw 7 swallows come out of the barn, then 5, then 3 ; how many did she see in all ? 6. Harvey went a fishing 3 times; the first time he caught 8 fishes, the next 6, and the next 3 ; how many in all ? 7. Samuel found 4 hen's nests; in the first were 2 eggs, in the next 4, in the next 7, and in the next 5; how many in all ? 8. A little girl had three names; in the first were 4 letters, in the second 7, and in the last 8 ; how many letters made her name ? 9. Nine birds were on a tree; then 6 joined them, then 5 more ; how many were then on the tree ? 10. Ten doves were on the ground, 5 on the fence, and 6 on the roof; how many in all ? 11. In Kate's garden were 8 roses, 6 pinks and 3 dahlias ; how many flowers were there ? 12. In the hall were 10 caps in one row, 8 in another, and 6 in another; how many in all? 13. In the orchard are 9 apple-trees, 7 pear-trees, and 5 plum-trees ; how many trees are these ? 14. If there are 5 fingers on the right hand, 5 on the left, 5 toes on the right foot, and 5 on the left, how many fingers and toes are there ? 24 ADDITION. « LESSON xiy. Carry out eacli following line as indicated. 1. How many are 1 and 10? land 20? 1 and 30?&c. 2 2 and 10? 2 and 20? 2 and 30? 2and40?&c. d. 3 and 10? 3 and 20? 3 and 30 ? 3 and40?&c. 4. 5 and 10? 5 and 20? 5 and 30? 5and40?&c. 5. 7 and 10? 7 and 20? 7 and 30? 7 and40?&c. 6. 8 and 10? 8 and 20? 8 and 30? 8 and 40 ? &c. 7. 9 and 10? 9 and 20? 9 and 30? 9 and40?&c. 8. land 11? 1 and 21? 1 and 31? 1 and41?&c. 9. 2 and 11? 2 and 21? 2 and 31? 2and41?&c. 10. 4 and 11? 4 and 21? 4 and 31? 4 and 41 ? &c. 11. 5 and 11 ? 5 and 21? 5 and 31? 5and41?&c. 12. 6 and 11? 6 and 21? 6 and 31? 6and41?&c. 13. 7 and 11? 7 and 21? 7 and 31? 7 and41?&c. 14. 8 and 11? 8 and 21? 8 and 31? 8 and41?&c. 15 1 and 12? land 22? land 32? 1 and42?&c. 16. 2 and 12? 2 and 22? 2 and 32? 2and42?&c. 17. 3 and 12? 3and^? 3 and 32? 3 and42?&c. 18. 4 and 12? 4 and 22? 4 and 32? 4and42?&c. 19. 6 and 2? 6 and 12? 6 and 22? 6 and 32 ? &c. 20. 8 and 2? 8 and 12? 8 and 22? 8and32?&c. 21. 9 and 2? 9 and 12? 9 and 22? 9 and 32 ? &c. 22. 1 and 3? land 13? 1 and 23? 1 and 33 ? &c. 23. 3 and 3? 3 and 13? 3 and 23? 3 and 33 ? &c. 24. 5 and 3? 5 and 13? 5 and 23? 5 and 33 ? &c. 25. 6 and 3? 6 and 13 ? 6 and 23? 6 and 33 ? &c. 26. 7 and 3? 7 and 13? 7 and 23? 7and33?&c. 27. 8 and 3? 8 and 13? 8 and 23? 8 and33?&c. 28. 9 and 3? 9 and 13? 9 and 23? 9 and 33 ? &c. 29. 2 and 4? 2 and 14? 2 and 24? 2and34?&c. 30. 3 and 4? 3 and 14? 3 and 24? 3 and34?&c. 31. 4 and 4? 4 and 14? 4 and 24? 4 and34?&c. 32. 5 and 4? 5 and 14? 5 and 24? 5and34?&c. 33. 6 and 4? 6 and 14? 6 and 24? 6and34?&c. 34. 8 and 4? 8 and 14? 8 and 24? 8 and34?&c. 35. g 9 and 4? 9 and 14? 9 and 24? 9and34?\ \>\ \>\ \,\ \>\ \,\ \,\ I Count this row by twosj saying two^ four, six, &c. If you cannot do this at first, then begin by saying the omitted number mentally, and the desirca number aloud; thus, — one, two, three, four, &c. When you have learned to do this, omit saying any number mentally, and count only by twos. Now separate this row of marks as follows : — M M I.I I.I I.I I.I I.I I.I I.I I.I I Count this row from 1, by ticosj saying one, three, jive^ seven, &c. Note to Teachers. — Make this a blackboard exercise, till the pupil can readily count a small number by twos. Care should be taken not to press it to high numbers at first, defer- ring that till the pupil is more advanced. When the blackboard exercise has become familiar, then make a pile of books, the backs and edges alternating to assist the eye, and let the pupil count them by twos, spacing them off with his fingers. Then use coins in piles of twos, desks, &c., till the art is acquired. LESSON XVII. When you add columns of figures, you should only state the results as you go, doing the addition silently in 4 the mind. Thus, in this example, you 2 should not say in full 1 and 2 are 3, 1 and 4 are 7; but thus: 1, 8, 7; and — write the last result, or sum, under the 7 line. fi — - ~~ W ADDITION. 27 (1) (2) G^) (4) (5) (6) (7) (8) (9) (10) 2 1 o 2 3 3 2 3 3 3 2 3 3 2 3 3 4 2 4 1 1 1 2 2 3 2 4 3 (11) (12) as) a4) (15) (16) (17) (18) (19) (20) 4 2 3 4 4 3 5 6 5 6 3 2 1 2 3 3 4 4 4 4 2 2 4 3 3 3 4 4 4 1 2 3 5 2 3 1 1 2 3 (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) 4 5 4 5 5 5 7 6 5 3 4 4 4 4 5 5 1 7 7 3 4 4 5 5 5 6 3 4 4 4 6 4 5 4 5 6 4 3 7 (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) 2 2 2 3 3 4 6 6 7 1 2 2 1 2 4 1 1 2 2 3 3 3 3 5 6 7 8 3 1 2 1 2 2 1 1 4 2 3 4 3 , 5 6 7 8 8 5 1 2 1 2 JL 1 1 1 2 6 (41) (42) (43) (44) m (48) (47) (48) (49) (50) 1 3 4 5 4 9 7 6 8 9 4 4 3 8 8 7 4 8 2 5 3 3 2 1 9 8 6 7 1 3 2 1 2 2 6 4 6 2 1 1 1 8 4 5 2 2 3 1 3 7 * 7 1 4 6 9 5 6 5 6 6 5 3 7 1 9 7 9 4 2 1 3 2 e 28 SUBTRACTION. SUBTRACTION. LESSON I. Subtracting from a number is making it less by taking away a part of it. When we subtract from a number, we wisb to find bow much remains after taking away a part. The remainder, or difference, is what is left after sub- tracting. 1. If 1 of two trees falls, 1 tree is left standing. One taken from two leaves how many? 2. If 1 of 3 balls is taken, how many are left ? One from three leaves how many? 3. If 2 of 4 cars be taken, how many will be left? Two from four leaves how many? 4. If 3 of 5 tumblers break, how many are whole? Three from five leaves how many ? 5. If 2 of 6 chairs are thrown down, how many re- main standing ? Two from six leaves how many? 6. Four from ten leaves how many ? SUBTRACTION. 29 LESSON 11. 1 from 0, impossible. 1 from 1 leaves from 1 leaves 1 1 from 2 leaves 1 1 from 2 leaves 1 1 from 3 leaves 2 2 from 3 leaves 1 1 from 4 leaves 3 3 from 4 leaves 1 1 from 5 leaves 4 4 from 5 leaves 1 1 from 6 leaves 5 5 from 6 leaves 1 1 from 7 leaves 6 6 from 7 leaves 1 1 from 8 leaves 7 7 from 8 leaves 1 1 from 9 leaves 8 8 from 9 leaves 1 1 from 10 leaves 9 9 from 10 leaves 1 1. Albert had, 2 chickens, and 1 of them died; how many had he left? Answer. — 1, because 1 from 2 leaves 1. 2. Julia had 5 cents, and spent 1 of them; how many cents had she left? 3. There were 7 doves on the barn, and 1 flew away; how many remained ? 4. Thomas caught 3 mice, but 1 of them escaped; how many were left ? 5. John brought home 6 eggs, but found 1 of them broken ; how many whole eggs remained ? 6. Henry had 4 apples, and gave 1 of them away; how many had he left ? 7. Lucy put 9 pins on the cushion, and then took one of them to pin her shawl ; how many remained on the cushion ? 8. There were 8 horses in a field, but 1 jumped out; how many remained in the field ? 30 SUBTRACTION. -» LESSON III. 2 from less , iqapossible. 2 from 2 leaves from 2 leaves 2 2 from 3 leaves 1 1 from 3 leaves 2 2 from 4 leaves 2 2 from 4 leaves 2 2 from 5 leaves 3 3 from 5 leaves 2 2 from 6 leaves 4 4 from 6 leaves 2 2 from 7 leaves 5 5 from 7 leaves 2 2 from 8 leaves 6 6 from 8 leaves 2 2 from 9 leaves 7 7 from 9 leaves 2 2 from 10 leaves 8 8 from 10 leaves 2 2 from 11 leaves 9 9 from 11 leaves 2 1. Sarah^s rose-bush had 4 roses, and she picked 2 of them ; how many remained on the bush ? 2. Jacob is 6 years old, and his brother 2 years old; how much older is Jacob than his brother? 3. Jane bought 8 yards of calico, and cut off 2 for aprons ; how many yards were left ? 4. There were 10 houses on one side of the street, and 2 were burned ; how many remained ? 5. Mary found 3 eggs in the hen's nest, and took 2 of them ; how many were left ? 6. There were 5 children in a family, and 2 of them died ; how many remained ? 7. There were 9 boys playing ball, but 2 of them went home; how many remained ? 8. If 7 chairs are in a room, and you take out 2 of them, how many will be left? 9. There were 11 trees in the orchard, but the wind blew down 2 of them ; how many remained ? FOB THE SLATE OR BLACKrOARD. 4 6 8 10 3 5 9 7 11 2 rk 2 2 2 2 2 2 2 2 2 SUBTRACTION. 31 LESSON IV. 3 from lesS; impossible. 3 from 3 leaves from 3 leaves 3 3 from 4 leaves 1 1 from 4 leaves 3 3 from 5 leaves 2 2 from 5 leaves 3 3 from 6 leaves 3 3 from 6 leaves 3 3 from 7 leaves 4 4 from 7 leaves 3 3 from 8 leaves 5 5 from 8 leaves 3 3 from 9 leaves 6 6 from 9 leaves 3 3 from 10 leaves 7 7 from 10 leaves 3 3 from 11 leaves 8 8 from 11 leaves 3 3 from 12 leaves 9 9 from 12 leaves 3 1. If you have 5 cents in one pocket, and 3 in another, how many more are in one than in the other ? 2. If there ^re 7 boys and 3 girls in a class, how many more boys than girls are in the class ? Answer. — As many more as 7 persons are more than 3 persons ', that is, 4 more. 3. How many more animals are in a field containing 12 cows, than in one containing 3 horses ? 4. One town is 3 miles distant, and another 9, in the same direction ; how far apart are the towns ? 5. I left home with 11 dollars, and returned with 3 dollars ; how many dollars did I spend ? 6. John caught 8 fishes, but 3 were so small that he put them back ; how many did he keep ? 7. He owed James 10 cents, and paid him 3 cents; how many cents did he still owe? 8^. A man carried 6 bushels of potatoes to market, and sold 3 ; how many had he to carry home ? FOR THE SLATE OR BLACKBOARD. 5 7 12 9 11 8 10 6 4 3 3 3 3 3 3 3 3 3 3 3 ,., ~~~~ — — — — "~~ X 32 SUBTRACTION. LESSON V. 4 from less impossible. 4 from 4 leaves from 4 leaves 4 4 from 5 leaves 1 1 from 5 leaves 4 4 from 6 leaves 2 2 from 6 leaves 4 4 from 7 leaves 3 3 from 7 leaves 4 4 from 8 leaves 4 4 from 8 leaves 4 4 from 9 leaves 5 5 from 9 leaves 4 4 from 10 leaves 6 6 from 10 leaves 4 4 from 11 leaves 7 7 from 11 leaves 4 4 from 12 leaves 8 8 from 12 leaves 4 4 from 13 leaves 9 9 from 13 leaves 4 1. Harriet had a party of 10, but 4 left early in tbe evening ; how many stayed ? 2. How many more are 6 days than 4 days ? 3. The parlor has 8 chairs, and the dining-room 4; how many more has one than the other ? 4. How many more letters has John Dascomb in his jsecond name than in his first ? 5. A man lost the thumb of one hand; how many more members had the whole hand then ? 6. Of 12 plates, 4 got broken ; how many kept whole ? 7. The upper sash has 4 panes, and the lower 4 ; how many more panes has one than the other ? 8. James caught 4 fishes one day, and 11 the next; how many more the last time than the first ? 9. His hooks cost 4 cents, and his line 13 cents ; how much less did the hooks cost than the line ? 10. Harry had 9 cents, and gave 4 for an orange; how many cents had he left ? FOR THE SLATE OR BLACKBOARD. 10 6 8 7 5 12 4 11 13 9 4 4 4 4 4 4 4 4 4 4 SUBTRACTION. 33 LESSOiN VI. 5 from less, impossible 5 from 5 leaves from 5 leaves 5 5 from 6 leaves 1 1 from 6 leaves 5 5 from 7 leaves 2 2 from 7 leaves 5 5 from 8 leaves 3 3 from 8 leaves 5 5 from 9 leaves 4 4 from 9 leaves 5 5 from 10 leaves 5 5 from 10 leaves 5 5 from 11 leaves 6 6 from 11 leaves 5 5 from 12 leaves 7 7 from 12 leaves 5 5 from 13 leaves 8 8 from 13 leaves 5 5 from 14 leaves 9 . 9 from 14 leaves 5 1. A man had 8 dollars, and paid a debt of 5 dollars; how many dollars had he left ? 2. A man owned 11 acres of land, and his neighbor 5; hpw many more had he than his neighbor ? 3. A farmer had 14 cows, but sold 5 of them when winter came ; how many had he left ? 4. A ship had a crew of 13 sailors, but 5 of them de- serted ; how many remained ? 5. Frank had 5 cents, and gave 3 cents for cake and 2 for candy ; how many had he left ? 6. A hen came out with a brood of 9 chickens, but soon 5 of them died ; how many had she left ? 7. There were 7 hooks on the hat-rack, but 5 of them broke off ; how many remained ? 8. Robert had 10 buttons on his coat, but 5 of them got pulled off; how many remained ? 9. Harry owns 6 chickens, and owes William 5 ; how many would Harry have, if he paid William ? FOR THE SLATE OR BLACKBOARD. 8 11 14 13 5 9 7 10 6 11 5 5 5 5 5 5 5 5 6 5 34 SUBTRACTION. LESSON VII. 6 from less^ impossible. 6 from 6 leaves from 6 leaves 6 6 from 7 leaves 1 1 from 7 leaves 6 6 from 8 leaves 2 2 from 8 leaves 6 6 from 9 leaves 3 3 from 9 leaves 6 6 from 10 leaves 4 4 from 10 leaves 6 6 from 11 leaves 5 5 from 11 leaves 6 6 from 12 leaves 6 6 from 12 leaves 6 6 from 13 leaves 7 7 from 13 leaves 6 6 from 14 leaves 8 8 from 14 leaves 6 6 from 15 leaves 9 9 from 15 leaves 6 1. How much more does a pine-apple cost, at 12 cents, than an orange at 6 cents ? 2. A boy earned 10 cents one day, but spent 6 of them for food ; how many did he clear ? 3. Annie spelled 6 words of her lesson, and Lucy 8 ; how many more did Lucy spell than Annie ? 4. Mary had 15 cents, and spent all but 6 of them ; how many did she spend ? 5. A boy put 11 cents in his " savings-bank-box,^' and then got out 6 ; how many remained ? 6. John had 14 hills of corn, and the hens scratched up all but 6 ; how many did they scratch up ? 7. If school is kept 9 months in the year, and 6 are gone, how long is school yet to be kept ? 8. There were 7 pins on the cushion, and Jane took 6 of them ; how many remained ? 9. There were 13 pupils in the spelling-class, and 6 of them were girls ; how many were boys ? FOR THE SLATE OR BLACKBOARD. 12 10 8 15 11 14 9 7 13 6 6 _ 6 6 6 6 6 6 6 6 6 SUBTRACTION. 85 LESSON VIII. 7 from lesS; impossible. 7 from 7 leaves from 7 leaves 7 7 from 8 leaves 1 1 from 8 leaves 7 7 from 9 leaves 2 2 from 9 leaves 7 7 from 10 leaves 3 3 from 10 leaves 7 7 from 11 leaves 4 4 from 11 leaves 7 7 from 12 leaves 5 5 from 12 leaves 7 7 from 13 leaves 6 6 from 13 leaves 7 7 from 14 leaves 7 7 from 14 leaves 7 7 from 15 leaves 8 8 from 15 leaves 7 7 from 16 leaves 9 9 from 16 leaves 7 1. I started to ride 10 miles, but, after going 7, my carriage broke down ; how far had I yet to go ? 2. I ordered 12 loads of coal; after 7 had been de- livered, how many were yet to come ? 3. A merchant bought 14 barrels of molasses ; after he had sold 7 of them, how many remained ? 4. He bought 16 pounds of spice; after he had sold 7 pounds of it, how many remained ? 5. Thirteen boys chose sides at ball ; after 7 had been chosen, how many were to be chosen ? 6. One side got 8 runs, and the other got 7; how many more did one side get than the other ? 7. Eleven boys chose a captain; after 7 had voted, how many were yet to vote ? 8. James got 15 blocks at the carpenter's, and Helen 7 ; how many more did James get than Helen ? 9. From a 9-gallon keg of syrup, I drew 1, 2, 1, and 3 gallons ; how much remained ? FOB THE SLATE OR BLACKBOARD. 10 12 14 16 13 8 11 15 9 7 7 7 7 7 7 7 7 7 7 7 36 SUBTRACTION. LESSON IX. 8 from lesSj impossible. from 8 leaves from 8 leaves 8 from 9 leaves 1 1 from 9 leaves 8 f>om 10 leaves 2 2 from 10 leaves 8 from 11 leaves 3 3 from 11 leaves 8 from 12 leaves 4 4 from 12 leaves 8 from 13 leaves 5 5 from 13 leaves 8 from 14 leaves 6 6 from 14 leaves 8 from 15 leaves 7 7 from 15 leaves 8 from 16 leaves 8 8 from 16 leaves 8 from 17 leaves 9 9 from 17 leaves 8 1. If school has 12 weeks* vacation in a year, and one vacation is 8 weeks, how long is the other ? 2. The parlor has 15 yards of carpet, the chamber 8 ; how many more has one than the other ? 3. Mary's mother baked 9 • loaves and 8 pies ; how many more loaves than pies did she bake ? 4. Susan bought 16 sheets of paper; after she had used 8, how many had she left ? 5. John traded with 8 cents till he had 1 7 cents ; how many cents did he make by trading ? 6. Alfred gave 8 cents for a sled, and sold it for 8 cents ; how much did he make ? 7. George bought a knife for 14 cents, and sold it for 8 cents ; how much did he lose ? 8. Charles bought a ball for 10 cents, and sold it for 8 cents ; how much did he lose ? 9. If you begin business with 8 cents, and leave off with 13 cents, how much do you make ? SUBTRACTION. 37 LESSON X. 9 from less^ impossible. 9 from 9 leaves from 9 leaves 9 9 from 10 leaves 1 1 from 10 leaves 9 9 from 11 leaves 2 2 from 11 leaves 9 9 from 12 leaves 3 3 from 12 leaves 9 9 from 13 leaves 4 4 from 13 leaves 9 9 from 14 leaves 5 5 from 14 leaves 9 9 from 15 leaves 6 6 from 15 leaves 9 9 from 16 leaves 7 7 from 16 leaves 9 9 from 17 leaves 8 8 from 17 leaves 9 9 from 18 leaves 9 9 from 18 leaves 9 1. There was a row of 10 cars, and the engine took away 9 of them ; how many were lefl ? 2. If you trade a sled at 15 cents, for a ball at 9 cents, and money, how much money must you get ? 3. There were 12 panes in a window, and the hail broke 9 ; how many remained whole ? 4. Edward set a trap and caught 9 out of a flock of 17 pigeons ; how many escaped ? 5. Anna had 14 beads, but the string broke and she lost all but 9 } how many did she lose ? 6. There were 11 gas-lights in the street, but the wind blew out 9 ; how many kept burning ? 7. A fleet of 16 vessels went to sea, but a storm de- stroyed all but 9 'j how many were lost ? 8. One of them had 18 persons on board, but only 9 reached shore ; how many were lost ? 9. Another had 13 persons on board, and 9 were lost; how many reached land ? FOR THE SLATE OR BLACKBOARD. 10 15 12 17 14 11 16 18 13 9 9 9 9 9 9 9 9 9 9 9 38 SUBTRACTION. LESSON XL 10 from less , impossible. 10 from 10 leaves from 10 leaves 10 10 from 11 leaves 1 1 from 11 leaves 10 10 from 12 leaves 2 2 from 12 leaves 10 10 from 13 leaves 3 3 from 13 leaves 10 10 from 14 leaves 4 4 from 14 leaves 10 10 from 15 leaves 5 5 from 15 leaves 10 10 from 16 leaves 6 6 from 16 leaves 10 10 from 17 leaves 7 7 from 17 leaves 10 10 from 18 leaves 8 8 from 18 leaves 10 10 from 19 leaves 9 9 from 19 leaves 10 1. A merchant sold at 10 cents, muslin marked 12 cents a yard ; how much reduction did he make ? 2. Of 14 officers, only 10 answered at roll-call after a battle; how many were missing ? 3 A farmer had 19 sheep, and the dogs killed all but 10 of them; how many did they kill ? 4. He had 18 chickens, and a fox killed 10 of them; how many chickens had the farmer then ? 5. A owes B 16 dollars, and B owes A 10 dollars; how much must A pay to B when they settle ? 6. At another time B owed 17 dollars to A, and A 10 dollars to B ; which must pay, and how much ? 7. If C owes D 11 dollars, and D owes C 10 dollars, which pays, at settlement, and how much ? 8. If you owed 15 cents, and paid 10 cents, how many cents would you still owe? 9. If you had 13 cents, and owed 10 cents, how many cents would you have clear of debt ? FOR THE SLATE OR BLACKBOARD. 12 14 19 18 16 17 11 15 13 10 10 10 10 10 10 10 10 10 10 10 SUBTRACTION. 39 LESSON XII. REVIEW. 1. 6 from 12 leaves how many ? 7 from 12? 2. 5 from 12 ? 8 from 15 ? 9 from 10 ? 3. 7 from 15 ? 10 from 15 ? 5 from 9 ? 4. 8 from 12 ? 4 from 9 ? 4 from 12 ? 5. 7 from 11 ? 3 from 7 ? 4 from 11 ? 6. 4 from 7 ? 9 from 18 ? 2 from 11 ? 7. 6 from 15 ? 5 from 14 ? 4 from 7 ? 8. 5 from 8 ? 6 from 9? 7 from 10 ? 9. 3 from 8 ? 8 from 13 ? 9 from 15 ? 10. 2 from 8 ? 2 from 10 ? 10 from 18 ? 11. 8 from 10 ? 8 from 16 ? 10 from 13? 12. 9 from 12 ? 8 from 11 ? 3 from 6 ? 13. 1 from 3 ? 4 from 6 ? 6 from 8 ? 14. 10 from 12 ? 7 from 13 ? 8 from 13 ? 15. 9 from 13 ? 6 from 13 ? 5 from 13 ? 16. 4 from 13 ? 3 from 13 ? 6 from 11 ? 17. 5 from 11 ? 9 from 11? 3 from 11 ? 18. 3 from 10 ? 4 from 10? 5 from 10 ? 19. 6 from 10 ? 3 from 9? 7 from 9 ? 20. 9 from 9 ? 8 from 8? 7 from 7? 21. 6 from 6 ? 5 from 5? 4 from 4? 22. 3 from 3 ? 2 from 2? 1 from 1 ? 23. If only 7 apples were in a basket, could you get 8 apples out of it ? Why ? 24. If you take 8 from 14, the difference is the same as if you took .5 from what ? Ten from what ? 25. From what must you take 9, to have the same difference as 6 from 14 gives ? 26. From what must you take 8, to have the same difference as 9 from 18 gives ? 27. From what must you take 9, to have the same difference as 10 from 17 gives ? Seven from 14 ? 28 Nine from 14 leaves how many ? Ten from 19 ? 29. Two and 3 are the same as 4 from what? ^ g 40 SUBTRACTION. LESSON XIII. PROMISCUOUS EXERCISES. 1. If you have 10 cents, and give 3 for an orange, and 2 for a lenion, how many cents have you left? 2. Jane had 15 cents, and gave 6 for needles, and 3 for thread ; how many cents had she left ? 3. John earned 8 cents one day, and 10 cents the next day; he then spent 7 cents for paper, and 5 cents for pens ; how many cents had he left '/ 4. Four birds alighted on a tree, then 7 more; then 3 flew off, followed by 5 ; how many remained ? 5. There were 6 boys and 7 girls in a party; when 3 boys had left, each with a girl, how many persons re- mained ? 6. If you buy 12 sheets of paper, how many have you loft after using 9 of them ? 7. If there are 16 pupils in a school, and 5 boys and 4 girls are called out to spell, how many pupils stay in / their seats ? 8. There were 8 houses on one side of a certain street, and 6 on the other; after a fire, 4 were left on one side, and 3 on the other; how many were burned ? 9. A shoemaker had 8 pairs of boots, and 9 pairs of shoes ; he sold all the shoes, and 3 pairs of boots ; how many pairs had he left ? 10. If you have only a ten-cent-piece and a five-cent- piece, can you buy and pay for a thing which costs 20. cents ? Why ? 11. If you had 18 cents, and paid 6 cents for fare in a car, and 5 cents for cake, how many cents would you have left ? 12. If you had 15 cents, and spent 9 cents at one time, and 6 at another, how many would you have ? 13. If you earn 20 cents, and spend 15, are you richer than le who earns 10 cents and spends 5? 14. Seven and 2 are the same as 3 from what ? iS — SUBTRACTION. S9 41 LESSON XIV. Carry out each followinor line as indicated. 1. How many are 1 from 10 ? 1 from 20? lfrom30?&c. 2. 2 from 10? 2 from 20? 2 from 30? 2from40?&c. 3. 3 from 10? 3 from 20? 3 from 30 ? 3from40?&c. 4. 4 from 10? 4 from 20 ? 4 from 30? 4 from 40 ? &c. 6. 5 from 10? 5 from 20? 5 from 30? 5from40?&c. 6. 6 from 1^? 6 from 20 ? 6 from 30? 6from40?&c. 7. 7 from 10? 7 from 20? 7 from 30 ? 7from40?&c. 8. 8 from 10? 8 from 20? 8 from 30? 8from40?&c. 9. 9 from 10? 9 from 20? 9 from 30 ? 9from40?&c. 10. 2 from 11 ? 2 from 21 ? 2 from 31? 2from41?&c. 11. 3 from 11? 3 from 21? 3 from 31? 3 from41?&c. 12. 4 from 11? 4 from 21 ? 4 from 31? 4from41?&c. 13. 5 from 11? 5 from 21? 5 from 31? 5 from 41 ? &c. 14. 6 from 11? 6 from 21? 6 from 31 ? 6 from 41 ? &c. 15. 7 from 11 ? 7 from 21? 7 from 31? 7from41?&c. 16. 2 from 2? 2 from 12? 2 from 22? 2from32?&c. 17. 3 from 12? 3 from 22? 3 from 32? 3from42?&c. 18. 4 from 12? 4 from 22 ? 4 from 32 ? 4from42?&c. 19. 5 from 12? 5 from 22? 5 from 32? 5from42?&c. 20. 6 from 12? 6 from 22? 6 from 32 ? 6from42?&c. 21. 8 from 12? 8 from 22? 8 from 32? 8from42?&c. 22. 3 from 3? 3 from 13 ? 3 from 23 ? 3from33?&c. 23. 4 from 13? 4 from 23? 4 from 33? 4from43?&c. 24. 5 from 13? 5 from 23? 5 from 33? 5from43?&c. 25. 6 from 13 ? 6 from 23? 6 from 33 ? 6from43?&c. 26. 7 from 13? 7 from 23? 7 from 33 ? 7from43?&c. 27. 8 from 13? 8 from 23? 8 from 33? 8from43?&c. 28. 9 from 13? 9 from 23 ? 9 from 33 ? 9from43?&o. 29. 2 from 4? 2 from 14? 2 from 24? 2from34?&c. 30. 3 from 4? 3 from 14? 3 from 24? 3from34?&c. 31. 4 from 4 ? 4 from 14? 4 from 24? 4from34?&c. 32. 5 from 14 ? 5 from 24? 5 from 34? 5from44?&c. 33. 6 from 14? 6 from 24? 6 from 34? 6from44?&a 34. 7 from 14? 7 from 24? 7 from 34? 7from44?&c. 35. g 8 from 14? 8 from 24? 8 from 34? 8from44?&c. 4* 42 SUBTRACTION. LESSON XV. 1. How many are 2 from 5 ? 2 from 15 ? &c. 2. 3 from 5? S from 15? 3 from 25? 3 from 35?, tc. 3. 4 from 5? 4 from 15? 4 from 25? 4from35?&j. 4. 5 from 5 ? 5 from 15 ? 5 from 25 ? 5 from 35 ? &c. 5. 6 from 15? 6 from 25? 6 from 35? 6from45?&c. 6. 7 from 15? 7 from 25? 7 from 35? 7from45?&c. 7. 8 from 15? 8 from 25? 8 from 35? 8from45?&c. 8. 3 from 6? 3 from 16? 3 from 26? 3from36?&c. 9. 4 from 6? 4 from 16? 4 from 26? 4from36?&c. 10. 5 from 6? 5 from 16? 5 from 26? 5from36?&c. 11. 6 from 6? 6 from 16? 6 from 26? 6from36?&c. 12. 7 from 16? 7 from 26? 7 from 36? 7from46?&c. 13. 8 from 16? 8 from 26? 8 from 36? 8from46?&c. 14. 2 from 7? 2 from 17? 2 from 27? 2from37?&c. 15. 3 from 7? 3 from 17? 3 from 27? 3from,37?&c. 16. 4 from 7? 4 from 17? 4 from 27? 4from37?&c. 17. 5 from 7? 5 from 17? 5 from 27? 5from37?&c. 18. 6 from 7? 6 from 17? 6 from 27? 6from37?&c. 19. 7 from 7? 7 from 17? 7 from 27? 7from37?&c. 20. 8 from 17? 8 from 27? 8 from 37? 8from47?&c. 21. 2 from 8? 2 from 18? 2 from 28? 2from38?&c. 22. 3 from 8? 3 from 18? 3 from 28? 3from38?&c. 23. 4 from 8? 4 from 18? 4 from 28? 4from38?&c. 24. 5 from 8? 5 from 18 ? 5 from 28? 5from38?&c. 25. 6 from 8? 6 from 18? 6 from 28? 6from38?&c. 26. 7 from 8?*^7froml8? 7 from 28? 7from38?&c. 27. 8 from 8? 8 from 18? 8 from 28? 8from38?&c. 28. 9 from 18? 9 from 28? 9 from 38? 9from48?&c. 29. 2 from 9? 2 from 19? 2 from 29? 2from39?&c. 30. 3 from 9? 3 from 19? 3 from 29? ^from39?&c. 31. 4 from 9? 4 from 19? 4 from 29? 4from39?&c. 32. 5 from 9? 5 from 19? 5 from 29? 5from39?&c. 33. 6 from 9? 6 from 19? 6 from 29? 6from39?&c. 34. 7 from 9? 7 from 19? 7 from 29? 7from39?&c. 35. 8 from 9? 8 from 19? 8 from 29? 8from39?&c. 36. 9 from 9? 9 from 19? 9 from 29? 9from39?&c. SUBTRACTION. 43 LESSON XVI. COUNTING DOWNWARD. Courting downward is a process of subtraction. If you begin at 20, and count thus, — 20, 19, 18, &c., — ^you mean that, by taking 1 from 20, 19 are left; and 1 from 19 leaves 18, &c. You can find, in this way, the number of a thing in its order in a certain collection of things. Thus, you can say, in counting 20 things dow^awards, 20th, 19th, 18th, &c., as though they had first been counted and numbered the other way. Now make twenty marks upon the slate or blackboard, and count them downward, after first counting them upward. Now separate the twenty marks into twos with commas; thus — I \\\ M \,\ \,\ \,\ \,\ \,\ \,\ \,\ I Count this row by twosj saying two, four, &c., up to twenty. Then begin at twenty^ and count downward by twos. Now separate this row of marks as follows : — I. I I. I i> I i> I i> I i. I I. I i> I i> I i> I I Count this row from 1, by twos, saying one, three, &c. Then begin at twenty-one, and count downward by twos. When you have learned to count thus with 20 marks, make a greater number of them, and proceed in the same way, as far as a hundred. Note to Teachers. — Make this a blackboard exercise, till the pupil can readily count downward both by ones and twos. Care should be taken not to press it to high numbers at first. When the blackboard exercise has become familiar, use, as counters, books, desks, persons, coins, &c., till the art is acquired. I -^ 44 MULTIPLICATION. MULTIPLICATION. LESSON I. If you write the same number two or more times, you are said to repeat that number. By multiplication we find the sum of the repetitions of a number, without adding them. 1. If you pay I cent each time you cross a bridge, and you cross 3 times, how many cents do you pay ? Answer 1 ^"® ^^^^ *^^ °°^ ^^^^ ^^^ ^^^ ^®°' *^® three cents. BY Audition j © O © ©©© Answer by Multiplication. Three; because three times I are 3. 2. How many gloves are there in 4 pairs ? Si m Si fis Ans. Eight. Four times 2 gloves are 8 gloves. 3. Four times 3 men are how many men ? p VJ In m m I]] iM VJ 1 it a n li a it li 4. Three times 4 men are how many men ? 5. Four times 5 balls are how many balls ? ##### (i)#i)#/\iHT 1 r-i t. When there is a /rzaZ 102) 310845 (3047 | 51 Rem. remainder, it may beVrit- ten by itself, as a remainder, 102) 310845 (3047 AV ^^ ^^ "^^^ ^^ P^^ ^^ ^^^ ^^S^^ / *^ hand of the quotient, with the divisor under it. ao) 123) 62313 ( , (20) 234) 142100 ( (21) 345) 244309 ( (22) 456) 75361 ( (23) 567) 84036 ( (24) 678) 90062 ( (25) 789) 163598 ( (26) 891)402006( (27) 982) 563365 ( <28) 873) 701803 ( (29) 705) 340062 ( (30) 604) 470309 ( (31) 180) 57026 ( (32) 290) 129067 ( (33) 370) 182089 ( (34) 460) 300300 ( ® (35) 550) 400567 ( (36) 640) 128871 ( s -m 88 FRACTIONS. FRACTIONS. LESSON I. 1. If a stick of candy is divided into 2 equal parts, wliat is one part called ? Ans. — One-half. One-half. One-half. How many halves has any thing? Ans. — Two. 2. If a stick is divided into 3 equal parts, what is one part called ? Ans. — One-third. What are two parts called ? Ans. — Two-thirds. OneAhird. OneAhird. One-third. IgOgOgLlgOgOgL '2gL-2gL'2gLlgOgOgL IgOgOgOgOgOgL How many thirds has any thing ? Ans. — Three. 3. If a stick is divided into 4 equal parts, what is one part called ? Ans. — One-fourth. What are three parts called ? Ans. — Three-fourths. One-fourth. One-fourth. One-fourth. One-fourth. :^^^^ igag^gLigL igogogagL igagog^j^ How many fourths has any thing ? Ans. — Four. 4. If a stick is divided into 5 equal parts, what is one part called ? Ans. — One-fifth. What are two parts called ? Ans. — Two-fifths. Three parts ? Ans. — Three-fifths. Four parts ? Ans. — Four-fifths. One-fifth. One-fifth. One-fifth, One-fifth. One-fifth. IgOgLlgL IgOg^I^L IgOgO^ IgOgOg^ IgOgOgL How many fifths has any thing ? Ans. — Five. 5. If a stick is divided into 6 equal parts, what is one part called ? Ans. — One-sixth. Five parts ? Ans. — Five-sixths. One-sixth. One-sixth. One-sixth. One-sixth. One-sixth. One-sixth. IgOgOgL igagL'^L igagogL igogagL ig^gog?: IgOgOgL How many sixths has any thing ? Ans. — Six. How many sevenths has any thing ? Ans. — Seven. ffi- FRACTIONS. 89 LESSON II. A FRACTION is a number expressing one or more parts of a unit. In writing a fraction, we write above a line the num- ber of parts we mean to express, and below the line the number of these parts in a unit. Thus — One-half One-third One-fourth One-fifth &c. One-sixth J One-seventh ^ One-eighth | One-ninth ^ &c. 4 Three-tenths Four-elevenths j-j Five twenty-seconds ^^^ Ten twenty-firsts ^^ &c. In a fraction the number below the line is called the denominator, (that is, the namer,) because it names the parts into which the unit is supposed to be divided. In a fraction the number above the line is called the numei'ator, (that is, the number er,) because it states the number of parts expressed by the fraction. Pronounce the followinoc fractions : — 2 . 3 > ^ . 4 f 4 . ^) 5 . E> 6 . 1) 7 . 146 . 3Z1> SI . 2 . 2 . 2 . 2 . 2 . 2 . 2 . -E> T > VP T3> IZi 7t; 79; 23; 3 . 3 . 3 . 3 . 3 . 3 . 3 • Sf H > tt; 21; 37; 42; /?; 4 . 4 . 4 . 4 . 4 . 4 . "5 f TO f 71; 17; -B^y 03 ; 74; & . 5 . 5 . 5 . 5 . 5 . ^ f H f 73 ; Z^J 52" ; 7?; B€f; ■gg; j\; A; 3%} A; 6%; 6 . 56 ; iS) B%; 7 . 17 . 2^ . 37 . 47 . 57 . 67 . 77 . -65) V^) "3^; 44 ; Z5) 69 ; 5H ; 59; 207 . 275 . 42 2 . fif; 7 27 . 9 4 1 4 0T^ III; III; 333 ; 14^; SS9; ?47- Write in figures the following fractions : — Two-sevenths; three thirty-thirds; six forty-firsts; twenty-five thirty-seconds ; seventeen nineteenths ; eight forty-fifths; ten twentieths; twenty thirtieths; thirty forty-sevenths; forty fifty-eighths; six sixty-seconds; two twenty-ninths ; fifty-one seventy-fourths ; seventy-six eighty-sixths. 8* 90 FRACTIONS. LESSON III. A MIXED NUMBER is composed of one or more units, and a fraction. The fraction is written at the right hand of the units ; thus — Three and one-half is written 3^. Four and one-third is written 4|. Six and two-fifths is written 6|. Ten and three-eighths is written 10|. Fifteen and two-ninths is written 15|. Pronounce the followin^: mixed numbers :• Two and five-sevenths. Six and one-half. Four and two-thirds. Five and eight-ninths. Three and one-tenth. Seven and two-fifths. Eight and one-fourth. Nine and five-sixths. Ten and four-elevenths. One and one-twelfth. Thirteen and nineteen twenty-fifths. Seventeen and fifteen-thirtieths. Nineteen and seven teen-fortieths. Twenty-seven and eight fifty-firsts. Thirty- two and nine sixty-seconds. Eighty- three and fifty-one fifty-thirds. Seventy and eighty eighty-eighths. Sixty and ninety ninety-ninths. Fifty and fifty-one lOlsts. Forty and thirty-two 502ds. Fourteen and fourteen 803ds. Twenty-five and twenty-four 125ths. Eighty and eight llSths. & FRACTIONS. 91 LESSON IV. 1. How many halves have 3 apples? Ans. — 6 lia,Ves. Two halves. Two halves. Two halves. dD 3D U If 1 apple has 2 halves, 3 apples have 3 times 2 halves, that is, 6 halves. 2. How do we find how many halves a numher has ? Ans. — Bi/ multiphjing the numher hy 2. 3. How many halves in 4 ? 6 ? 7 ? 9 ? 10 ? &c. 4. How many thirds in 5 oranges ? Ans. — 5 times 3 thirds, that is 15 thirds. 5. How many thirds in 2 ? 3 ? 4 ? 6 ? 7 ? &c. 6. How many fourths in 2 ? 3 ? 4 ? 5 ? 6 ? &c. 7. How manj fifths in 2 ? 3 ? 4 ? 5 ? 6 ? &c. 8. How many sixths in 2 ? 3 ? 4 ? 5 ? 6 ? &c. 9. How many sevenths in 2? 3? 4? 6? 6? &c. 10. How many eighths in 2 ? 3 ? 4 ? 5 ? 6 ? &c. 11. How many ninths in 2? 3? 4? 5? 6? &c. 12. How many to/As in 2 ? 3? 4? 5? 6?&c. 13. How many halves in 3 J pears ? Ans. — 3 pears have 6 halves, and a half-pear is 1 half more, that is, 7 halves. 14. How many thirds in 5f pears ? Ans. — 5 pears have 15 thirds, and two-thirds more are 17 thirds. 15. How many halves in 41 ? 5| ? 6 i ? 7i ? &c. 16. How many thirds in l| ? 2i ? 3| ? 4| ? &c. 17. How many fourths in 1| ? 21 ? 31 ? 4| ? &c. 18. How many //ifAs in 1^ ? 1§? If? l|?&c. 19. How many sixths in 1^ ? 2| ? 3| ? 4| ? &c. 20. Ho^ many sevenths in r^? 2f? 3f ? 4f ? &c. 21. How many eighths in 1| ? 2| ? 3| ? 5| ? &c. Work out on the slate or blackboard that 45| are 272 83| are ^p 142i are 8|3 418| are 33^47 562 1 are 45^01 6215 are^V^ 804-p3- are 8|17 975y% are ^\\^^ 423/^ are ^771 92 FRACTIONS. LESSON V. 1. How many whole apples in 6 half-apples ? Ans. — Since 2 halves are 1 whole apple, 6 halves are as many apples as 2 halves are contained times in 6 halves ; that is, 3 whole apples. I? \^? ^/? ^^'^? &C, I ? L^ ? L6 ? 2_0 ? 2^4 ? &c. 5. How many units in K^ ? U ? %o ? 25 ? so ? &c. 6. How many units in ^^^ ? \^ ? ^ ? 3^0 ? 3^6 ? &c. 2. How many units in 3. How many units in 4. How many units in ; I? 6? 7. How many units in ^^^ ? 28? V? 8. How many units in 3^2 ? 4^8 ? 6^4 ? 8^0 ? 7^2 ? 9. How many units in \'7? 4^5? 6^3? 5^4? 8^1 ? &c. 10. Howmanyunitsin |g? fg? fg? |o? |o? &c. 11. What is one-half of 10? Ans. — 5. We find one-half of a number hy dividing it by 2. V? 'V?&c. 12. What is 13. What is 14. What is 15. What is 16. What is 17. What is 18. What is 19. What is 20. What is ^ 21. What is 1 I of iof ^of 4 of I of iof Vof I of ? 12? 15? 24? 8? 24? 20? 35? 30? 24? 21? 28? 32? 72? of 6? 8 9? 16? 10? 18? 42? 64? 81? 72? 45? 20? 30? 40? 12? 18? &c. 27?&c. 36? &c. 40? &c. 12? &c. 14? &c. 40? &c. 63?&c. 50? &c. Ans.— 8. Analysis. — One-third of 12 is 4, and two-thirds of 12 must be 2 times 4, that is, 8. 22. What 23. What 24. What 25. What 26. What 27. What 28. What 29. What s I of 8? 12? s|of 10? 15? ' of 10? 15? of 6? 12? of 7? 14? of 35? 42? of 8? 16? of 9? 18? 16? 20? &c. 20? 25? &c. 20? 25? &c. 24?&c. 28? &c. 56? &c. 32? &c. 18? 21? 49? 24? 27? 36? &c. FRACTIONS. 93 LESSON VL I. What is iof 7? Ans. — 3J. Since J of 6 is 3, and J of the remaining 1 is J, J of 7 must be 3 J. This explains why we put the divisor under the last remainder in division. 2. What is i of 8? 10? 11? 14? 16? &c. 3. What is i of 5? 7? 13? 15? 18? &c. 4. What is I of 6? 7? 8? 9? 12? &c. 6. What is i of 7? 11? 17? 19? 22? &c. 6. What is 4 of 8? 9? 10? 11? 12? &c. 7. What is ^ of 9? 11? 13? 15? 19? &c. 8. What is ^ of 10? 11? 13? 14? 23? &c. 9. How many units in | ? Ans. — 3 J. Analysis. — Since 2 halves equal 1 unit, 7 halves equal as many units as 2 is contained times in 7. 10. How many units in ^ ? y ? ^ ? 1^5 ? rr ? &c. II. How many units in I ? |? -J? |? |?&c. 12. How many units in f ? | ? '/ ? V ? ^8 ? &c. 13. How many units in i? V^ f? V? V ? &«. 14. How many units in | ? \9? %^ ? 3_9 ? 4^3 ? &c. 1. >. How many units in ^^ ? ^ ? s^i ? ^^^ ? ^ ? &c. 16. How much is 3 times |? Ans. — ^3^, or 2|. 17. How much is 4 times f ? | ? f ? /j ? &c. 18. How much is 5 times 4? |? /j? /^? &c. 19. How much is 6 times J? 4? fj? -f^'i &c. 20. How much is 7 times I ? | ? | ? | ? &c. 21. How much is 8 times I? I? 4? 5?&c. 22. What is I of 7? Ans.— 4§. Since J of 7 is 2J, 2 thirds of 7 must be 2 times 2J. Now, 2 times 2 are 4, and 2 times J are f : 4 and f are 4f . 23. What is I of 4? 10? 13? 16? 19? &c. 24. What is I of 5? 6? 7? 9?10?ll?&c. 25. What is I of 6? 7? 8? 9?ll?12?&c. 26. What is | of 6? 7? 8? 9? 11? 12? &c. 27. What is I of 7? 8? 9? 10? 11? 13? &c. 28. What is f of 8? 9? 10? 11? 12? 13? &c. 29. What is I of 9? 10? 11? 12? 13? 14? &c. © I 94 FRACTIONS. LESSON VII. 1. How many are ^ and ^? Ans. — |, or 1. 2. How many are | and J ? i and f ? | and f ? 3. How many are | and | ? | and | ? | and | ? 4. f and |?/oand/^? I and |? | and |? 5. j\ and If? I and |? /^ and 1^ ? f4 and f|? 6. V and V? S' and y ? jf and 1|? |o and fg? 7. land I and f? | and | and |? 8. Yj and ii and f«? j| and jf and ji ? 9. jl and jf and j§ and |^ and jf and /^? 10. II and II and || and || and i| and |g? 11. From I take f . Ans.— |. 12. From -| take |. From | take |. From | take J. 13. From | take |. From f take |. From | take I. 14. From | take f . From | take |. From | take |. 15. From | take |. From ^ take |. From | take |. 16. From /_ take y%. From /^j take yS^. From /^ take y^. 17. From y\ take y\. From j\ take /_. From |^ take -jfij-. 18. From -^^ and ^^^ take j% and -j^^. 19. From || and || take || and j%. 20. From || and |f and || take ff and y^^ and /_. 21. What part of 3 is 2 ? Ans.— f . Analysis. — Since 1 unit is J of 3 units, 2 units must be 2 times J of 8 units ; that is, f of 3. 22. What part of 4 is 3 ? What part of 5 is 4? 23. What part of 5 is 3 ? What part of 5 is 2? 24. What part of 6 is 5? What part of 7 is 5? 25. What part of 7 is 6? What part of 7 is 4? 26. What part of 10 is 5? Ans.— y^^, or A. Why is 5 one-half of 10 ? Ans. — Because ^ is con- tained in 1 two times, and 5 is contained in 10 two times. 27. What part of 6 is 2? What part of 6 is 3? 28. What part of 6 is 4 ? What part of 15 is 3 ? 29. What part of 12 is 3 ? What part of 18 is 3 ? &c. &c. FRACTIONS. 95 LESSON VIII. 1. If 4 melons, of equal price, cost 12 cents, how many cents do 3 of them cost? Ans. 9 cents. Analysis. — If 4 melons, of equal price, cost 12 cents, 1 melon costs J of 12 cents; that is, 3 cents. If 1 melon costs 3 cents, 3 melons of the same price cost 3 times 3 cents ; that is, 9 cents. 2. If 3 pounds of sugar cost 27 cents, how much will 5 pounds of the same cost ? 3. If 2 pounds of coffee cost 24 cents, how much will 6 pounds of the same cost ? 4. If 3 pounds of beef cost 30 cents, how much will 2 pounds of the same cost ? / b. If 4 yards of muslin cost 32 cents, how much will 9 yards of the same cost ? 6. If a man, walking regularly, walks 24 miles in 8 hours, how far does he walk in 5 hours ? 7. If a boat, sailing regularly, goes 44 miles in 4 hours, how far does it sail in 3 hours ? 8. If 10 boxes of raisins cost 20 dollars, what cost 7 boxes of the same ? 9. If 4 oranges cost 10 cents, what do 3 of them cost? What would 6 of the same kind cost ? 10. If 4 pencils cost 25 cents, what would 12 of the same cost ? What would 3 of them cost ? 11. If 3 yards of cloth cost 9 dollars, how much of the same can you buy for 10 dollars ? 12. If 4 barrels of cider cost 8 dollars, how many barrels of it can you buy for 11 dollars ? 13. If 2 barrels of apples cost 5 dollars, how much will 3 barrels cost ? 4 barrels ? 5 barrels ? 14. If 5 pounds of coffee cost 75 cents, how much of the same can be bought for 65 cents ? 15. At the rate of 80 cents for 8 pounds of starch, how much can be bought for 25 cents ? 16. A merchant bought 40 barrels of potatoes, and sold at one time \ of them, and at another time | of the remainder; how many had he left? 96 FRACTIONS. LESSON IX. 1. If i of a pound of tea is worth 10 cents^ liow much is a whole pound of the same worth ? Analysis. — If ^ of a pound of tea is worth 10 cents, | of a pound, that is, a whole pound, will be worth 5 times 10 cents, that is, 50 cents. 2. If I of a yard of muslin costs 2 cents, how much does a whole yard cost ? 2 yards ? 3| yards ? 3. If -1 of a yard of silk costs 40 cents, how much does a whole yard cost ? 4. If ^ of a pound of honey costs 10 cents, how much does a whole pound cost? 2 pounds? 4^ pounds? 5. At the rate of 2 miles in half an hour, how fa'* would a man walk in 4 hours ? 6. At the rate of 3 dollars for | of a yard of cloth, how much will 5 yards cost ? 7. At the rate of 8 cents for | of a dozen, how much will 9 dozen of eggs cost ? Analysis. — If J of a dozen of eggs cost 8 cents, | will cost J of 8 cents, that is, 2 cents. If ^ of a dozen costs 2 cents, a whole dozen will cost 5 times 2 cents, that is, 10 cents, and 9 dozen will cost 9 times 10 cents, that is, 90 cents. 8. At the rate of 9 cents for | of a pound of coffee, how much will 9 pounds cost ? 9. At the rate of 6 dollars for | of a barrel of flour, how much will 5 barrels cost ? 10. When | of a certain school were present, there were 30 pupils ; what was the whole number at school ? 11. If f of the cost of a watch is 60 dollars, how much would 5 such watches cost ? 12. If I of a quire of paper cost 14 cents, how much would 10 quires of the same cost? 13. At the rate of 28 dollars for ^ of a month, how much would a person spend in 6 months ? 14. If I of a bushel of clover-seed cost 3 dollars, how much does ^ of a bushel cost ? 15. If 6liimes a number is 72, what is | of it? TABLES. 97 TABLES OF MONET, WEIGHTS, AND MEASURES. LESSON I. UNITED STATES MONEY. 10 mills (marked m.) make 1 cent marked ct. 10 cents " 1 dime " d. 10 dimes " 1 dollar " $ 10 dollars " 1 eagle " E. 1. How many mills are there in 2 cents? 3 cents? &c. 2. How many dimes are there in 2 dollars ? 3 dollars ? &c. 3. How many dollars are there in 2 eagles ? 3 eagles ? &c. 4. How many cents are there in 20 mills ? 30 mills ? &c. 5. How many dimes are there in 20 cents ? 30 cents ? &c. 6. How many eagles are there in 20 dollars ? 30 dollars? &c. 7. How many mills are there in ^ of a cent ? 8. How many mills are there in | of a cent ? | ? <&c. 9. How many mills are there in ^ of a cent ? | ? | ? &c. 10. How many mills are there in 1| cents ? 21 ? &c. 11. How many mills are there in 2i cents ? 3| ? &c. 12. How many cents are there in | of a dime ? 4 ? &c. 13. How many cents are there in 2i dimes? 3|r &c. 14. How many cents are there in 10 dimes? 5 dimes ? &c. 15. How many cents are there in 7^ dimes? 8| ? &c. 16. How many cents are there in 1 dollar ? 17. How many cents are there in 2 dollars ? &c. . 18. How many cents arc there in i of a dollar ? | ? &c. 19. How many cents are there in i of a dollar ? | ? &c. 20. How many dollars in | of an eagle ? | ? &c. 21. How many dollars in 2 eagles? 2i eagles? &c. 22. How many dollars in 1000 mills ? 100 cents ? &c. -e H— ^ Q 98 TABLES. LESSON II. ENGLISH MONEY. 4 farthings (qr. or f.) raake 1 penny (d.) 12 pence " 1 shilling (s.) 20 shillings " 1 pound or sovereign (X) 21 shillings " 1 guinea (g^in.) 5 shillings " 1 crown. 1. How many qr. in 2 d. ? 3d.? 4 d. ? 5 d. ? 6 d. ? &c. 2. How many d. in 2 s. ? 3 s.? 4 s.? 5 s.? 6 s.? &c. 3. How many s. in 2 X? 3 £? 4 X? 5 X? 6 X? &c. 4. Howmany d.inl2f.? 20 f.? 28 f. ? 32f.? 36f.?&c. 5. How many s. in 36 d. ? 60 d. ? 72 d. ? 84 d. ? 96 d. ? &c. 6. Howmany X in 30 s.? 45 s.? 55s.? 70s.? 95s.?&c. 7. Howmany f. in }^d.? |d.? |d.? 1-Jd.? f" ' " " 8. How many d. in ^ s. ? | s. ? | s. ? 1 J s. ? 2\ 9. How many s. in I X? §X? |X? llX? 2| 10. How many shillings in half a crown ? ?&c. LONG OR LINEAR MEASURE. 12 inches (in.) make 1 foot (ft.) 3 feet " 1 yard (yd.) 5i yards, or 16^ feet, " 1 rod, pole, or perch (rd.) 40 rods " 1 furlong (fur.) 8 fur., or 320 rods, " 1 mile (m.) 3 miles " 1 league (lea.) 1. How many inches in 2^ ft. ? 3| ft. ? 4| ft. ? 5| ft. ? &c. 2. How many feet in 2 yd.? 31 yd.? 4f yd.? 5lyd.?&c. 3. How many yards in 36 ft. ? 48 ft.? 21ft.? 24 ft. ? &c. 4. How many yards in 2 rd. ? 4 rd. ? 6 rd. ? 8 rd. ? &c. 5. How many rods in 2 m. ? 1^ m. ? 3| m. ? 41 m. ? &o. 6. How many miles in 6 lea. ? 12 lea. ? 30 lea. ? &c. 7. How many leagues in 5 m. ? 7 m.? 8 m.? &c. 8. How many feet in 10 rd. ? 20 rd.? 30 rd. ? 40 rd.? m J TABLES. 99 LESSON III. ENGr)fEERS' AND SURVEYORS^ MEASURE. 7j%\ inches (in.) make 1 link (1.) 25 links ^^ 1 pole, or rod (p.) 4 poles, or 66 feet, " 1 chain (ch.) 10 chains " 1 furlong (fur.) 8 furlongs, or 80 chains, " 1 mile (m.) 1. How many links in 2 p. ? 3 p. ? 4 p. ? 5 p. ? &c. 2. How many links in ^ p. ? 2^ p. ? 3| p. ? 4| p. ? &c. 3. How many poles in 2 ch.*? 2^ ch. ? 3| ch. ? 4| ch. ? &c. 4. How many feet in 1| ch. ? 2 ch. ? 4 ch. ? 5 ch. ? &c. 5. How many chains in 2 fur. ? 3| fur. ? 4| fur. ? &c. 6. How many furlongs in 2^ m. ? 3| m. ? 5| m. ? &c. 7. How many chains in 3 J^ m. ? 4^ m. ? 6| m. ? &c. 8. How many miles in 720 ch.? 800 ch.? 320ch.?&c. 9. How many miles in 32 fur. ? 64 fur. ? 80 fur. ? &c. 10. How many chains in 12 p. ? 20 p. ? 36 p. ? &c. CLOTH MEASURE. 2i inches (in.) make 1 nail (na.) 4 nails, or 9 inches, " 1 quarter of a yard (qr.) 4 quarters " 1 yard (j^O 3 quarters " 1 Flemish ell. 4 qr. 11 in. " 1 Scotch ell. 5 qr. " 1 English ell. 6 qr. " 1 French ell. . ? 3 qr. ? 5 qr. ? 6 qr. ? &c. |yd.?l^yd.?l|yd.?&c. yd.?iyd.?|yd.?&c. , ^ _. . _ ^ i.? 3 yd.? 4yd.? &c. 5. How many feet in li yd. ? 2| yd. ? 3| yd. ? 4| yd. ? &c. 6. How many yards in 36 in. ? 54 in. ? 72 in. ? &c. 7. How many yards in 3 ft. ? 4 ft. ? 5 ft. ? 6 ft. ? &c. 100 TABLES. LESSON IV. SURFACE OR SQUARE MEASURE. A square inch is a square surface 1 inch long and 1 inch broad. A square foot is a square surface 1 foot long and 1 foot broad. A square yard is a square sur- face 1 yard long and 1 yard broad. A square rod-is a square surface 1 rod long and 1 rod broad. A square mile is a square surface 1 mile long and 1 mile broad. 144 square inches (sq. in.) make 1 square foot (sq. ft.) 9 square feet " 1 square yard (sq. yd.) 30 i square yards, or ") a ^ square rod, or ^p . 272 i square feet j pole, or perch ^ '^ 40 square rods ^^ 1 rood (R.) 4 roods, or 10 sq. ch. " 1 acre (A.) 640 acres " 1 square mile. (sq. m.) 1. How many square inches in a page 6 inches long and 4 inches broad ? Ans. 24. To find the quantity of any square surface^ we multiply its length by its breadth^ using the same liriear units for both. 2. How many square inches in 2 square feet ? In a surface 2 feet square ? 3. How many square feet in 2 square yards? In a surface 2 yards square ? 4. How many square rods in 3 roods ? 5. How many square rods in 1 acre ? 2 acres ? 6. How many square miles in 1280 acres ? 7. How many acres in 2 square miles ? 3 square miles ? 8. How many acres in 320 square rods ? 9. How many acres in a farm 800 rods long and 80 rods broad ? 10. How many square feet in a floor 16^ feet long and 12 feet broad ? How many square yards ? 11. How many square inches in ^ of a square foot ? 9 TABLES. 101 LESSON V. SOLID OR CUBIC MEASURE. A cube is a body having six square surfaces. A cubic inch is a cube, each of whose edges is an inch long. A cubic foot is a cube, each of whose edges is a foot long. A cubic yard is a cube, each of whose edges is a yard long. 1728 cubic inches (cu. in.) make 1 cubic foot (cu. ft.) 27 cubic feet " 1 cubic yard (cu. yd.) ' 128 cubic feet " 1 cord of wood (C.) 42 cubic feet " 1 ion of shipping. 1. How many cubic inches in a stick 10 inches long, 3 inches broad, and 2 inches thick ? Ans. 60. To find ike cubical quantity of any square thing, we multiply its length by its breadth , and that product by its thickness, 2. How many cubic inches in 2 cu. ft. ? 3 cu. ft. ? &c. 3. How many cubic feet in 2 cu. yd. ? 3 cu. yd. ? &c. 4. If a load of wood is 8 feet long, 4 feet broad, and 4 feet high, how much wood is it ? 5. If a ship can carry 1000 tons, how many cubic feet are allowed for her load ? 6. If a cellar is 80 feet long, 30 feet broad, and 5 feet deep, how many cubit feet of earth were dug oiit ? 7. How many cubic feet in a room 18 feet long, 15 feet broad, and 12 feet high ? How many cubic yards ? 8. How many cubic inches in a box 3 feet long, 2 feet wide, and 2 feet high ? 9. How many cords of wood can be packed in a shed 24 feet long, 8 feet wide, and 8 feet high ? 10. How many cubic feet of water in a full cistern 10 feet long, 7 feet wide, and 6 feet deep ? 1^ ^ 102 TABLES. LESSON VL AVOIRDUPOIS WEIGHT. Avoirdupois Weight is used in weighing almost all articles taken in large quantity, such as groceries, &c. 16 drams (dr.) make 1 ounce (oz.) 16 ounces " 1 pound (lb.) 25 pounds '^ 1 quarter (qr.) 4 quarters, or 100 lbs. " 1 hundredweight(cwt.) 20 cwt. or 2000 lbs. " 1 ton (T.) 1. How many drams in 2 oz. ? 4 oz.? 5 oz.? 6 oz. ? &c. 2. How many ounces in 2 lb.? 3 lb.? 4 lb.? 5 lb.? &c. 3. How many pounds in 2 qr. ? 3 qr. ? 5 qr. ? 6 qr. ? &c. 4. How many quarters in 2 cwt. ? 3 cwt. ? 4 cwt. ? &c. 6. How many hundredweight in 2 T.? 3 T.? 4 T.? &c. 6. How many cwt. in 8 qr. ? 24 qr. ? 32 qr. ? &c. 7. How many lb. in 2 tons? 3 tons? 7 tons? &c. 8. How many cwt. in 300 lb.? 1000 lb.? 1500 lb.? &c. 9. How many oz. in 32 dr.? 48 dr.? 64 dr.? &c. TROY WEIGHT. Troy Weight is used in weighing coins, precious metals, jewels, and liquors. 24 grains (gr.) make 1 pennyweight (pwt.) 20 pennyweights " 1 ounce (oz.) 12 ounces " 1 pound (lb.) The ounce and pound of Troy Weight are not the same weights as the ounce and pound Avoirdupois. 1. How many gr. in 2 pwt.? 3 pwt. ? 4 pwt.? &c. 2. How many pwt. in 2 oz. ? 3 oz. ? 4 oz. ? &c. 3. How many oz. in 2 lb.? 3 lb.? 4 lb.? &c. 4. How many oz. in Hb.? i lb.? IJ lb.? &c. 9 — ■ 9 TABLES. 103 LESSON VIL apothecaries' weight. Apotliecaries' Weight is used in medical prescriptions. 20 grains (gr.) make 1 scruple (9) 3 scruples " 1 dram (3 8 drams " 1 ounce (J) 12 ounces " 1 pound (ib) In this weight the grain, ounce, and pound are the same as in Troy Weight. 1. How many gr. in 2 3 ? 3 9? 49? 5 9 ? &c. 2. How many 9 in 2 5? 3 s^? 4 3? 5 5? &c. 3. How many 3 in 2 g ? 3 § ? 4 g ? 5 § ? &c. 4. How many ^ in 2 ib ? 3 ib ? 4 tb? 5 ib ? &c. 6. How many ib in 60 g ? 72 g ? 84 g ? &c. 6. How many g in 48 5? 56 5? 64 3? &c. 7. How many 5 in 18 9 ? 21 9 ? 24 9 ? &c. 8. How many 9 in 100 gr.? 140 gr.? 180 gr.? &c. apothecaries fluid measure. Apothecaries' Fluid Measure is used in measuring the fluid portions of medical prescriptions. 60 minims (TTL) make 1 fluidrachm (f^;) 8 fluidrachms " 1 fluidounce (fg; 16 fluidounces " 1 pint (0.) 8 pints " 1 gallon (Cong.) 1. How many minims in 2 f^? 3 %? 4 %? &c. 2. How many f^ in 2 fg ? 3 f g ? 4 f g ? &c. 3. How many fg in 2 pints? 3 pints? 4 pints? &c. 4. How many pints in 2 gallons? 3 gallons? &c. 5. How many f^ in 240 fit? 300 IT^? &c. 6. How many f J in 64 £5 ? 72 f^ ? &c. 104 TABLES. LESSON VIII. LIQUID OR WINE MEASURE. Wine Measure is used in measuring the bulk of all kinds of liquids. 4 gills (gi.) make 1 pint (pt.) 2 pints " 1 quart (qt.) 4 quarts " 1 gallon (gal.) 1. How many gills in 2 pints? 3 pints? &c. 2. How many gills in 1^ pints? 4i pints? &c. 3. How many pints in 2 quarts? 3 quarts? &c. 4. How many pints in 5^ quarts? 10 i quarts? &c. 5. How many quarts in 2 gallons ? 3 gallons ? &c. 6. How many gallons of wine would 10 barrels hold, each barrel holding 31^ gallons? 7. How many gallons of oil would 20 barrels hold, each barrel holding 40 gallons ? 8. How many gallons of syrup would 8 hogsheads hold, each hogshead holding 63 gallons? 9. How many gallons of wine would 5 pipes hold, each pipe holding 126 gallons ? 10. How many gallons of molasses in 12 casks, each cask holding 84 gallons? BEER MEASURE. Beer, ale, and milk are sometimes measured with ves- sels larger than those used for other liquids. 2 pints make 1 quart. 4 quarts " 1 gallon. This gallon is 282 cubic inches in capacity, but the wine gallon is only 231 cubic inches. In England the gallon for all liquids is 277j%'^|j% cu. in. a TABIiES. 105 LESSON IX. DRY MEASURE. Dry Measure is used in measuring such things as grain, truits, salt, &c. 2 pints (pt.) make 1 quart (qt.) 8 quarts '^ 1 peck (pk.) 4 pecks " 1 bushel (bu.) The pint and quart of dry measure are not the same as those of Liquid Measure. 1. How many pints in 2 qt. ? 3 qt. ? 4 qt. ? &c. 2. How many quarts in 2 pk. ? 3 pk. ? 4 pk. ? &c. 3. How many pecks in 2 bu. ? 3 bu. ? 4 bu. ? &c. 4. How many bushels in 24 pk. ? 36 pk. ? 40 pk. ? &c. 5. How many pecks in 32 qt. ? 48 qt. ? 64 qt. ? &c. 6. How many quarts in 12 pt. ? 24 pt. ? 30 pt. ? &c. 7. How many quarts in 3 J pk. ? 4i pk. ? 5| pk. ? &c. ANGULAR OR CIRCULAR MEASURE. Portions of the circumference of a circle are expressed as parts of the whole circumference, and not with refer- ence to any absolute length. 60 seconds (") make 1 minute (') 60 minutes " 1 degree (°) 360 degrees " 1 circumference (C) Hence, the size of a degree depends upon the size of the circle. 1. How many" in 2'? 3'? 47 57 &c. 2. How many' in2°? 3°? 4°? 5°? &c. 3. How many ° in 2C? 3C? 40? 50? &c. 4. Howi any°in-^0? iO? iO? |0? &c. 5. How many ' in F? i°? T? ^^ &c- 106 TABLES. LESSON X. MEASURE or TIME. The natural units of time are days and years. These are further divided and arranged thus : — 60 seconds (sec.) . make 1 minute (min.) 60 minutes " 1 hour (hr.) 24 hours " 1 day (da.) 7 days " 1 week (wk.) 12 calendar months " 1 year (yr.) 365 days (or 52 wk. 1 day) " 1 common year. 366 days (or 52 wk. 2 days) " 1 leap year. 365 da. 5 hr. 48 min. 49j'^^ sec. " 1 solar year. 100 years " 1 century. The Earth turns from west to east one complete revo- hition in 24 hours, thus making one day. The Earth moves around the Sun one complete circuit in 365 da. 5 hr. 48 min. 49 ^"^^ sec, thus making a year. Calendar months are those months which are called by distinct names in a calendar. They are twelve, and their names are January, February, March, April, May, June, July, August, September, October, November, December. 1. How many seconds in 2 min.? 3 min.? 4 min.? &c. 2. How many minutes in 2 hr. ? 3 hr. ? 4 hr. ? &c. 3. How many hours in 2 days? 3 days? 4 days? &c. 4. How many days in 2 wk. ? 3 wk. ? 4 wk. ? &c. 5. How many months in 2 yr. ? 3 yr. ? 4 yr. ? &c. 6. How many days in 2 yr. ? 3 yr. ? 4 yr. ? &c. 7. How many days in leap-year? 8. How many years in 2 centuries? 3 centuries? &c. | 9. How many seconds in ^ min.? i min.? f min.? &c. | 10. How many minutes in ^ hr. ? \ hr.? f hr. ? &c. 11. How many hours in I day? \ day? f day? &c. TABLES. 107 LESSON XL CALENDAR DAYS AND MONTHS. The days of the week are Sunday, or 1st day. Thursday, or 5th day. Friday, or 6th day. Saturday, or 7th diy. February, March, or or April, May, June, or or or July, August, September or or ,or Monday, or 2d day. Tuesday, or 3d day. Wednesday, or 4th day. The calendar months have days as follows : — January, or 1st month, has 81 days. 2d month, has 28 days ; in leap-year 29. 8d month, has 31 days. 4th month, has 30 days. 5th month, has 31 days. 6th month, has 30 days. 7th month, has 31 days. 8th month, has 31 days. 9th month, has 30 days. October, or 10th month, has 31 days. November, or 11th month, has 30 days. December, or 12th month, has 31 days. Commit to memory the following lines : — Thirty days have September, April, June, and November : And all the rest have thirty-one. Save February, which alone Has twenty-eight; and we assign To this, in leap-year, twenty-nine. Or, The ff^'irth, eleventh, ninth, and sixth, H'lve thirty days to each affixed : And all the rest have thirty-one, Except the second month alone, To which we twenty-eight assign, Till leap-year gives it twenty-nine. g « 108 TABLES. LESSON XIL MISCELLANEOUS TABLES. 1. Of collections of things. 12 things make 1 dozen. | 12 dozen, or 144 things. i( 1 gross. 12 gross, or 1728 things^ a 1 great gross. 20 things a 1 score. 2. Of Paper. 24 sheets make 1 quire. | 20 quires. or 480 sheets. a 1 ream. 2 reams (( 1 bundle. 5 bundles, or 10 reams. u 1 bale. 3. Of Books. A folio (fol.) is made of sheets folded in 2 leaves. 1 A quarto (4to) - - 4 " An octavo (8 vo) - - 8 " A duodecimo (12mo) - . 12 « An 18mo - - - 18 " A 24mo - - - 24 " A36mo - - - 36 " 1. How many things in 2 dozen? 3 dozen? &c. 2. How many things in 2 gross ? 3 gross ? &c 3. How many things in 2 score? 3 score? &c. 4. How many sheets in 2 quires ? 3 quires ? &c. 5. How many quires in 2 reams? 3 reams? &c. 6. How many sheets in 2 reams ? 3 reams ? &c. THE END. ^ OSGOOD'S PROGRESSIVE SERIES. Osgood's Primary Lessons, comprising fourteen cards on seven boards. Osgood's Progressive Primer, 36 pages, 12mo, with illustrations. Osgood's Progressive Speller, for common schools. Osgood's Progressive First Reader, for primarj classes in common schools. Osgood's Progressive Second Reader, conwii ing simple lessons in reading and spelling, far primarj and medium classes. Osgood's Progressive Third Reader, containing lessons in reading and spelling, together with the primary rules for reading, suitable for medium classes. Osgood's Progressive Fourth Reader, designed for grammar schools, containing extracts from our best authors, in prose and poetry, together with prominent principles and general rules for reading, and their application. Osgood's Progressive Fifth Reader, designed for the highest classes in schools and academies, and containing a complete system of elocutionary and rhetorical rules, with choice and elegant selec- tions from the best American and English authors. Dean's Primary Arithmetic, for primary classes in public schools. Dean's Public School Arithmetic, for public s< and academies. Burtt's Elements op English Grammar, 8ju and Analytic, for the use of school*?, academies] private learners.