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Principal of St. Patrick's Boys' H - School. Halifax. Prescribed for use in the Public Schools in Nova Scotia and New Brunswick. "Long is the road by rules, short and easy by examples." Seneca. PART ONE. PUBLISHERS GEORGE A. KNODELL, ST. JOHN, NEW BRUNSWICK T. C. ALLEN & CO., HALIFAX, NOVA SCOTIA. Antered according' to Act of the Parliament of Canada In the yeav tin by T. C Allen .% Co. in the Department of Agriculture. (Copyright Branch). •^ ,! PREFACE In teaching- Arithmetic, as in teaching anything- else, some knowledge on the part of the individual taught and some ability to learn may be presupposed. The mistake often made by teachers is that they do not properly gauge the one or the other. As every pupil differs from his fellows in both respects, the teacher must, so to speak, strike an average, when framing an exercise for the simultaneous development of several. In this book this fact has been kept in view. Though the exercises are not arranged specially for either the graded or the miscellaneous school, or any particular conditions, yet it is hoped they will be found well adapted to any school and even to the private pupil. Every new principle in Arithmetic should be introduced by an oral lesson, and oral lessons should be continued until the principle is mastered. The best oral lessons are those given by the teacher, and should refer to objects and trans- actions familiar to the pupil. The ''Committee of Ten," appointed by the National Educational Association of the United States, in 1892, say, *' The simple operations of Arithmetic can be better exemplified by problems set on the spur of the moment and springing naturally from the environment of teacher and pupil, than by those given in a text-book ; and have the inestimable advantage of exciting the interest of the pupil." PREFACE. ] Those given in this book are merely suggestive. They must be followed by many others. It is of the utmost importance that pupils be trained to obtain correct answers without a second trial. Every ** mistake " in the use of the fundamental rules is so much development of carelessness, and will afterwards cause much unnecessary labor to both pupil and teacher. The exercises in the lower grades should be so simple, at first, that there would be no possible excuse for a mistake. By gradually introducing more difficult ones, absolute accuracy in lengthy processes may be secured. This accuracy should be exacted in both mental and written work. Frequent review is also necessary in order that principles and processes may make a lasting impression. The compilers wish to acknowledge their indebtedness to Prof. A. G. Macdonald, of the Normal School, Truro ; to Prof. James Little, of the Colchester County Academy, and especially to the Superintendent of Education and to Supervisor McKay, of Halifax, for assistance in revising the manuscript, and for many valuable suggestions during the progress of the work. I CONTENTS. Introductory Oral Lesson, .....^. m Notation and Numeration, - - - - _ 8, i^^ Addition, -----._._.. ,o Concrete and Abstract Number, 12 Analysis of Numbers, = M» '4 Equal Increments, -----. -.jq Multiplication, -------... 28 Continued Product, ----.. ,.31 Factors, -•-......_ -jj Division, ------. -...c^ Long Divisior:, -•-...... 61 Signs and Brackets, -•■-.....66 Averages, --, 5^ Roman Notation, -o.-.-.-.^^o Canadian Money, ..----. ._^i Addition, ..<>'•. ....'^2 Multiplication, .i^*-.-...y-i Subtraction, -- r -^ l ..*..... ^4 Division, -. ^^o^.... -yr Bills of Goodsj <...»,,. ^8 Unitary Method - ^ ..«-■.. 81 I ARITHMETIC. 1, The teacher should begin each part of the subject with an oral lesson and should use freelj such objects as pencils, pens, marbles, cents, splints, etc., as well as afoot rule, a yard stick, a meter stick and their convenient sub- divisions. Common weights and measures, such as the ounce, pound, pint, quart, grain, gram, liter, should also be found in every class-room where Arithmetic of an elemen- tary character is taught. 2* The following will serve as a sample lesson for be- ginners : What do I hold in my hand? Pencils. How many? 8. Now let 4 boys come up. I wish to divide the 8 pencils among the 4 boys. How many shall I give each ? Try 3. The first boy gets 8 and the second boy 8 and I have how many left? Only 2. Then I must get all the pencils back and try again. Shall I try this time to give each boy more or less than 3 ? Less. Try 2. Very well, I give each boy 2 and I have none left. How many boys now have 2 each ? 4. How many pencils had I ? 8. How many 2's are in 8 ? 4. When 8 is divided into 4 equal parts how many are in each part ? 2. Now let us collect the pencils. I get 2 from the first boy, 2 from the second, 2 from the third and 2 from the fourth. How many times did I get 2 ? 4 times. When 1 get 2 four times how many do I get ? 8. Then 4 times 2 are—? 8. We will give out the pencils again. Let the first boy take 2. How many are left ? 6. [The teacher holds them so that the children can count if necessary.] When 2 is taken from 8 how many are left ? 6. Let the second boy take 2. How many have I now ? 4. Then 2 from 6 leaves — ? 4. Let the third boy take 2. What number (7) 8 ORAL LESSON. remains in my hand ? 2. Then 2 from 4 leaves — ? 2. When the fourth boy takes 2 there are none left. 2 from 8 ? 6. 2 from 6 ? 4. 2 from 4 ? 2. 2 from 2 ? 0. Now let us get the pencils collected again. Let the first boy place his 2 pencils on the desk. Now I take 2 pencils tiom the second boy and I add them to those on the desk. How many are on the desk now? 4. When 2 and 2 are added what number do they give? 4. Now let the third boy put his 2 pencils on the desk. How many are now on the desk? 6. Then 2 added to 4 make — ? 8. The fourth boy now puts his pencils on the desk, and I wish to know how many are there now ? 8. When we add 2 and 2 and 2 and 2 how many do we have ? 8. Yes, the sum of 2 and 2 and 2 and 2 is 8. 3« The numbers we have been using in talking about pencils can be written either in words or in figures. In- deed, we can write all numbers by means of the following figures : Figures : 1 2 8 4 Words : nought. one. two. three. four. Figures : 5 6 7 8 9 Words : five. six. seven. eight. nine. 4* The figures are often called digits. 5« When we wish to write in figures a number larger than 9 we use two figures. Ten is written 10, that is 1 ten and no ones. Fifteen is written 15, that is 1 ten and 6 ones. Twenty-four is written 24, that is 2 tens and 4 ones. Ninety- nine is written 99, that is 9 tens and 9 ones. When we wish to write a number larger than 99 we use three figures. One hundred is written 100, that is 1 hun- dredy no tens, and no ones. Seven hundred sixty-four is written 764, that is 7 hundreds^ 6 tens^ 4 ones. Eight hundred five is written 805, that is 8 hundreds, no te?is, and 5 ones. ORAL LESSON. 9 Five hundred ninety is written 590, that is 5 hundreds^ 9 tens^ and no one^. EXERCISE I. Read the following" numbers and write them in words if you can ; 1. 7. 6. 48. 11. 99. 16. no. 2. 11. 7. 69. 12. 12.5. 17. 107. 3. 17. 8. 6G. 13. 1()H. 18. 441. 4. 26. 9. 70- 14. 180. 19. 709. 5. 38. 10. H8. 15. 117. 20. 911. Set down the following numbers in figures : 21. Eighty. 22. Ninety-one. 23. One hundred six. 24. Two hundred forty. 26. Three hundred seventy- seven. 26. Six hundred nineteen. 27. Nine hundred eleven. 6« Oral. — What are these ? Cards of matches. Count them as I split them up and drop them on the desk. How many are on the desk ? 20. I wish some girl to come and divide them into groups of four each. Who will come ? Ethel. Now let us see what Ethel does ? She takes them all in her hand and counts out 4 matches and lays them on one part of the desk, then another 4 near them, fhen another and another and another. She has laid them all down. Are there 4 matches in each group, Ethel? Yes. Thank you, you may sit down. How many matches had we ? 20. How many groups are there ? 6. How many matches in each group ? 4. How many 4's are there in 20 ? 6. Now, Maggie, will you please give me the groups ona at a time ? Thank you. How many times did Maggie give me 1 group? 6 times. How many matches in each group? 4. How many matches did I get? 20. What do b fours make ? 20. Let a boy now take 4 matches and lay them on that desk. How many are left ? You do rwDt know, so we must count. How many now ? 16. Then 4 from 20 10 ADDITION. leaves — ? 16. 'eft in my hand Then 4 from 16 How many are Well, what do 8. Now, when try to know the 4. 1 now place 4 is taken from 8. 4 from 8 ? Let another boy ? Let us count. leaves — ? left now ? we fiind ? take 4. How many are How many now ? 12. 12. Let another 4 be taken. What ! must we count again ? 8. Then 4 from 12 leaves — ? we place another 4 on the desk you must remainder without counting*. How many ? the last 4 on the desk. What is left when 20? 16. 4 from 16? 12. 4 from 12? 4. 4 from 4 ? 0. I now lay the groups on my desk and wish you to add the numbers in each group without counting. I lay down 4 and now I add another 4 mc^king — ? 8. And another 4 making — ? 12. And another 4 making — ? 16. And an- other 4 making — ? 20. How many 4's in 20 ? 5. 4 from 12 ? 8. 4 and 4 and 4 ? 12. T, If one girl has 4 cents, another 9, another 6, another 5 and another 7, how many cents have the five girls ? To work this on a slate or on paper, we set down the numbers under each other, thus : Example 1, '' 4 cents. 9 ♦* Addends : ^ 6 - 5 " I, 7 *' We say 7 and 5 are 12; 12 and 6 are 18; 18 and 9 are 27 ; 27 and 4 are 31. With some practice, we will be able to add thus: 7, 12, 18, 27, 31. Sum: 31 cents. EXERCISE II. Write down the following numbers and add them: 1. . 2 2. 2 3. 1 4. 2 5. 8 8 4 3 1 2 1 1 2 4 4 2 8 4 5 1 4 1 1 3 5 3 4 6 2 6 ADDITION. 11 I 6. 4 2 8 6 1 7. 3 5 1 6 2 3 8. 5 2 6 8 2 4 9. 4 2 8 6 1 _2 10. 2 8 4 6 6 7 11. 6 4 8 6 7 8 12. 8 5 7 4 2 6 18. 13. 14. 15. 18. 17. 4 5 6 7 8 _9 8 7 2 8 8 4 i^ 4 8 1 7 2 _9 31 48 70 62 62 52 6;^ 81 40 78 48 81 52 70 92 19. 94 60 21 40 84 20. 21 43 90 11 74 21. 801 li!4 488 1:11 22. 324 131 202 132 23. 132 404 61 402 24. 825 20 211 802 25. 26. 27. 8 1 4 2 6 8 7 _9 4 8 7 5 9 2 8 7 6 8 5 9 4 7 6 23. 5 9 4 8 8 6 9 29. 3 4 5 6 7 8 9 4 80. 2 3 4 5 6 7 8 9 ; 5 12 ADDITION. 8* When we say "17 cents," or "6 books," each one^ or unit^ in the 17 is 1 cent, and each one^ or unity in the 6 is 1 book. In such expressions, the 17 cents and the 6 books are concrete numbers. 9. If the units in two or more numbers are all alike, as in 4 pens, 6 pens and 9 pens, the 4, 6 and 9 are like numbers; but if the units are unlike, as in 4 pens, 6 pencils and 9 crayons, the 4, 6 and 9 are unlike numbers. 10. All concrete numbers are either like or unlike. When no particular unit is named or understood, as in 6, 8, 11, the 6, 8 and 11 are abstract numbers. 11. All abstract numbers can be added ; but of concrete numbers, only like numbers can be added. The sum of 3, 4 and 8 is 15. The sum of 3 horses, 4 horses and 8 horses is 15 horses. What is the sum of 3 horses, 4 cows and 8 sheep? Of 3 men, 4 lectures and 8 minutes? 12. Oral. — 1. Name the abstract numbers in the fol- lowing: 20 dogs, 8 men, 19 eggs, 12 inches, 9, 3 cords, 12, 23 hens, 50, 2, 8 robins, 9 birds, 5 inches, 6 eggs, 14. 2. Name the concrete numbers. 3. Name the concrete numbers that are like numbers. 4. Name each concrete number that is unlike all the others. EXERCISE HI. 1. A girl who had 63 cents in her bank earned 32 cents more. How many had she then ? 2. A boy carried 2 baskets of apples from the orchard. There were 74 apples in one basket and 83 apples in the other. How many apples did the boy carry ? 3. A boy who was looking for eggs in the barn found one nest with 8 eggs, one with 5, one with 7 and one with 9. How many eggs did he find ? ANALYSIS OF NUMBERS. 18 in 4u A g-entleman sold a horse for 92 dollars, a cow for 84 dollars, a calf for 11 dollars and a Iamb for 2 dollars. How much money did he get ? 5. January has 31 days, and February, except in leap years, has 28. How many days have the first 2 months of the year ? 6. March has 31 days ^pril 80, May 31 and June 30. How many days in these 4 months ? 7. The month of July has 31 days, Aui^ust 31, Sep- tember 30, October 31, November 30 and December 31. How many days in the last 6 months of the year ? 8. If one farmer has 72 sheep, another ()(j and another 81, how many sheep have the three farmers? 9. A boy shoots an arrow 235 feet up the road and another arrow 163 feet down the road. How many feet are the two arrows apart ? 10. A gfirl walked to her aunt's house, which was 324 yards aw; •, and came back again. How many yards did she wall ' 11. dd thirty-one, fifty-three, forty-two and seventy. 12. Add twelve, three hundred forty-two, two hundred eleven and four hundred thirty-three. 13. Analysis of the Number 6. Questions to be asked by the teacher : 1. If I have 6 pens to be put in boxes, 2 in each box, how many boxes will I require ? When I put 3 in each box? 2. How many 2's in 6 ? How many 3's ? 3. What do 2 threes make ? 3 twos ? 4. What part of 6 is 3 ? What part is 2 ? 5. 3 is one-half of what number? 2 is one-third of what number? 14 ANALYSIS OF N U M B E K S . 6. 2 times 3 are how many ? 3 t-mes 2 ? 7. How many 2-cent stamps will 6 cents buy? How many 3-cent stamps ? 8. V/hen there are 6 boxes of pens on a table, with 6 pens in each box, what different number of pens could you take from each box, and how many would be left in each box? 9. A boy who has both ha-nds closed says that he holds 6 marbles. How many can possibly be in each hand ? 14. Analysis of 18. Questions to be asked by the teacher : 1. How many 2's in 18? How many 3's ? 6's ? 9's ? 2. How many are 2 nines ? 3 sixes ? 6 threes ? 9 tv/os ? 3. What part of 18 is 9 ? What part is 6 ? 3 ? 2 ? 4. Of what number is 9 one-half? 6 is one-third of what number ? 3 is one-sixth of what number ? 2 one- ninth ? 5. 2 times 9 make whar number ? 3 times 6 ? 9 times 2? 6 times 3? 6. Count 18 by 3's. Ans.: 3, 6, 9, 12, 15, 18. Count 18 by 2's. By 6's. By 9's. 7. When you gfive away 18 cents by 2's how many are left each time? When you g-ive away by 3's? By 6's? By 9's? 8. Name all the different numbers which can be taken from 18, one at a time, and the number that will be left each time ? 9. What different numbers, taken two at a time, can be added to make 18? What numbers, each larger than 3, ca added to make 18 ? Ans. 6, 6, 6. 4, 5, 9, etc. i I NOTATION. u 15. The following table illustrates our system of notation : Periods. 6th. 5th. 4th. 3rd. 2nd. 1st. Names of Periods. Places. CA c o -a 3 C/) T3 ^ C. c _^ K) ^ (A -a c CA s o J3 C r^ (U 3 53 c c O 7) 73 C r« 0) rcHO kho xho xho x^o x^o 8 2 9 2 3 04 600 080 3 4 078 726 000 850 129 The first number is read eight hundred hventy-nine thousand^ two. The second three hundred four million, six hu?tdred thousand^ eighty. The third thirty four quadrillion, seventy-eight trillioHy seven hundred twenty-six billion, eight hundred fifty thousand^ one hundred twenty-nine. A thousand ones we call a thousand, written A thousand thousands we call a million << A thousand millions we call a billion, •* A thousand billions we call a trillion, A thousand trillions we call a qua- drillion written 1,000,000,000,000,000. The periods above quadrillions are quintillions, sex- tillions, septillions, octillions, etc. 1,000. 1,000,000, 1,000,000,000. " 1,000,000,000,000. :if m 16 NOTATION. EXERCISE IV. (a). Write the following^ numbers in words : 1. 310. 7. 7506. 13. 58604. 19. 104401 2. 906. 8. 4404. 14. 47080. 20. 808030. 3. 8172. 9. 9005. 15. 90630. 21. 760025. 4. 4R77. 10. 1001. 16. 70206. 22. 900843. 5. 8019. 11. 32748. 17. 86005. 23. 710006. 6. 7033. 12. 12409. 18. 623715. EXERCISE IV. (b). 24. 190190. Write the following- numbers in words: 1. 8018. 7. 7100800. 13. nilllllll. 2. 701003. 8. 6130049. 14. 9000000019. 3. 650010. 9. 9;)OO0O9. 15. 3200070500700000. 4. 600700. 10. 8372694. 16. 6473851927364. 5. 800119. 11. 1020304. 17. 1300013013. 6. 7016130. 12. 70806910. 18- 7001010200005050. $5 14. 423 534 645 15. 821 654 987 16. 456 789 123 324 693 804 351 472 907 174 859 550 619 384 816 21. 22. 23. 24. 25. 26. (a). 293 759 88(5 977 8907 4863 7592 346 7816 3094 947 8305 1070 963 7409 875 5409 9073 8007 480 7489 6900 9385 7063 8999 1234 5678 9088 7699 8787 27. 721 8906 7593 998(' 761 28. 937r 867^1 92(i 871 M)27 29. 30. 6:-'928 79372 5843(; 94957 37489 86935 59612 38754 8()000 75998 (]0093 80907 50026 98754 G0909 8771 3905 86438 32. 59897 67389 75903 47603 9006 75847 31. <« 22 1. ADDITION — ORAL Q UESTIONS. EXERCISE VII. (b). 780064 8. 987642 5. 7206 7. 8069 911870 88049 100139 80690 880000 7564 876700:) b06900 12999 9007 27109 806900J 46878 698 690004 806 700809 85 7770 80896 80 8069000 29 4. 789647 6. 900 8. 8156789 817 908 8700 815678 6980 87496 98000 98456 77894 79 61{i000 7898 694806 6608 7084000 45678 787895 971865 740500 8760.) 984567 8984567 9. Thirty million, forty-nine thousand; eig"ht million, eight hundred sixty-seven thousand, sixty-four; four billion, four hundred nineteen thousand; fifteen billion, six hundred nine million, five hundred; eleven million, eighty- six thousand, four. 10. Seventy-four trillion, three hundred eighty billion, six hundred eighty-seven; nine million, ninety; fifty billion, seventy-seven million, eighty-eight thousand ; nine hundred trillion, nine hundred thousand, nine hundred; twenty- nine quadrillion, seven hundred sixty-three million, eighty- nine. 19, Oral. — Many questions like the following ones should be asked by the teacher: 1. A girl who has 3 pencils of the same length finds that, end to end, they are as long as a foot rule. How long is each pencil ? 2. How many times would one of those pencils have to be laid on a foot rule to measure it? On a 2-foot rule? On a yardstick? 3. \ common match is 2 inches long. How many of ADDITION. ty- Lve le? of r I them, placed end to end, would measure a foot? 2 feet? A yard? Would 20 of them be more or less than a meter? 4. Write down what you think is the length of your desk. Also its breadth. The heig^ht of your chair. Let a pupil measure. What was the difference between your answer and the correct number of inches? 5. If a boy sleeps 9 hours of the 24 hours in a day, how many h«urs is he awake ? 6. How many hours are there in 2 days? In 3 days? 7. What is the sum of the dibits in the number 365? Ans. 14. In 724? 863? 879? 706? 8. How many days are there in 2 weeks? In 8? 4? 5? 9. If a boy g^ets 6 cents on Monday and 1 cent more each day than he got the day before, up to and including Saturday, how many cents will he get on Saturday? How many altogether? 10. Let the teacher analyze the number 10 as G is analyzed on page 13. 20. The sign + is called ////.f, and when placed between two numbers it means that they are to be added. 7 + 4 = 11, reads 7 plus 4 equals 11. EXERCISE VIII. (a). Find the sum of the following : 1. 71 + 48 + 96 + 84 + 100. 2. 140 + 397 + 962 + 754. 3. 874 + 986 + 375 + 897 + 769. 4. 1200 + 8750 + 8720 + 4910 + 2000. 5. 7035 + 7350 + 8609 + 9608 + 8960. 6. 8796 + 6005 + 887 + 6090 + 8431. fU ADD-ITION. 7. 7488 + 6666 + 7080 + 900 + 147. 8. 1010 + 7009 + 198 + 7304 + 80930. 9. 80804 + 906 + 16 + 9406 + 73101. 10. 7384 + 1000 + 10010 + 30137 + 3137. 11. 50315 + 72 + 8917 + 138 + 493. 1 2. 98764 + 47689 + 99983 + 87699 + 88677. 13. Thirty-seven, p/us eig-ht hundred nine, p/us forty thousand, forty, />/us ninety-eig'ht thousand, seven hundred sixteen, p/us twenty-nine thousand, seven hundred. 14. Ninety thousand, nine, //z^5 fifty-four thousand, six hundred eighty-five,////^ five hundred t^n, plus one thousand one hundred, plus seventy-seven thousand, seventy, plus seven hundred eig"hty-nine. EXERCISE VIII. (b). 1 5. 872004 + 910019 + 100789 + 6898746 + 8067. 1 6. 7000 + 77077 + 81808 + 540009 + 7286914 + 861374. 1 7. 723764 + 9876543 + 5400106 + 808 + 7639054. 1 8. 6937504 + 3800589 + 29 + 80046 + 3700 + 116699. 19. Four milHon, eighty-eight thousand, eighteen, //wj seventy-nine million, three hundred sixty eight, plus five hundred ninety million, eight thousand, twenty-seven, plus seventy-one thousand, six hundred thirteen, plr^^ nine hun- dred eleven million, ninety-nine thousand, fifty-five. 20. Seventeen billion, sixty-seven million, forty-nine, plus two hundred sixty-eight billion, seven hundred nine million, four hundred twenty thousand, plus ninety-nine trillion, four hundred eighty-six thousand, two, plus eight quadrillion, eight hundred thirty-nine trillion, six hundred forty-seven thousand, eighty-three. I ADDITION. 25 I EXERCISE IX. 1. A gfirl carried 4 books to school. The first book had 112 pages, the second 97, the ^hird 143 and the fourth 88. How many pages in the four books. 2. Find the number of days in a year by adding the number of days in each of the 12 months as given in Exer- cise III. 3. A man paid 125 dollars for a horse, 110 for a wairon, 36 for harness and 420 for a barn. How manv dollars has he paid altogether ? 4. In one car there are 76 sheep, in another 33, in another 69, in another 50 and in another 77. How many sheep in the five cars ? 5. A lady travelled 245 miles by boat, 719 by rail, 18 by stage coach and then walked two miles. What distance did she travel ? 6. In a large orchard there were 106 apple trees, 63 pear trees, 48 plum trees, 59 cherry trees and 40 peacii trees. How many trees in the orchard ? 7. In a certain wood there are H075 spruce trees, 923 beech trees, 6018 maples, 710 elms, 87 ash and 7719 birch. How many trees ? 8. A lady has 3500 dollars in one bank, 1775 dollars in another, 5670 dollars in another and 229 dollars in her private safe. How many dollars has she altogether .^ 9. If there are 6870 cattle on one ranch, 304S on another, 927 on another, 70HH on another and on another 5600, how many cattle on the 5 ranches? 10. In the year 1891 the population of Inverness County was 25779, of Victoria 12432, of Cape Breton 84244, and of Richmond 14399. What was the papulation of the whole Island of Cape Breton? 'ir, 26 ADDITION. 11. In 1891 Dartmouth had a population of 6249, Yarmouth 6089, Truro 5102, Springhill 4873, Lunenburg 4044, Amherst 8781, New Glasgow 3777, and Pictou 2999. What was the total population of the 8 towns ? 12. In the same year Halifax had 38556 people, St. John 89179, Charlottetown 11374, and Winnipeg 25642. What was the united population of the four ? 13. In 1891 the population of the counties of the peninsula of Nova Scotia was as follows : Guysboro 17195, Halifax 71358, Lunenburg 31075, Queens lOGlO, Shelburne 14956, Yarmouth 22216, Di-by 19897, Annapolis 19350, Kings 22489, Hants 22052, Cumberland 34529, Colchester 27160, Pictou 34541, and Antigonish 16114. What was the population of the 14 counties? 14. In the same year Kings County, P. E. Island, had a population of 20633, Queens 45975, and Prince 36470. What was the population of the Island ? 15. The population of the different counties of New Brunswick in 1891 was as follows : Albert 10971, Carleton 22529, Charlotte 23752, Gloucester 24897, Kent 23815, Kings 23087, Northumberland 25713, Queens 12152, Resti- gouche 8308, St. John 49574, Sunbury 5762, Victoria 18217, Westmoreland 41477, York 30979. What was the population of the whole province ? 16. The following is the population of the provinces of the Dominion of Canada in 1891 : Nova Scotia 450396, New Brunswick 321263, P. E. Island 109078, Quebec 1488535, Ontario 2114321, Manitoba 152506, British Columbia 98178, and the Territories 98967. Find the population of the Dominion. Note. — In all addition exercises, studentscmay test the correct- •ess of their work by beg^inning^ at the top and adding- down. I ADDITION — SQUARES, 27 E amine the following squares, adding the lines hori- zontally, vertically and diagon- ally : 1. 4 9 2 3 5 7 8 1 6 1 23 10 2 14 21 17 8 15 19 22 6 13 20 4 18 5 24 7 11 9 12 16 3 25 1 12 13 8 14 7 2 11 4 9 16 5 15 6 3 10 5. Prepare a square similar to the first, in which the sum of each column will be 12. Do not use the same digit more than once. 1 12 16 27 31 42 46 24 35 39 43 5 9 20 47 2 13 17 28 32 ... 36 1 21 25 29 40 44 6 10 37 48 3 14 18 22 33 11 15 26 30 41 45 7 34 38 49 4 8 19 23 i^ nULTIPLICATION. 21. 1. Oral. — Let the teacher repeat the oral lesson on pag-e 9, using- J>5 splints, dividing- them into bundles of 6 each, and then into bundles of 7. 2. How many eyes have 5 children ? 7? 9? 11? 13? 3. A yardstick is 3 feet long". What is the leng-th in feet of 2 yardsticks ? Of 4 ? Of 6 ? Of 8 ? Of 12? 4. When 1 side of a square room is 12 feet long-, what is the leng^th of 2 sides ? Of 3 ? Of 4 ? 5. When there are 3 horses in a stable, how many hoofs are there ? When there are 4 horses ? 5 ? 7 ? 9 ? 6. Let the teacher ask 20 questions similar to those on page 14, all bearing on the number 20. If a boy has 6 cents in each of his 5 pockets, how many cents has he altogether? He has 6 + 6 + 6 + 6 + 6 or 30. In this question all the addends are the same, and if we know without adding that 5 sixes make jc>, we shorten the work very much. 374 374 374 t/3 •a 374 S 374 5 374 < 2244 Sum. 374 Multiplicand, is shortened, 6 Multiplier. 2244 Product. The sign of multiplication is x . Thus, 4 X 6 = 24, reads 4 multiplied by 6 equals 24. 22. The multiplier must always be regarded as an abstract number. 23* The product will be like the multiplicand. 24. The teacher should have the pupils in all cases build up their own Multiplication Table. This has already been done in working Ex. 6. Let the exercise be repeated (28) I MULTIPLICATION. 29 13? i over and over again if necessary until the pupil can readily increase, by itself, eleven times, any number up to 12. Begin with 1 and increase by I's eleven times, then begin with 2 and increase by 2's eleven times, then with 3 and with all the other numbers up to and including 12. Set down the results in each case in a single line, thus : 1 2 3 4 5 6 7 8 9 10 11 12 2 4 6 8 10 12 14 16 18 ?0 22 24 8 6 9 12 15 18 21 24 27 30 38 36 4 8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 36 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 GQ 72 7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 BO 88 96 9 18 27 36 45 54 63 72 81 90 99 108 10 20 30 40 50 60 70 80 90 100 110 120 11 22 33 44 55 66 77 88 99 no 121 132 12 24 36 48 60 72 84 96 108 120 132 144 This, it will be observed, is an ordinary Multiplication Table. Vertical and horizontal lines may be drawn if desired. !35« When one number is to be multiplied by another we proceed as follows ; Example 5. Multiply e023 by 3, 6023 Multiplicand. 3 Multiplier. 180(59 Product. We say 3 threes are 9 ; 3 twos are 6 ; 3 noughts are 0; 3 sixes are 18. EXERCISE X. Multiply : 1. 21431 x2. 2. 31431 x2. 3. 40342x2. 4. 62134x2. 11. There are 144 pens in 1 gross, are in 2 gross ? 5. 31023x3. 6. 53102x3. 7. 91132x3. 8. 83120x3. 9. 84304x2. 10. 70312x3. How many pens < ;0 t; .'I So MULTIPLICATION. 12. There were 42 pupils in 1 class. How many would have been in 4 such classes ? 13. If there are 824 two-dollar bills in a drawer, how many dollars are there ? 14. How many cents would you have to pay for 412 4-cent stamps? 15. If in 1 barrel there are 322 apples, how many would there be in 4 such barrels ? 16. If there are 514 leaves in a book, how many pages are there ? 17. A sheet of paper has 4 pages. How many pages has 802 sheets of paper ? 26* Oral. — Samples for the teacher's talks on numbers. 1. John spent 15 cents for oranges at 8 cents apiece. How many did he buy ? 2. Write on the blackboard three dollars and twenty- five cents, $3.25. Four dollars and fifty cents, $4.50. Twelve dollars and seven cents, $12.07. Ten dollars and ten cents. 245 cents. 390 cents. 3. A farmer sold sheep at $3.25 each. What did he get for 2 ? For 3 ? For 4 ? 4. How many 25 -cent pieces in 75 cents ? In 2 dollars ? 5. What would a farmer get for 2 bushels of potatoes at 75 cents a bushel ? For 3 bushels ? For 4. 6. What is the sum of all the digits ? 7. How many strokes will a clock that strikes the hours make in 12 hours ? 8. What different numbers, two at a time, can be added to make 11 ? Note. — The cent point must be placed between the places ot tens and hundreds. MULTIPLICATION 81 lid I i 9. If a g"irl buys a quart of milk each day how many pints does she buy in a week ? 10. Analyze the numbers 27 and 28 as on pai^^e IH. Example 6. 73i()9 We say 6 nines are 54; set down the 4 and add the ^^ to the next part of the product. sixes .'ire 'M\, antl five are 41 ; set down 1. 41 Av/v, or 4 hundreds and 1 /fw ; set down 1 ten and leave the 4 hundreds to he added in with the hundreds. 4 hundreds, taken ('» times, equals 24 hundreds, and four hundreds left over make 28 hundreds, or 2 thousands and 1. 2. 3. 10. 11. 12. 13. 14. 15. 16. Multiply . l)()824x 7892G X EXERCISE XI. 8729G X H7412x HS277 X 88140 X 87109 X 75109 X 89()48 X 93857 X 17. 68047 X 18. 77298 X 19. 50963 X 20. 88249 X 21. 69806 X 22. 87012 X 2. 2. 2. 5. 3. 5. 5. 4. 5. 3. 6. 6. 6. 6. 4. 7. 4. 91738 X 5. G1829X 6. 74518 X 23. 7142GX 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 57091 X 81739 X 9808G X 379(18 X 4GG88 X 908G7 X 45G78 X G9828 X 92SG7 X 75821 X 9G288 X 7193GX 2. 3. 3. 7. 7. G. 7. 7. 7. G. 7. G. 7. 8. 8. 8. 7. 84G89x 3- 8. 7080GX 3. 9. G1374 X 4. 36. 29187 X 8. 37. G8045x 9. 38. 827 IGx 9. 39. 587 iHx 9. 40. 92GS5 X 9, 41. 872{).sx 10. 42. 5!)21()x IK 43. 88124 xll. 44. 61)188 X 11. 45. 87281 xl2. 46. G2838 X 12. 47. 908 17 X 9. 48. 84G57 X 12, •Tf" 82 MULTIPLICATION. Example 7. Or thus; 709 , 048 ^" 5672 283G 4254 4504;^2 so we set the 4 in 1. Multiply : 73G19X 4. 2. 58037 X 7. 3. 81927 X 8. 4. 70689 X 9. 6. 29568x11. 6. 88479 X 12. 7. 7486 X 34. 8. 9374 X 52. Example 8. multiplying- by the second figure, the 4, we multiply 9 ones by 4 tens and get 36 tens, so that the six we set down is 6 tens, and it must be set down in the place of tens. And in the third figure we are mul- tiplying by G hundreds, and 'J ones multi- plied bv ') h'tndreds will give 54 hundreds; the place of hundreds. 709 648 5672 28360 425400 459432 EXERCISE XII. (a). 9. 1839 X 46. 10. 730G X 65. 11. 9847 X 27. 12. 8074 X 64. 13. 3849 X 37. 14. 9286 X 67. 15. 8:-;94 X 82. 16. 5988 X 66. 580693 6459 5226237 2903465 2322772 3484158 17. 9708x48. 18. 4736x39. 19. 7419x76. 20. 7496x87. 21. 6074x89. 22. 6789x64. 23. 8940x78. 24. 5678x89. 3750696087 Multiply : 1. 560837x85. 2. 693428x68. 3. 930062x54. 4. 769254x39. 5. 572906x97. 6. 193704x89. 7. 432634x214. EXERCISE XII. (b). 8. 703615x423. 9. 462837x526. 10. 538807 x634. 11. 296078x627. 12. 751352x375. 13. 754836x734. 14. 866749x713. ^ MULTIPLICATION. 88 M 15. 57290G X 678. 16. 128456 X 789. 17. 59842G X 8214. 18. 982516 X 8416. 19. 719688 X 4625. 20. 758806 X 3529. Example 0. 8869 506 50214 41845 4234714 21. 642978x6874. 22. 190624x7568. 23. 892706x689. 24. 57H4()9x8762. 25. 876594 X 7864. 26. 693758 X 698758. Example 10. 8070 8004 12280 2456 21572280 Note. — Tlie pupil's practice in numeratioti should now he extended to include the third or millions period. Example 11 7184 20700 5028800 14868 148708S00 Example 12. 800890 700600 480234000 560278 560758284000 In example 9 whon we multiply the 9 ones by 5 hundreds we g-«it 45 hundreds, and of course the 5 must be set dovvn under the place of hundreds. In example 10, when we multiply the 7 tens by the 8 thousands, we g:et 5(5 tens of thousands, so the G must be set under the place of tens of thousands. In multiplying^ 4 ones by 7 hundreds in example 11, the product is 28 hufuireds, so as the 8 we set down is 8 hundreds, we indicate the same bv placing- two noiights on its rig-ht. So also in example 12 our first product 54, is thousands, and the 4 is written as such. Note.— Hence the product of any two digits will be set down as many places from the right hand side as are equal to the sum of the digits on the right of both the digits multiplied together. m u MULTIPLICATION — FACTORS. Multiply: EXERCISE XIII. (a) 1 > 1. 71M6 X 402. 7. 68069 x870. 18. 6900x8007. 2. 87386 X 804. 8. 89674 X yOU. 14. 8600 X 10208 S. 74892 X 706. 9. 8506 X 7108. 16. 8649x6800. 4. 89368 X 809. 10. 7620 X 8006. 16. 7960x78000. 5. 68672 X 680. 11. 8707 X 5006. 17. 8070x6090. 6. 46280 X 740. 12. 8098 X 9028. 18. 8900x67002. Multiply : EXERCISE XIII. (b). 1 1 19. 829157 X 70040. 25. 309700x800700. 20. 781000 X 187000. 26. 670089x678900. 21. B00960 X 8100G. 27. 900008x800009. 22 911007 X 80500. 28. 208040x506070. 23. 700809 X 700809. 29. 800202x202008. 24. 800607 X70G008. 30. 70G) < 8008200. 27, Continued Product Factors. 10x2 = 20; 20x3-60. 7x6 = 35; 86x8=105; 105x2 = 210. The continued product of 10x2x8 = 60. The continued product of 7x5x8x2 = 210. 10 and 2 are factors of 20; 20 and 8 are factors of 60. So, also, 7, 6, 8 and 2 dive factors of 210. The factors of a number, when multiplied together, will produce the number, as 10x2x8 = 60. 8 x 4 x 5 = 60. 2x2x8x5 = 60. 36. Oral. 1. What is the continued product of 5, 8 and 2? Of 3, 4 and 6? 2. What are the factors of 6? 9? 10? 12? 21? 89? 3. Two coach-houses, with 8 wagons in each, would have in them how many wheels? 8, with 6 wagons in each? 8, with 7? 4. Name three factors of 12. Of 18. Of 24. Of 80. Of 27. Of 48. 5. What is the continued product of the digits from 1 lo 6, inclusive? 6. Name 2 factors of 82. Name 8 factors of 82. Of 45. !^l MULTIPLICATION — FACTORS. 4 EXERCISE XIV. Find the continued product of the following" : ' < 1. 26 X 8 X 4. 11. 76x125x87. 2. 84 X 5 X 3. 12. 85 X (}4 X 79. 3. 07 X 5 X 0. 13. 12x11 X 9x8x7. 4. 7 X H X 97. 14. 18x8x6x4x2. 5. 120x9x8. 15. 700 X 800 X 101. 6. 9 X 7 X () X 8. 16. 20x4 x25x 16 X 16. 7. ] 7 X 1 X 9 X 2. 17. 8x40x5x8x 12. 8. oHxGOx 18. 18. 8 X 7 X 8 X 250. 9. 92x()l X 13. 19. 72 X 68 X 54 X 45. 10. H2:. X 7 X G. 20. 44 X 4 x206x 108. 29. Instead of the multiplier we can always use its factors, thus : Example 18. 167 167 48 12 •1886 2004 668 4 8016 8016 167 8 167 8 1886 6 8016 501 2 1002 2 2U04 2 4008 2 8016 EXERCI5E XV. ii Multiply- the following" numbers, usingf factors not 1 greater than 12. f 1. 872x24. 8. 97268x72. 15. 72006x108. 2. 916x27. 9. 75868x88. 16. 63082x121. ! 3. 7384x16. 10. 75808x96. 17. 88196x182. ',. 4. 8691 X 15. 11. 50906x99. 18. 27891x84. ii 5. 7108x86. 12. 75268x81. 19. 986087x48. iM 6. 3946x42. 13. 60678 X 105. 20. 694089x144. 7. 8302x64. 14. 69884x210. 86 MULTIPLICATION — MISCELLANEOUS. EXERCISE XVI. 1. There are 258 apples in one basket. How many would there be in 8 such baskets? 2. A g-irl lives 875 yards from the school. How many yards will she walk in gfoin^ over the road 6 times ? 3. In a certain wall there are 38672 bricks. How many bricks would there be in 7 such walls? 4. How many yards are there in 28 miles, 1760 yards being- the leng-th of 1 mile ? 5. What would a drove of 87 oxen weigh when the average weight of each ox is 1896 pounds? 6. Sound travels about 1142 feet in a second. How far from a cannon could the sound be heard 9 seconds after the cannon is fired ? 7. How many oranges in 49 cases when there are 896 in each case ? 8. If 8756 people, on an average, cross a certain bridge each day, how many will cross in a year, that is in 865 days ? 9. There are 5280 feet in a mile. How many feet would you travel in going 8 times between two towns that are 9 miles apart ? 10. A man has 8 rolls of five-dollar bills. In the first there are 86 bills, in the second 27 and in the third 18 bills. How much money has he ? 11. If there are 97 regiments in an army and 678 men in each, how many men are in the army ? 1 2. What would the 7695 cattle on a certain ranch be worth at $26 per head ? 13. How many bushels of oats can be stored on the 8 floors of a granary, when each floor has 18 bins holding 86 bushels each. 14. A field has 59 rows of corn, and there are 287 stalks In each row. How many stalks in 8 such fields ? I ■ 1 EXAMINATION PAPER. NO. I. 87 15. A certain web o( calico has 5 1 (J checks on each yard. How many checks on 9 webs of 60 yards each ? 16. Fiow many steps will a boy take iti walking; 268 miles when he takes 205)7 steps in 1 mile ? 17. A merchant boutj^^ht H{u\ barrels of flour at $1 per barrel, and 48H at $B per barrel. How many dollars did the flour cost ? be I EXAMINATION PAPER. No. i. (Time: Onk Hour. Valuk of each Question, 10.) 1. Write in words 2009, 8101H and 70000040. 2. Set down in fij^ures : thirteen thousand nine hun- dred ; ten million, fifty thousand four ; nineteen million, eight hundred six thousand. 3. Find the sum of 8087 + 29 + 98704 + Hr,l 11 +4900 + 008. 4. Multiply 808679 by 7. 5. Four boys count their marbles. The first has 24, the second 37, the third 19, and the fourth as many as the other three. How many have all ? 6. There are 9 rooms in a house; each room has 2 windows, and each window 8 panes of glass. How many panes of glass in the house ? 7. How many cents could you get for OH twenty-five cent pieces ? 8. If a boy walks 3 miles every forenoon and 4 every afternoon for 18 days, how many miles does he walk ? 9. A freight t ain consists of 20 cars, and each car contains 80 barrels of flour. What is the value of the flour at $5 per barrel ? 10. A farmer bought 15 acres of land at $24 per acre and 27 acres at $9 per acre. How much money did he pay for the land ? SUBTRACTION. 30. A girl who had 10 cents, spent i cents for an orange. How many cents has she left? She has the whole 10 cents except the 4 cents she spent. The 4 cents she spent added to what she now has would make 10 cents. Now how many cents must be added to 4 sents to make 10 cents ? 6 cents. Then 4 taken from, or lubtracted from, 10 leaves — ? 6. 31. Oral. — Samples for the teacher ; 1. What number must be added to 8 to make 12? 8 from 12? 4 from 12? 2. What number must be added to 5 to make 13? 5 from 13? 8 from 18? 3. What number must be added to 7 to make 16 ? 7 from 16? 9 from 16? 4. What change should you get when you buy 2 peaches at 3 cents each and give a 10-cent piece in payment ? 6. What change when you buy 8 pounds of rice at 6 cents a pound and give a 25-cent piece ? 6. When you buy slates at 11 cents each with a 50-cent piece, how many slates will you get and what change ? 7. Begin with 60 and subtract 3 each time as often as possible. Diminish 60 by 4's. By 5's. By 6's. By 7's. By 8's. By 9's. 32. The sign of Subtraction is — , and is called minus, 7-4 = 3, reads 7 minus 4 equals 3. EXERCISE XVII. Write down the following expressions and fill in the part wanting in each : -4 = ( ). 3. ll-6 = ( ). 5. 13-7 = 1. 7-4 = ( ). 2. 9-4 = ( ). ( ). 4. 10-3 = ( ). ( ). 6. 14-6 = ( ). I SUBTRACTION. 7. 16-8 = ( ) 8. 18-9 = ( ) 9. 17-8 = ( ) 10. 9-( ) = 5 11. 12-( ) = 7 12. ( )-6 = 5. 17. 21-8 = ( ). 13. 7 + 8-9 = ( ). 18. 34-7 = ( ). 19. ( )-7 = 10. 20. 24 -( ) = 16, 14. i6-( ) = 6. 15. ( )-8 = 5. 16. 29-7 = ( ). The teacher should put dozens of exercises like the above on the board. 33. When one number is to be taken from another we arrange them as in addition, always placing the one which is not greater than the other below. Example 14. 837395 Minuend. 234812 Subtrahend. 2 from 5 leaves 3 ; set down 8. 1 from 9 leaves 8 ; set down 8. 603083 Remainder. 3 from 3 leaves 0; set down 0, et^. )• Example 15. 283946 2708 281 248 EXERCISE XVIII. S btract the following ; 1. 2684 1342 7. 88466 25413 13. 946873 224422 19. 972846 552403 2. 3745 2182 6485 4133 9467 4153 84689 44214 34968 14742 8. 9. 10. 11. 12. 96875 62522 14. 15. 16. 17. 18. 008749 181645 20. 21. 22. 23. 24. 864987 251624 3. 687495 326134 768694 352844 086952 534720 846758 304046 888769 884052 718296 312052 786480 51 4820 4. 548678 1 10432 5. 749684 444444 866477 724163 6. 830476 388888 927360 721320 40 SUBTRACTION. 25. 791884 260154 26. 846977 82918 27. 983755 272152 28. 844987 43811 29. 756834 758481 30. 748684 41004 31. 893240 198130 32. 798406 98106 34. The minuend and subtrahend must both be either abstract or like numbers. EXERCISE XIX. 1. A farmer who had 94 bushels of barley sold 63 bushels. How many bushels had he left? 2. John has 39 marbles and James has 16 less. How many has James ? 3. Annie, who has 98 cents, has 67 cents more than Ruth. How many has Ruth? 4. A barrel of flour weighs 196 pounds. When a gfrocer has sold 54 pounds out of a barrel, how much flour is left ? 5. A boy who started to run a mile, that is 1760 yards, became tired at the end of 240 yards. How many yards had he still to run ? 6. Arthur has 25 marbles and William 24. They put them into the same box and then took out 16. How many were left in the box ? 7. A lady, who had a barrel containing 297 apples, used 144 of them. How many had she left? 8. A boy who was carrying a basket with 4 dozen eggs broke 15 of them. How many were unbroken ? 9. John had 52 marbles and James 37, all of which they put into a box. Horace had 81 and Charles 42, all of which they put into another box. How many more were in the one box than in the other ? 10. In one box there are 7 dozen buttons, and in another 6 dozen and 8. How many more in the first box than in the second? SUBTRACTION, 41 11. From 289 take 12 times 18. 12. From the continued product of 5x5x3 take the continued product of 3x8x2x2x2. 13. From the continued product of 9x8x4 take the continued product of 7x3x3x2. 14. From the sum of 258G and 2431 take 24G3. 15. From the sum of 2883 and 5486 take 7125. 16. From the sum of 2006, 3840 and 1152 take 3726. 17. A merchant got $2739 from one man, $4276 from another and $2061 from another. He then paid out $4063. How many dollars had he left? 18. From a town where there were 9675 people, 1180 went to Manitoba. How many remained in the town? 19. A company bought a gold mine for $7685 and sold it for $5620. What did they lose? 20. A company bought a coal mine for $48480, and spent $12625 in opening it. They then sold it for $65775. What did they gain ? 35. Oral. — Let the teacher take an apple and divide it into two equal parts, then into four. Let another apple be divided into three equal parts, then into six. Describe a circle on the board and draw one diameter. Take another circle and draw two diameters, cutting each other at right angles. In a third circle draw three radii, making equal angles with each other. In a fourth circle place radii as in the last, and produce them until the lines so produced become diameters. Get the class to name the parts of the apples. Let the divisions of the circles be then named and written down by figures thus : ^, ], J, ^. 1. When an apple is divided into G parts, what is each part called? How many of the parts must you get to have Ofie-lialf ? What do you call 2 of the parts ? 6 of them ? 2. When an orange is divided into 8 equal parts, what do you call 1 of the parts ? 2 of them? 3? 4? 5? 6? 7? I', 42 SUBTRACTION, 3. Into how many halves can anything" be divided? Into how many thirds? Fourths? Fifths? Sixths? Sevenths ? Eighths ? Which is greater, 2 halves or 8 eig^hths ? 3 thirds or 7 sevenths ? 4. If a pineapple is divided into 9 equal parts 'xnd you get one of them, what part of the pineapple is !eit? If you get 2 of them? 3? 4? 5? 6? 7? 8? 9? 5. A boy who had 2 10-cent piec**.. and 3 cents, paid 9 cents for a slate. What money had he left ? Ans. 1 ten and 4 ones. 6. Another boy who had 5 ten-cent pieces and 2 cents, paid 35 cents for an Arithmetic. What money had he left ? [Questions like the last two may be used by the teacher in explaining^ subtraction where it is necessary to add to the number in the minuend]. 36. In our system of notation, which is the decimal system^ 1 taken from any column becomes 10 in the next column to the right ; and any two adjoining columns taken by them- selves may be regarded as tens and ones. When any column is thoug-ht of as representing^ cents,, the next on the left may be regarded as representing" 10-cent pieces. Example 16. 7528354 We cannot take 9 ones from 4 ones so we take 2584739 1 of the 5 tens (leaving- there 4 tens) and put it with the 4 ones which g^ives us 14 ones, then 9 ones from 4J43615 14 ones leaves 5 ones. 3 from 4 leaves 1. 7 cannot be taken from 3 so we take 1 from 8 and with the 3 it g-ives 13 ; 7 from 13 leaves 6. 4 from 7 leaves 3. 8 cannot be taken from 2 so we take 1 from 5 which with the 2 g-ives 12 ; 8 from 12 leaves 4. 5 cannot be taken from 4 so we take 1 from 7 which with the 4 makes 14 ; 5 from 14 leaves 9. 2 from 6 leaves 4. More briefly : 9 from 14 leaves 5. 3 from 4 leaves 1. 7 from 13 leaves 6. 4 from 7 leaves 3. 8 from 12 leaves 4. 5 from 14 leaves 9. 2 from 6 leaves 4. Another method is to reg-ard the 54 as 40 and 14. Then 9 from 14 leaves 5. 3 from 4 leaves 1. Again 83 is 70 and 18. 7 from 13 leaves 6. 4 from 7 leaves 3, etc. Note. — Exercises in subtraction are proved by adding the sub' trahend and the remainder to get the minuend. SUBTRACTION, 48 EXERCISE XX. ^ 1;.^ 1 Subtract and prove : 1. 7674 1828 11. 82737 28192 2. 7589 3924 3. 8468 3623 4. 9825 7263 5. 8765 2729 6. 9382 3836 7. 9273 4787 8. 6484 3927 9. 7486 3728 10. 1 72648 17362 J EXAMPl 73046 57353 lo693 12. 84294 71886 13. 86276 27629 14. 75482 37625 16. 53932 28266 21. 22. 23. 24. 16. 94630 25265 74391 65498 85628 67677 90821 37298 34567 34098 25. 472865 174827 26. 573911 184288 17. 93825 48777 18.~75611 48123 19. 53724 19836 20. 68708 23774 27. 638420 239378 28. 708217 83649 29. 176391 98727 30. 246134 77139 31. 146875 146298 32. 837042 764238 33. 606111 372483 34. 711082 572835 35. 573216 475839 36. 671438 366529 37. 730425 689347 38. 637148 289158 39. 504216 192347 40. 742104 593344 In subtracting- the 5 we cannot take 1 from 0, so we take 1 from 3 which in the place where the stands is 10 ; then we take 1 from this 10 which with the 4 makes 14 ; 5 from 14 leaves 9. 3 from 9 leaves 6. 7 from 12 leaves 5. 5 from 6 leaves 1. Or reg"ard the 304 at once as 290 and 14, and say 5 from 14 leaves 9. 6 from 9 leaves 3, etc Example 18. 700005 9 from 15 leaves 6. 8 from 9 leaves 1. 4 from 9 362489 leaves 5. 2 from 9 leaves 7. 6 from 9 leaves 3. 3 from — 6 leaves 3. H!£15 700005 is equal to 699990 and 15. Note. — In cases like the above each nought becomes nine and the first sig-nificant figure is diminished by ene. \ ■■ 44 SUBTRACTION, EXERCISE XXI. Subtract and prove : 1. 59046 24873 9. 72030 47258 17. 724000 298765 25. 134005 112738 2. 60592 24678 10 . 46032 27809 18. 825000 654321 26. 200300 107108 3. 73402 15488 11. 56024 15028 19. 903000 276004 27. 800000 765432 4. 84601 77777 12. 80672 20839 20. 710022 300758 28. 100000 2006 5. 92730 39299 13. 720803 478629 21. 370004 52738 29. 400011 320013 6. 87200 27488 14. 430062 112389 22. 806108 207304 30. 711000 241008 7. 93024 88888 15. 500600 293456 23. 730009 249183 8. 27003 18276 16. 901030 278364 24. 740002 662078 EXERCISE XXII. 1. John was carrying a bag- with 213 marbles, but when he counted them he had only 174. How many did he lose ? 2. A house was bought for $1648 and sold for $1950. What was the gain ? 3. The battle of Hastings which was fought in the year 1066 was how many years before the battle of Water- loo fought in th:. year 1815? 4. A man who had 7000 acres of land sold 3075 acres. How many had he left ? 5. A man who earns $1600 a year spends $128 every month. How much does he save ? IS m SUBTRACTION. 45 6. In the year 1881 there were 1799 school sections in Nova Scotia, and in 1891 there were 1908. What was the increase ? 7. The population of St. John in 1871 was 28806, and in 1891 it was 39179. What was the increase in the 20 years ? 8. A man who paid $245 for a horse, $165 for a waggon and $86 for harness, sold the three for $500. How much did he g^ain or lose ? 9. Montreal had 155237 people in 1881, and 216660 in 1891. What was the increase ? 10. Toronto had a population of 96196 in 1881, and 181220 in 1891. What was the increase ? 11. A man who owed $2050, paid at one time $686, and at another time $758. How many dollars did he still owe ? 12. A man bought goods one day for $895, and the next for $1042. He made two payments, one of $966 and another of $684. How many dollars remained unpaid ? 13. The population of Halifax in 1881 was 36100, and in 1891 was 38556. The population of Quebec in 1881 was 62446, and in 1891 was 63090. Which city had the greater increase, and how much greater was it ? 14. The population of Ottawa in 1881 was 31307, and in 1891 was 44154. That of Winnipeg in 1881 was 7985, and in 1891 was 25642. By how many did the increase in Winnipeg exceed that in Ottawa? 15. In 1881 Cumberland Co. had 27368 people, and Lunenburg Co. 28583. In 1891 Cumberland had 34529, and Lunenburg 31075. How much greater was the in- crease in Cumberland than in Lunenburg ? M ( ft 4« SUBTRACTION — SIGNS, EXERCISE XXIII. SIGNS. Note.— The operation of Multiplication will always be performed htfore that of Addition or Subtraction. 1. 7280-2496. 2. 189x6-709. 3. 769x9 + 250-130. 4. 8068x4 + 3789-7600. 5. 7582x7 + 38462-7774. 6. 8192x12-9876 + 6789. 7. 8924-7899 + 6984-5868. 8. 5486 + 7789 + 4006-16864. 9. 7763-4498-2268-199. 10. 5986x8-36892-9386. 11. 59006 + 880-59885. 12. 746x86x3-74686. 13. 120004-73089-654-8848. 14. 780x9x8-8234-18679-20008. 16. 19x28x17 + 998-7409. 16. 80061-38708 + 12566-7644. 17. 7608 X 708 X 3 - 407629 - 70089. 18. 9009 X 909 + 808087 + 96884 - 128004. 19. 2x8x4x6x6x7x8x9-98765. 20. 12x18x14x15-20707 + 7070. 3&« Oral.— The teacher should ask the following questions and many others of a similar character : 1. What is the sum of 18 and 17? 9, 8 and 6 ? 16 and 25? 2. What number must you add to 9 to make 30 ? To 12? To 16? 3. How much greater is the product of 4 and 3 than their sum? Of 5 and 6? 8 and 4 ? 9 and 8? 4. Mary, who had a fifty-cent piece, bought a picture book and had 18 cents left. What did she pay ? 5. What is the remainder when you take the difference il \ SUBTRACTION — ORAL. 47 ed tl Is 16 To han ture ;nce I of 12 and 8 from their sum ? When you do the same with 7 and 11? 20 and 8? 9 and 15 ? 6. The difference between 5 and each of two other numbers is 2. Wliat are the numbers ? Between I) and two other numbers the difference is 4. What are the numbers ? 7. The product of two numbers is 85 and one oi' them is 7. What is the other? Product 54 and one of tliem G? 8. What is the product of the sum and difference of 4 and 2 ? Of 5 and 3 ? 8 and (5 ? 7 and 4 ? 5) and 2 ? 9. When a fruit cake is cut into 20 pieces, how many of them must you g"et to have .V of the cake? To liave ^ ? 5 • T U • 10. How many cents in \ of a dolhir ? In I of a dollar? TniP 35 4^ "Jp fiO aV EXERCISE XXIV. (a). TERMS. 1. Find the sum of 96 and G7. 2. Find the product of 96 and 67. 3. Find the difference between 96 and 67. 4. What is the sum of 806, 97, 1097 and 640 ? 5. What is the product of 7084 and 708 ? 6. What is the difference between 70081 and 8706 ? 7. When the addends are 984, 817, 6083 and 649, what is the sum ? 8. When the multiplicand is 867 and the multiplief 768, what is the product ? 9. When the minuend is 26405 and the subtrahend 14888, what is the remainder ? 10. The sum of two addends is 121 and one of them is 75. What is the other? 11. If the remainder is 84 and the minuend 81, what is the subtrahend ? ill 46 SUBTRACTION — TERMS. 12. The sum of four addends is 9®7 and three of the addends are 69, 465 and 388. What is the other ? 13. When the subtrahend is 7486 and the remainder 2906, what is the minuend ? 14. When the minuend is 7486 and the remainder 2906 what is the subtrahend ? 15. When the minuend is 7486 and the subtrahend 2906 what is the remainder ? 16. Find the sum of the product and difference of 9 and 6. 17. Find the difference of the product and sum of 27 and 7. 18. Find the product of the sum and difference of 34 and 16. 19. Find the difference between the sum and product of 903 and 87. 20. Find the difference between the sum and product of 807 and 96. 21. When 3 boys counted their money they found th« sown to be 136 cents. One had 54 cents and another 39. How many had the third ? 22. A man who paid $2765 for a house finds that he has $789 left. How many doliars had he ? 23. What is the sum of the prod'uct and difference of 8»24 and 906 ? 24. Find tlfve product of the sum and difference of 2004 and 1127. 25. Find the differe^kce between the S'U*m and product of 918 and 1006. EXERCISE XXIV. (fe). 1. If the muitip&an.d is 89736 and the multiplier 58007, r $18. He also paid $45 to each of his 2 hired men. How many dollars had he left? 9. A farmer sold 05 sheep at $8 per head and 8 cows at $24 per head. He paid $17 for tea and sugar, $28 for flour antl coriimeal and $125 for a new reaper, and then put the rest oi' his money in the bank. How much money did he put in ihe bank? 10. A man bought 8 building lots in a city. For the first he paid $205, for the second twice as much as f he first, and for the third twice as much as for the sec^.id. What did he pay for the three ? 1 1 . A man who earns $125 per month pays a yearly rent of $285 and $88 taxes ; he pays for light and fuel $109, for household expenses $725, and gives away $186. What can he save per year? 12. If 18 men couM shingle a building in 8 days, in how many days could 1 man shingle it? 13. If 136 horses eat 12 tons of hay in 6 days, how long would the same number ot tons last 1 horse ? 14. A drover who bought 46 head of cattle at $23 per head, and 57 at $27 per head, sold them all at $26 per head. What was his gain or loss ? 14 '" i EXAMINATION PAPER. NO. 2. 61 How ii 15. A book which has 866 pages has 88 lines on each page and an average of 9 words in each line and of 7 letters in each word. How many letters in the book ? 16. A farmer sent 25 loads of wheat to market. I^ach load consisted of 16 bags, and each hag lield 8 bushels. How much did he get for the wheat at $1 per bushel? 17. An agent bought 7.") acres of land for if^'if) an acre, and 1H6 acres for $IU an acre. He then sold 100 acres for $2'! an acre and the remainder for $8J3 an acre. Did he gain or lose, and how much ? 18. Two trains leave the same depot at the same lime and I/O in the same direction. One i^oes at the rate of 10 miles an hour and the otlier 21). What distance will they be apart at the end of 13 hours ? 19. Find the distance the trains would be apart in the last question if they had giMie in opposite directions. 20. What did a grocer gain on a barrel o'C flour which he bought for $5 and retailed at -4 cents per pound ? EXAMINATION PAPER. Nc. 2. (Time : 1 Hour. Value of each Question, 10). 1. Find the sum of .-«396, 9D3, 807.SG, 9504, HcSHH. 2. Multiply ninety-four million, eighty-seven thousand, forty-six, by seven thousand sixty-eight. 3. From 3700026, take 2701028. 4. Three of four addends whose sum is 1000 are 276, 129 and 544. What is the other ? 5. Find the continued product of 21, 25, 19 apd 7. 6. Multiply 12 by 8 and subtract 8 from 12, writing th j name of each part of the question. 7. John lives 1245 yards from the school house and James 967. How much further would John have to walk in a day than James, both going home to dinner ? 'ii •r I 62 ORAL EXERCISES. 8. From the product of 3008 and 80030 take their sum. 9. If 6786 men eat 10,000 boxes of biscuit in 28 days, how long" would the biscuit last 1 man ? 10. If a merchant buys 48 barrels cf flour at $4 a barrel, and 29 barrels at $6 a barrel, and sells it all in one lot at $5 a barrel, what does he gain? 38. Oral. — Samples for the teacher : 1. What three pieces of money make 7 cents? 11? 12? 15? 16? 21? 25? 27? 30? 31? 35? 36? 2. How many horses can be shod with 12 horse-shoes? With 28? 36? 48? 60? 80? 100? , 3. How many eggs in ^ of a dozen ? | of a dozen ? J P 4 • 4. Three boys picked 25 pints of strawberries. John picked 7 pints and Georg^e 8 pints. How many quarts did Frank pick ? 5. A baker made 20 cakes in the morning and 16 in the afternoon. He sold | of them in his shop and sent ] of them out in the wagon. How many had he left ? 6. What can 1 man earn in a day when 4 men can earn $8 ? When 4 men earn $5 ? $6 ? $7 ? 7. If the leng-th of your book is 6 inches and the length of your desk 40 inches, how many exact lengths of your book in the desk, and how many inches over ? If the book is 7 inches long? 8? 9? 8. Name the following:—^, ^, |, ^, J, |, ^, ^, y'g, f , |, 234623457 7 9 6» 6> 5' «> 7» 7» 7» 5' ?» TIJ' TO* 9. Let all the pupils write down their estimate of the number of pints the water-bucket will hold. Let one measure and report. Then let each pupil state the num- ber of pints the estimate was greater or less than the cor- rect number. 10. How many times must the glass by the bucket be emptied into the quart measure to fill it ? DIVISION. '■ I 37. Division, no less than multiplication, depends on the multiplication table, and it is in connection with the multiplication table it is most easily taug-ht. Very many oral lessons should be gfiven before any written exercise beyond results of one figure is attempted. Sample lesson : 1. Let the class repeat six times of the table. 2. How many 6's in 6? In 12? 18? 24? 30? 36? 42? 48? 54? 3. How many 6's in 6? In 7? Ans., 1 and 1 over. In 8? Ans., 1 and 2 over. In 9? 10? 11? 4. How many 6's in 12? 13? 14? 15? 16? 17? [In the next six questions beg-in with 18, 24, 30, 36, 42, 48 respectively]. 11. How many 6's in 54? 55? 56? 57? 58? 59? 12. How many 6's in 0? Ans., and over. In 1? Ans., and 1 over. In 2? Ans., and 2 over. In 3? 4? 5? 15? 34? 44? 59? Not less than 432 separate questions for the teacher are to be found in the table practice for division. Let the first lesson, oral and written, be confined to 2, the next to 2 and 3, and so on, adding a new number as the pupil becomes familiar with those already used. 38* The sign of division is -r. 12-r4 = 3, reads 12 divided by 4 equals 8. -'/- also means that 12 is divided by 4. J^ = 3. 13-r5 = 2 and 3 over, or 13~5-2|. (r,3) '( (;;, 64 DIVISION. EXERCISE XXVI. Set down the following expressions and fill in any num> ber wanting in each : 1. 8-2 = ( ). 2. 12-2 = ( ). 3. 18-^2 = ( ). 4. 8-( ) = 4. 5. 9-y = ( ). 6. V= ( ). 7. 24--B = ( ). 8. 15-^( ) = r). Example 19. Divide 13S into sixes. Dividend. Divisor. G)138(23 Quotient. 12 18 18 9. 20^4 = ( ). 10. 32-4 = ( ). 11. ¥= ( ). 12. ( )-4 = 6. 13. 35^5=:( ). 14. V= ( ). 15. (^) = 6. 16. {e) = S. 17. 18. 19. 8 + 9 = ( ). 15-8 = ( ). 7x( ) = 42. 20. 114-3 = 3}. 21. 42-G = ( ). 22. ( )--6 = 9. 23. V=( ). 24. (^^) = 4;. Example 20. Divide 600525 into ei^/iis, or by 8. Dividend. Divisor. 8)G00525(750C5§ Quotient. _5(i_ 40 40 In 13 there are 2 sixes and 1 over. In 18 tJiere are 3 sixes. 52 48 45 40 5 Remainder. In 00 there are 7 eights and 4 over. But as the GO is tens ofthou' sands the quotietit 7 and the remainder 4 are tens of thousands. Place the next digit in the dividend on the right of the remainder. In 40 there are 5 eights and no remainder. As the 40 is thousands the quotient '> will be thousan is. Bring down the next digit in the divi- dend. Then as there are no eights in •"> bring down the 2. In 52 there are G t'ii;h(s and 4 over. The 52 is tens^ so the quotient G and the remainder 4 are tt'n^. On bringing down the 5 we get 5 ones in the quotient and a remainder of 5 ones. This remainder Wv» write |, called five-eighths. Note. — To prove an exercise in division multiply the quotient by ^He divisor ^ adding in the lemainder. This ought to give the dividend. DIVISION. 55 ). Divide : 1. 4826-1-2. 2. 8609-^3. 3. 3576 -r 2. 4. 4305 4-3. 5. 51392-^2. 6. 73608^3. 7. 97300^4. 8. 53744^4. 9. 74256^3. 10. 612948^4. 11. 894213-^3. 12. 712715^5. 13. 882580-:- 4. 14. 856710-^6. EXERCISE XXVII. 15. 777532 -f 4. 16. 739368^6. 17. 865932^6. 18. 578934-^3. 19. 134472^4. 20. 253486 -f 6. 21. 708060^5. 22. 889315^5. 23. 856961 -f- 7. 24. 176687 --7. 25. 978672^8. 26. 274843^8. 27. 208278 -^ 9. 28. 128270^9. 29. 258063- - 8. 30. 412737- - 8. 31. 872905 - - 6. 32. 509884 - - 8. 33. 468070- - 9. 34. 874081 - - 7. 35. 256918- -10. 36. 156467- -11. 37. 897692- -12. 38. 742687 - -11. 39. 764896- -12. 40. 886919- -12 These exercises may also be done by Short Division, thus : Example 21. 774806^3. Divisor. 3 )77480 6 Dividend. 258268- Quotient. 7 divided by 3 gives 2 and 1 over. This 1 with the next number in the dividend placed on its rig'ht gives 17 ; 17 divided by 3 gives 5 and 2 over. 24 by 3 gives 8 and nothing over. 8 by 3 gives 2 .ind 2 over. 20 by 3 gives 6 and 2 over. 26 by 3 gives 8 and 2 over which is written |. Or thus : 3's in 7, 2 and 1 over. 3's in 17, 5 and 2 over. 3's in 24, 8. 3's m 8, 2 and 2 over. 3's in 20, and 2 over. 3's in 26, 8 and 2 over. 1( Example 22. 581342-^9. 9)581842 64593i '^ I 1 56 Divide : 1. 64842^2. 2. 832452 -^ 2. 3. 547638 -r 2. 4. 743852-^2. 5. 936342 -h 3. 6. 473642 -f 2. 7. 754376^2. 8. 456789^2. 9. 507088-^2. 10. 456789 H- 3. 11. 725626-^3. 12. 987654 -^3. 13. 848532'^4. 14. 648576^4. 15. 580574 -r 4. . 16. 769308-^3. 17. 672744^4. 18. 915910^4. 19. 607120 -r 5. DIVISION, EXERCISE XXVIII. 20. 712265^5. 21. 774806 -^ 8. 22. 7678224-5. 23. 728478-^6. 24. 849672^6. 25. 908544-^6. 26. 870855 -^ 6. 27. 786355 4 28. 939834 5 29. 102752 6 30. 849884 7 31. 997095 7 32. 167026 33. 241657 34. 178584 8 35. 258600 36. 433963 8 37. 209178 9 38. 291096 9 39. 245456^11. 40. 376020-^12. 41. 572480^11. 42. 758479^12. 43. 938026 -^ 11. 44. 995977 4-12. Let the pupils now work by Short Division, all the questions in Exercise XXVII. Example 23. 8)340029 Example 24. 9)675026 42503§ 75002§ EXERCI5E XXIX. 1. 761257 4-2. 7. 7543664-5. 13. 840372^7. 2. 975810 -^ 2. 8. 7950264-5. 14. 2837404-7. 3. 422415 -^ 8. 9. 696174 4-6. 15. 900264 4- 7. 4. 671528-^8. 10. 959448 4-6. 16. 496052 4- 6. 5. 5627394-4. 11. 739S69 4-4. 17. 462315 4-7. 6. 796312^4. 12. 2S1577 4-6. 18. 884499 4- 5. 5-7. --7. -^7. 1^6. -7. 4-5. DIVISION — MISCELLANEOUS, 67 19. 976504- ^8. 23. 552047 -=-8. 27. 715039 -f- 4. 20. 256032- ^8. 24. 755705 -r 6. 28. 387299 4-9. 21. 992005 r8. 2o. 927364 -^ 9. 29. 949234-^5. 22. 507820- ^7. 26. 378126 -^ 9. 30. 800026 -^ 8. 31. 104406 35. 666666 38. 507054 9 7 12 32. 593617 36. 800726 39. 700139 7 9 12 33. 888888 37. 528773 40. 951588 9 11 12 34. 777700 8 Example 25. How many oranges at 4 cents each can we buy for 56 cents ? Number of oranges we can buy for 4 cents = 1 orange t, 1 »„„. _ 1 orange tt it tt tt tt 1 cent = 56 cents = 1 orange x 56 = 14 oranges Or thus : Since 4 cents buys an orange, we can buy as many oranges as we have groups of 4 cents. In 56 cents we have ^_^ ^— " - or 14 groups of 4 cents each ; and as each group buys an orange, we can buy 14 oranges. 39. The quotient will always be of the same kind as- the dividend. EXERCISE XXX. 1. How many three-cent stamps can be bought for 93 cents ? 2. When apples are selling- for $3 per barrel, how many barrels can be bought for $615 ? 3. A man divided his fortune of $7,614 equally among his 6 children. What was the share of each ? 4. How many yards in 5280 feet, 3 feet being equal to 1 yard ? y^' \-i \'. i 6a • DIVISION. 5. How many four-dollar bills would pay a debt of $8468 ? 6. There are 8 quarts in 1 peck. How many pecks in 80000 quarts ? 7. When flour is $6 per barrel, how many barrels can be purchased with $17804 ? 8. How many four-bushel bags would be needed to hold 5008 bushels of oats ? 9. How many half-dozens are there in a barrel con- taining- 294 eggs ? 10. How many boxes, each holding 7 bushels, would be required for 80008 bushels of bran ? 11. In 1891 there were in Pictou County 84510 people. How many houses would they require allowing 5 to each house? 12. There are 10080 minutes in a week. How many minutes in 1 day? 13. How many tents would be required for a brigade of 6840 men, allowing 1 tent for 8 men ? 14. If the number of men in 9 brigades is 69138, what 5s the average number in each brigade ? 15. If a wagon moves forward 11 feet each time the large wheel turns, how often does the wheel turn in going 16896 feet ? 16. There are 9 square feet in a square yard. How many square yards in 766167 square feet? 17. How many dozen in 16 boxes of oranges contain- ing 284 each ? 40. We found (Example 13) that the same product is obtained when we multiply one number by another, or by the several factors of that other. So, also, in division. The quotient is the same, whether we divide the first num« ber by the second or by the factors of the second. DIVISION, 59 f Example 26. Divide 114076 by 9. 9)114075 12675 Quotient. 8 )114075 8 )88025 12675 Quotient. Example 27. 37681-49. Example 28. 666859 -^ 84. 7)87681 7)666859 7 )5388 769 Quotient. 12)95265 ■•^•n* "»-iV,) + G). 14. (87x4Hx3G) + (21)xlGxl2). 15. (900 X 87) - (H79 X H9). 16. (17784 + 7G) + (20514 + 84). 17. (12 + 3)x(21-7)x(G + 2). 18. (90 + G)x(19-ll)x(7 + 5). 19. (.S8 + 2)x(27 + 27- 0- 20. (8^^ + 1^) ^ (•^^> - 12) X (80 X 12) X (36 + 12). Example 30. — Fiom the continued product of the sum, pro- duct, difTi-rence and quolionl ot' iJ and 4, take the difference between 410 and 77. (12 + 4) X (12 X 4) X ( 12 - 4) X (12 + 4) - (410 - 77). = 10x48x8x8-383 = 1M482-888 = 18099. EXERCISE XXXVIIL (a;. 1. What is the sum of the sum and diflerence of 806 and 297? 2. Find the sum of the product and quotient o^ 512 and 04. 3. What is the sum of the product, difference and quotient of 69 and 28 ? 4. What is the continued product of the sum, differ- ence and quotjf'nt of 2M and 7? SIGNS ANt) BRACKETS. 67 5. From the difFeretice of 97 and 49 take the quotient of 72 and 4. 6. John had 85 cents, James had 39 more than John and William had 14 less than James. What was the sum of their money ? 7. P'rom the continued product of 7, 8 and 9, take the sum of 93, 1()7 and 49. 8. When the multiplicand is 807 and the product 28403, what is the multiplier? 9. W^hen the minuend is 80060 and the remainder 17900, what is the subtrahend? 10. From the sum of 93, 88, 119 and 187 take the difTerence 904 and 595. EXERCISE XXXVIII. (b). 11. What number must be taken from the sum of 274, 98 and 3G9 to leave the product of 27 and 24 ? 12. Henry has $44 more than George who has $52. Horace's money is $5 less than the sum of what the other two have. How much money has Horace ? 18- What number, multiplied by 98, will equal the pro- duct of 279 and 29? 14. What number, divided by 67, equals the quotient of 14688 and 864? 15. What number, multiplied by 9, will give the same product as 7083 multiplied by 29? 16. Find the sum of the five largest numbers that can be expressed by 8, 9, 0, 7. 17. Of what number is 9184, both divisor and quotient? 18. What number must be added 89 times to 850 to give 2897? i ' 68 EXAMINATION PAPER. NO. 8. J9. From the continued product of the sum, product, difference and quotient of 27 and 9, take the sum of the same two numbers. 20. Divide the continued product of the digits, except nought, by their sum. EXAMINATION PAPER. No. 3. (Time: 1 Hour. Value of each Question, 10). 1. There are 36 inches in 1 yard. In 8947 yards, how many inches? 2. In 70020 inches, how many yards ? 3. There are 34 pounds in a bushel of oats. A man bought 286 bushels by measure, but each bushel was 6 pounds short of the proper weight. How many pounds did he buy? 4. Divide the sum of 837 and 966 by the difference between 606 and 209. 5. Simplify (16 - 12) x (27 -f 9) x (8 + 3 + 6 + 18 - 22). 6. What number must be added to 2498 so that it may be exactly divisible by 301 ? 7. A farmer gave 17 cows, worth $24 each, for 186 sheep. What did each sheep cost him? 8. A drover had 60 head of cattle, which cost him $27 per head, but he lost 6 of them. What must he ask per head for the remainder so as to lose nothing? 9. Construct 13 and 14 times of the multiplication table. 10. Multiply and divide 21978 by 64, using factors. AVERAGES. ' 44. If one boy has 10 cents, a second 15, a thira 35 and a fourth 12, what is the average number of cents owned by each? They have 10 cents -f 15 cents + 35 cents + 12 cents, or 72 cents altogether. Now, the 72 cents, divided equally among- the 4 boys, would give each one 18 cents. The average of 10, 15, 35 and 12 is 18. That is, if each boy had 18 cents, the amount owned by the four would be the same. Example 37. 77 sheep. 145 117 96 70 5 )505 loT ( ( (( ( ( ( ( (( i( In one pasture there are 77 sheep, in another 145, in another 117, in another 96 and in another 70. What is the average number of sheep in each pasture? Average number in each pasture. EXERCISE XXXIX. 1. In a certain school-room there were 85 pupils on Monday, 40 on Tuesday, 42 on Wednesday, 39 on Thurs- day and 34 on Friday. What was the average attendance each day? 2. The ages of 4 sisters are 8, 10, 13 and 16 years. What is the average age ? 3. In the dining-room of an hotel there were 27 people at breakfast, 55 at dinner and 35 at tea. What was the average number at a meal ? 4. One basket has 3 dozen and 8 eggs, another 4 dozen and 9, another 2 dozen and 5 and another 2 dozen and 10. What was the average number in each ? 5. Of 6 books on a table, one has 458 pages, another 316, the third 400, the fourth 256, the fifth 713 and the sixth 293. What is the average number of pages per book? 1 70 ROMAN NOTATION. I I 6. Find the averag^e of 123, 77, 14 and 29. 7. Find the average of 209, 807, 806, 903, 544, 678 . and 212. 8. At an examination, a pupil made a mark of 72 in history, 64 in g^eogfraphy, 47 in grammar, 78 in arithmetic and 56 in drawing-. What was the average ? 9. Ln a large school, there are 114 pupils in grade I., 108 in grade 11., 9H in grade MI., H5 in grade IV., 71 in grade V., 62 in grade VI., 57 in grade VII. and 4^ in grad* VIII. What is the average number of pupils in each grade? 10. A bicycle rider, in going 5 miles, did the first mile in 127 seconds, the sec(Mid in 125, the third in 134, the fourth in 14H and the fifth in 132. What was the average time for each mile? ROMAN NOTATION. 45. Numbers can be expressed not only by words and by figures but also by letters. The method of expressing numbers by letters is called the Roman Notation. In this notation, which is now used only to denote chapters in books, etc., the letters employed are : I. Denoting: one. C. Denoting: one hundred. V. i( five. D. (( five hundred. X. (( ten. M. ii one thousand. L. (( fiftv. In writing numbers in Kovtan ttumera's we a -d to the number expressed by any one of the above letters by placing- letters on its rigtit hand side, and we lessen the number which a letter represents by placing' a letter ot less value on its left. A bar over a letter increases its value one thousand times. Thus:"\'=. 5000. "M = 1000000. Example 38. Express 4, 6, 8, 9, 17, 20, in Roman characters. 4 is 5 - 1 or IV. 6 is 5 4- 1 or VI. 8 is 5 + 3 or VIII. 9is 10 - 1 or IX. IT is 104-5 + 2 or XVW. 20 is 10+10 or XX. L o CANAI>1AN MO>iEY» •u Example 89. Express 46, 72, 112, a40, S59>, 1111, 2795 in Roman CD Ar3.c tiers 46 ij> 50-10 + 5 + 1, or XLVI. 72 i^ 50+ 10+ 10 + 2^ ot LXXI I. 112 is 100 + 10 + 2, or CXII. 5340 i^ 800 + 50 - 10, or CCCXL. 659 is 500 + 100 + 50 + 10-1, or DCLIX. 1111 is 1000 + 100 + 10+1, or MCXl. 2796 is 1000 + 1000 + 500 + 100+100+100-10 + 5, or MMDCCXC V. EXERCISE XL. Write in figures : 1. IV., VII., IX., XXVIII. 2. XVIII., XXXIX., XL., LVI. 3. LI., LXVIL, XC, XCIII. 4. DCLXVI., CCCXXX., CDXL. 5. MDCLXVI., MMDIV., DCCCXLIX. Write in Roman Numerals : 6. 2, 8, 4, 8, 9. 7. 18, 15, 20, 22, 25. 8. 14, 16, 24, 29, 80. 9. 44, 55, 66, 77, 88, 99, 100, 138. 10. 251, 486, 520, 614, 892, 1894, 10000, 100000. CANADIAN nONEY. 46. In Canada money is counted in dollars and cents, 100 cents make 1 dollar. Cents are reckoned in ones and tetis^ but we do not speak oi hundreds of cents, for that means dollars. 47. Of copper coins we h.ave one, — the 1-cent piece. Of silver coins we have four, — the 5-cent piece, the 10-cent piece, the 26-cent piece and the 50-cent piece. 48. We have no Canadian gold coin. 49. Two dollars forty-five cents is written $2.45 ; two dollars is written $2.00: forty-five cents, $0.45; forty cents, $0.40 ; five cents, $0.05. r^ 72 ADDITION — DOLLARS AND CENTS, EXERCISE XLI, Write the following in words : 1. $2.45. 4. $6.56. 7. $9.05. 2. $3.75. 5. $17.25. 8. $10.10. 8. $4.18. 6. $26.26. 9. $20.08. 10. $72.07. 11. $39.01. 12. $375.67. Express in figures: 13. Eight dollars sixty cents. 14. Nineteen dollars nineteen cents. 15. Twenty dollars forty-five cents. 16. Thirty-three dollars eighty-six cents. 17. One thousand dollars. 18. One hundred dollars ninety cents. 19. Six hundred four dollars four cents. 20. Thirty thousand thirty dollars thirty cents. ADDITION. 50. Dollars and cents are added, etc., like ordinary numbers, care being taken to keep the point ^ota A7 which separates dollars from cents in its proper place. Example 40. Add $254.07, $63.90, $800.00, $17.06, and $904.10. 63.90 800.00 17.06 904.10 $2039.13 Add: 1. $8.25 9.02 7.68 5.50 2. $930.26 854.95 716.08 83.30 EXERCISE XLH. 3. $775.14 806.90 10.75 909.22 4. $8060.60 704.15 93.68 7400.00 917.17 5. $10500.00 9064.83 7586.44 900.00 77^ 6. $94680.35 94712.19 6984.10 87004.48 890.00 MULTIPLICATION — DOLLARS AND CENTS, 78 »7. 1. (, 7. A boy paid $10.75 for a suit ot clothes, $8.40 for an overcoat, $1.25 for a hat, $2.35 for boots, and $0.66 for gloves. What was the cost of the whole outfit ? 8. A lady, when out shopping-, paid $5.60 for a hat, $1.45 for gloves, $12.85 for cashmere, $8.67 for velvet, $0.23 for spools, and $1.08 for ribbon. What was the amount of her bill ? 9. A young man saved, in one week, two dollars seven cents, in aPDther two dollars thirty, in another one dollar ninety-five, and in another three dollars. How much did he save in the month ? 10. A man paid $145 for a horse, $112 for a wagon, $26.75 for harness, one dollar thirty-five cents for a whip, and two dollars and a-half for a knee-rug. What did he pay for the outfit ? nULTIPLICATION. 50. Example 41. $715.45 9 Example 42. $827.05 678 $G439.0l 1 ■ 661640 578935 496230 $560739.90 EXERCISE Multiply : 1. $807.25x8. XLIH. 6. $8008.50 x 97. 2. $750.20x9. 7. $6809.08 X :346. 3. $1086.46x12. 8. $9487.63x578. 4. $681.55x37. 9. $10700.40 x809. 5. $7658.35x68. 10. $87601.01 x817. 11. What is the cost of 9 yards of cloth at $1.18 per yard ? 12. What does a farmer get for a tub of butter weigh- ing 86 pounds at $0.23 per pound ? 13. What would a farmer get for 9 tubs of butter, each weighing 31 pounds, at 24 cents per pound ? }■ [ 7'4 aUBTIRACTIOJ^ — DOLLARS AND CENTS, 14. What would a w«b of 197 yards oi qloth be worth at 86 cents per yard ? 15. What is the value of IB webs of cloth each contaiiir> ing^ 148 yards at $1.15 per yard ? 16. A farm of 89 acres was bought at $8.75 per acre What wjis paid for it ? 17. A farmer sold 18 pounds of fresh butter at 26 cents per pound, 2 dozen heads of cabbai^e at G cents per head, 11 bushels of potatoes at 66 cents per bushel-, and 12 dozen of eg-gs at 22 cents per dozen. How much did he get for all? 18. A farmer hauled 8 loads of wheat to market, taking an average of 12 sacks holding B^ bushels each at each load. He sold the wheat for 66 cents per bushel. How much did he get ? 19. If a man earns $18.65 per week how much does he earn in a y^^ar ? 20. If i man earns $2.65 on each week day, what does he earn in a year? SUBTRACTION. p-n. Example 48. $10240.04 7008.65 S;}2:i 1 . :m I EXERCISE XLIV. 1. From $S7.50 take $;50.75. 2. From $'00.00 take $«S.21. 3. iM-om $010.10 take $17.05. 4. I'roni $1004.26 take $H70.H0. 5. From $2(575.08 take $1;-}S6.80. 6. From $80060.01 take $7714.05. 7. From $10000.00 take $0099.45. 8. From ten thousand dollars take eight thousand eighty-eight dollars lifly-four cents. DIVISION — 2>OvLJUA.R5. AjyUX CENTS. 7,4 9. A man to whom a debt of $871.15 was owing was able to collect only $609.50. How mwh did he lose ? 10. A man who built and furnished a house at a cost of $2159.47, sold it for $2400. What did he gain ? DIVISION. &3^ ExAM^wt 44i. Divide $44165,66 into 7 equal parts. 7) $44165.66 $6309.38 Example 45. When apples are $2.45 per barrel how many barrels can be purchased for $56.35 ? 2.45)$56.85(23 Here we find that in $56.85 the price of 1 barrel, $2.45, is contained 28 times. Hence we can buy 23 barrels. 49 735 735 Note. — In exercises like the above the pupil must be careful to have the same number of figures on the rig-ht hand side of the point which divides dollars from cents in both divisor and dividend. EXERCISE XLV. 1. Divide $320.35 into 5 equal parts. 2. Divide $H00.10 into 6 equal parts. 3. Divide $2743.06 into 7 equal parts. 4. Divide $12104.25 into 8 equal parts. 5. Divide $402.04 into 46 equul parts. 6. Divide $65099.16 into 763 equal parts. 7. Divide $140694.99 into 697 equal parts. 8. If $125.10 is divided among 9 persons what sum will each get ? 9. An estate valued at $11068.75 was left to a family of 8 children. W^hat was the share of each ? 10. If the cost of building 29 miles of railway is $263476.40, what is the average cost per mile ? 11. When butter is worth $0.24 per pound, how many pounds can be bought for $12.96? 12. How manv chairs, at $1.65 each, can be purchased for $28,05 ? w ' 76 MISCELLANEOUS. EXERCISE XLVI. MLSCELLANEOUS. 1. How much money would be required to pay 8 men for one week, at $1.45 per day? 2. How many pounds of tea, at 45 cents per pound, can be had for 9 dozen e^g's at 15 cents per dozen? 3. A man sold a horse for $118.50, and a wagon for $81.75. After paying bills to the amount of $106.86, how much had he left? 4. A farmer sold 3 cows at $22.50 each, 16 sheep at $3.35 each, and a horse for $120. He then bought a wagon for $110, and 48 yards of Brussels carpet at $1.85 per yard. How much money had he left? 5. A merchant bought three chests of tea, of an average weight of 112 pounds, for 22 cents per pound, and sold the lot at 30 cents per pound. What was his gain? 6. A lady who bought 18 yards of dress goods at $0.86 per yard, and trimmings costing $4.17, paid $10.45. How much was still owing? 7. A man sold 5 lots in a city for $275.25 each, and invested the money in a farm of 75 acres. What did the land cost him per acre? 8. A man goes into a grocery store with a twenty- dollar bill. He buys a barrel of flour at $6.20, a barrel of cornmeal for $3.85, 4 pounds of tea at 35 cents per pound, 18 pounds of butter at 24 cents per pound and 8 dozen eggs at 20 cents a dozen. What change ought he to get? 9. A man bought 37 acres of land for $800. He spent $350 in improving it, and then sold 20 acres at $35 per acre and the rest at $82. What did he gain ? 10. When flour is $5.35 per barrel, how many barrels can be purchased for $879.85 ? EXAMINATION PAPER. NO. 4. 77 11. A farmer qfave 3 tons of hay worth $12.60 per ton, a cow worth $2r), and 50 pounds of butter for a $75 mow- ing" machine. How much was he allowed per pound for the butter? 12. A drover bought 12 head of cattle at $17.50, 7 at $22 and 9 at $24.40. At what average price must he sell them so as to gain $HH.40? 13. Bought a chest of tea for $85.20 and sold half of it for $22 at the rate of 40 cents per pound. What was the weight of the chest, and what price per pound did I pay? 14. Bought a flock of 115 sheep for $873.75 and sold- 87 of them at $8.60 apiece and the rest at cost. What was the gain ? 15. A shopkeeper's receipts on Monday were $854.51, on Tuesday $860.40, on W'ednesday $402.12, on Thursday $875.08, on Friday $284.86 and on Saturday $529.87. What was the average amount taken each day ? EXAHINATION PAPER. No. 4, (Time: 1 Hour. Value of Each Question, 10). 1. What number increased by the difference between 5004 and 2806 will equal the sum of 2086, 977, 2986 and 809. 2. How many pounds of coffee at 28 cents can be bought for $11.76? 3. There are 1728 cubic inches in 1 cubic foot. Fin^ how many cubic feet in 7560000 cubic inches ? 4. Multiply together the numbers expressed *>y LXXXIX. and XIV., and give the product in Roman characters, 5. Add one cent; four thousand dollars four cents; three hundred three dollars three cents, and multiply their sum by 49. ve «XAM1 NATION PAPER. NO. 4, 6. A cubic foot of water weig^hs 1000 ounces. How many pounds of 16 ounces each in a cubic foot of water ? 7. A man went into business at the a^e cf 25, and re- tired at the a^e of 60 with a fortune of $80442.45. How many dollars did he save each year on an average ? 8. A g^rove of 55B6 maple trees is to be thinned by having" every seventh tree cut down. How many will be left ? 9. The circumference of the earth at the equator is 24H9H miles. In how many hours would a railway train moving- 36 miles per hour travel such a distance? 10. What can be saved in a year by a man who earns $500, and who pays $M.75 a week for board and $4.40 a week for clothing* and other expenses ? BILLS OF GOODS. 53. A Bill of Goods is a written statement of g"oods sold, giving dates, quantities and prices, |»4 A Statement of Account is a written statement of th«# total sums due according to bills previously rendered. 55. One to whom a debt is owed is called the Creditor^ and one who owes a debt is called the Debtor, SPECIHEN OF A BILL OF ITEMS. St. John, May 1, 1894. Mr. Robert Ross, Bought of DEARBORNE & CO. 1894. April. 11 15 lb. Java Coffee @ 35c. 10 1b. Mocha '* @ 46c. 7 lb. Cream of Tartar @ 82c. 9 ft). Tea @ 84c. 6 packages "Peerless" Ginger @ lie. 1 Box "Surprise" Soap BILi.S OF niiMS. 79 SPECIMEN OF A RECEIPTED BILL WITH CREDIT ITEMS. Halifax, N.S., May 15, IHOI. Mr. Thomas Forbes, Bot. of T. C. ALLKN cSc CO. IHDl April \) 12 copies Shakspeare (Mo- rocco) ((I $1.25 1 $15 00 10 qr. Note Paper. . . .(« .25 1 1 '^ 50 5 pkgs. Envelopes . . (a), .08 1 ' . . . 10 2 boxes Pens («' .35 ! 1 70 1 bottle Ink 1 •10 45 $28 1 8 reams F'oolscap. . .(«' 3.15 y 46 Less 3 chaldrons Svdnev Coal 1 C«^ 5.25 15 75 2 tons Hard Coal ( Nut) i («J 3.20 G 40 22 ~$0 15 30 Received payment, June 3, 1H94. T. C. ALLEN & CO., Per Harry Powell. SPECiriEN OF STATEHENT OF ACCOUNT RECEIPTED. Charlottetown, June 2, 1H^\, Messrs. Creighton & Congdon, To STEWART & GATES, Dr. 1894 June 12 To account rendered Received payment, June 18- 1894. STEWART & GATES, $29 65 Per D. A. F. ■IN ' 80 BILLS OF ITEMS. I EXERCISE XLVII. Make out bills for the following- accounts, supplying places and dates where these are not g-iven : 1. P. J. Grant, Pictou, bought of A. M. Bell, Feb. 27, 1H01, 60 lbs. ;-i-inch nails, ^ 4c.; L50 lbs. shingle nails. {(V 5c.; 2 dozen door hing^es, (a\ $1.05 per dozen; H dozer small cans paint, @ $1.25 per dozen. 2. Crofton Dickie bought of W. H. Cawsey & Co.y March 12, 1H94, 12 lbs. sugar, (a) Oc; 8 lbs. tea,' @ a2c.; 5 lbs. butter, Qi. 24c.; 4 lbs. beefsteak, @ 13c.; 3 lbs. cheese, («> 16c.; IH lbs. pork ham, (a, Vic. 3. W. E. Thompson, bought of Colwell Bros., 1 Melissa coat, @ $16.75; 2 all-wool shirts, («) $1.75; 1 silk umbrella, $1.25; 1 walking cane, $0.90; one-half dozen linen handkerchiefs, (a), $0.27 each. Make out receipted bill. 4. Miss Jessie Mcintosh bought of McPherson & Free- man, 1 pair kid g^loves, (a) $1.40 ; 13 yards Muslin, (a $0.1K; 8 yards lace, (a} $0.15; 9 yards dress serge, (a), $0.75; n yards lining, (a] f^O.lB ; 2 yards canvas, @ $0.20 ; 2 dozen buttons, Q^ $0.25 per dozen ; 2 spools silk, (oj, $0.05 ; 1 spool twist, (a> $0.06. 5. Miss Mary Chishclm bought of Barnstead & Sutherland, Halifax, June 6, 1894, 12 yards black silk, ^j $1.45; 9 yards flannel, (a! 40c.; 2 pairs silk g^loves, @ 65c.; 11 yards ribbon, ^, 17c.; 4 crash towels, @ 45c.; 2 linen tab'ie-cloths, @ $2.25 ; 1 chenille table-cover $4.50. 6. May 15, 1894, Duncan Grant, bought of R. McCiregor & Sons, 25 bbls. flour, (a $4.85 ; 18 bbls. rolled oats, («> $4.85 ; 9 bbls. kiln-dried cnrnmeal, (S) $8.30 ; 1 chest tea weighing- 115 lbs., (a) 28c.; 8 bbls. brown sugar, each 268 lbs., (a^ 4c.; 1 bbl. granulated sugar weighing 273 lbs., @ iSc. per lb. 7. G. J. Ross, bought of Isaac Creighton, March 12, 1894, 7 lbs. roast beef, (itl 12c.; 8 bushels potatoes, (d> 65c.; 8 bottles pickles, @ 25c.; 4 cans corn, @ 17c.; March 14, 6 lbs. beef steak, @ 13c.; 2 bunches celery, (a 7c.; 6 lbs. sugar, @ 7c.; 3 lbs. coffee, (a) 85c.; 1 package Peerless e ■' y UNITARY MKTU on 81 pepper, (u), He; March Ifi, lbs. roast beef, C« 12c.; i^ heads >al cabbag-e, (tc He. On March 15, p;iiJ $2, and March 10. Make out bill accordiii;;ly. 8. Messrs. Layton i\L Co., purcliased of Smitli Bros., bills as follows: Starch 1 .$) I. (*)•".; March 29, Ss(); April IH, $101.10; April 2."), JS():i.2."); May 2, Slid.?."). Draw up a statement oi' these bills, datei.1 May •">, and rcc>.'ipl it (May S) on behalf of Smith Hrc»... 9. Frank lulen bouj^ht of Cr.iLTL,'" Br^.^s., May I^ 6 (loz. coat-hooks, (n lOc; T) doc>r kiul's, (n Lie; ;{ r.ick pulleys, (d '\r)c. May 7, 25 lbs. cut n.iils, ('i Ic; 5 door locks, (r/ ;">.")c.; 9 doz. screws, (*/ lOc; li padii^cks, ('/ '27c.; 1 brass chain, ()5c.; 2 sets of lire-irons, (5. On June I 1, Alex, (irant i^-ot from James W, I'^-aser 2H lbs. of butter. Or $0.20, i'ud on June 21 a 15 lb. tub at the same rate. The balance was paid in cash on June 21. Make out bill. U.NITARY nETHOD. 56. If 8 oranjL:;"es cost 12 cents what will 5 cost? The natural method of solvini^" a question of this kind, ai-.J the one which the mind of a child will iinariably adopt, is to lind the price of <'//c article and, usiiii,'- that as a fresh starting" point, lind the value of the number required. Thus: Ex.\MPLE K). Co-»t of :'. orauL^es = 12 cents. 1 oranj/e — '.,• = 1 cents. < t .) iiran<''es - 1 cents X i) 20 cents. 82 UNITARY METHOD. Example 47. — If 6 bushels of wheat are worth $9.75 what are 87 bushels worth ? Value of bushels of wheat = $0. 75 $9.75 «* 1 bushel '" =6" $9.75x37 " 37 bushels '* = ^ $800.75 6 = $G0.1'2 + EXERCISE XI.VIII. 1. If () pounds of sui^-ar cost l>() cents, what will 11 pounds cost ? 2. When 4 quarts of salt can he bouiji-ht for 12 cents, what nui>t be paid for 13 quarts ? 3. When apples are sellini^ at 1 5 cents per dozen what would 20 apples cost ? 4. A i^irl paid 09 cents I'or 23 peaches. How much wns that per dozen ? 5. What will 7 pounds of tea cost ;^ hen 13 pounds cost $4.10 ? 6. W^ien $H|.75 is paid for 15 barrels of flour what is tiie value of 9 barrels ? 7. A man who had H chaldrons ci Sydne\- coal put uito his cellar, paid $10. HO for it. What would h.e have had to pay for 13 chaldrons? 8. If 14 acres o( land cost S()l.0O, what would 1 square mile (0 40 acres) cost ? 9. If 3 men can earn $22.50 in a week, wliat can 50 men earn ? 10. 27 men can thresh 450 bushels of oats in a day. How many bushels could 9 men thresh? 11. The man who works H hours a day, works 2RH00 seconds. How many seconds ^//ore does the man work who is employed 10 hours a day ? 12. A railway train that travelled from St. John to UNITARY METHOD. 88 ^5 Halifax, 275 miles, in 550 minutes, would require how many minutes to g"o from Truro to New Glas^'-ow, 48 miles? 13. A lady paid $22.95 for 17 yards of silk, but finding: that she had not enoug^h, she sent a i^Mrl with a $5 bill for 8 yards more. What chanj^-e oui,'-ht the girl to bring back? 14. A tiain that can run from Halifax to Sydney, a distance of 214 miles,, in 821 minutes (5 hours 21 minutes), would require what time to travel from Halifax to Quebec, a distance of 674 miles ? 15. How far would a man, who can walk 10 miles in 8 hours, walk in 15 days, travelling* 10 hours a day? 16. When 8 g-allons of molasses cost $1.05, what would a tierce containing 42 gallons cost ? 17. What would it cost to carpet a '^oom ha\ing an area of 20 scjuare yards, with carpet costing v$l.S5 per square yard ? 18. If the cost of carpeting ji room containing 20 square yards is $87.70, how much money would pay for similar carpet for a room of 21 square yards ? 19. A farmer, who has a herd of 17 Jersey cattle, o( equal value, ofT?rs 8 ot' them for $102.75. What is the value of the whole herd ? 20. A farmer sold an H-pound tub of butter for $1.90- What would he g^et fov 4 tubs of the same quality, con- taining 88 pounds each ? Example 4K. If 15 men dig a trench in 24 days, how many men could dig it in H days ? Men required to dig the trench in 24 days - 1 5 men. " " '♦ " 1 day =-15 men x 24 ^ . 1') men x 24 « « it <( 8davs^ _ = o 45 men. Example 49. If 15 men can dig a trench in 24 days, in how many days can 45 men dig it? Time required for 15 men to dig the trench = 24 days. ** 1 man " " ** =24 days x 15 24 davs X 15 ,^ , •' 45 men ' — y. -8 days. 45 4< C( ! IB t'i 84 UNITARY METHOD. EXERCISE XLIX. ^ . If 1) boys can pick the plums in an orchard in 16 days, how many boys could pick them in 21 days? 2. If 7 <4ir1s can pick the strawberries in a certain j^arden in {• days, how many jjfirls can pick them in ii days? 3. '{O horses can haul the brick for a new buildiiiLf in IH days. How many horses would be required to ilo the work in '20 da\ s ? 4. If 12 men can ploui^h a field in 11 days, how many men could plou_:4h it in \ days ? 5. If '5 men can dii,'' a cellar in 1:5 days, how many men would be retjuired to dii^'" il in lida\s? 6. If •"> men can dii;- a trench in 12 days, in how many days can 20 men dii,'' it ? 7. When ;I2 masons can build a wall in 27 tlays, in vyhat time could IH masons build it ? 8. If I''>0 workmen can i^rade a line of railway in J}2 davs, in how manv days can oOO men i^rade it ? 9. How liMii^ w'll 1)5 men require to do a piece ctf work which takes 15) men 'il davs? 10. In how many days could 23 men clear a piece oi' rouLjh land which took 1 1 men ii) days to clear? 11. If 9 printers can set up the type of a book in hO days, how many printers could set it up in 18 days? 12. If 10 looms weave 10000 yards of cotton in 15 days, liow many looms would produce the same number of yards in a davs'-^ 13. If 10 men can build half of a wall in 88 days, in what time can 80 men linish it, that is, do the same amount of work? 14. After 125 men had been throwin<*" up a rampart for 28 days it was found to be half done. A detachment of hO men were then sent to their assistance. In how many days from the arrival of these men will the wall be finished? 15. When 25 pounds o:*tea are boui>-ht for $9.25, what must be paid for 17 pounds of the same quality? UNITARY METHOn. 86 16. When $2H.;i5 is paid for 9 barrels of cornmeal, what will 4IJ barrels cost? 17. If 2S men can build a house in IH days, now many more men must be hired so that a second house of the same kind may be built in 7 days. 18. A contractor has 45 teams hauling stone for a rail- \v..y bridi^-'e. At the end of 21 days the work is half done and ]() of the teams y;o to work elsewhere, in how many da\s mo'/e will the stone be hauled. 19. When c^ranges are worth $0.85 a dozen, what will 10 orani^es cost ? 20. if 5-^5 men can cut 400 cords of wood in 7 days, in how many days can they cut 700 cords? Example 50. When 7 barrels oi' rolled oats can re boui;ht for $;M.()5, how many can be bcnij^ht for $lr{:{.()5 ? Nunibor of bbls. which can be hot. for SiU.C,") 7 bairols 7 « •< •* " '• si.o»; -- '* 34. (');') (C « « (( " $l;}3.G5^:ZiLli!!^l!i = 27 banols. 34.65 EXERCISE L. 1 f * I 1. When 5 yards of cloth can be bought for $4.25, how many yards can be boui^ht for $1().15 ? 2. If 11 men can be hired a day for $15.95, how many can be hired for $:M.HO? 3. If 47 pounds of su^ar cost $2.H2, how many pounds could be purchased for $1 1.10? 4. How many pecks of plums can be bought for $24.15, when $17.25 buys 15 pecks? 5. When $2.38 will buy 17 cans of tomatoes, how many cans will $4.20 buy? 6. If a railway ticket from Charlottetown to George town, 46 miles, costs $1.3H, what ought a ticket cost from Charlottetown to Tignish, 117 miles? 7. A man who invests $179.80 in land gets 31 acres. How many acres could he buy at the same rate for $539.40 ? 86 UNITARY METHOD. ) I 8. A man who pays $980 for land, bujs at same rate as a neighbor who got 70 acres for $661. How many acres does he buy? 9. If 4 yards of canvas can be bought for $0.86, how many yards can be bought for $2.15 ? 10. If 18 yards of calico can be purchased for $1.85, how many will $0.45 purchase ? 11. Wlien $17.50 will buy 50 pounds of coffee, how many pounds will $2.45 buy? 12. When a farmer gets $3.99 for a tub of butter weij^^iiing 19 pounds, how many pounds must he give to pay a bill of $9.24? 13. If a return ticket from Halifax to Truro, 62 miles, costs $2.79, what must be the distance between Halifax and Moncton, where a return ticket at the same rate would cost $.S.B7? 14. If 8 chests of tea, each weighing 67 pounds, cost $rj2.1:J(), what will H chests, each weighing 69 pounds, cost? 15. When $2. (SO buys 21 cans of peaches, at what rate per dozen are the cans selling ? 16. If 27 men can build a bridge in 25 days, in what time could 15 men build a similar one? 17. If 75 soldiers can be supplied with new boots for S2.'il.2r), how many could be supplied for $h04 ? 18. When 28 tons of hay bring $546.25, how many tons will pay a debt of $166.25 ? 19. It 204 men do a piece of work in 85 days, how t\iany men would be required to do it in 420 days ? 20. When 18 barrels of flour can be bought for $57 85. how many barrels can be bought for $481.65? 1 EXAMINATION PAPKR. NO. 5. 87 is s EXAMINATION PAPER. No. 5. (TiMK : 1 Hour. Value of EACii (Question, 10.^ 1. From 400500 take the product of 264 and 800. 2. Divide 5648897 by 4064. 3- What number must be added to the ditTerence between 88 and 59 to make 100? 4. Find the avera^^e of 85, 72, 88, 68, 55 and 29. 5. If half a dozen dozen peaches can be bought for $1.08, what will six dozen dozen cost ? 6. What was the value of a prize, divided equally amonL^f 842 sailors, when the 7 men from \'arinouth g"ot $899 ? 7. Multiply 2646 by 48 and divide the product by 27, usinij;- factors not i^reater than 4. 8. A merchant boutrht 685 barrels of flour, at $4.62 per barrel, and after pav'nj^'- 27 cents freis^'ht per barrel, he sold for $5.10 per barrel. What was his g^ain ? 9. If $84,72 will buy 16 yards of silk, how many yards in a web of the same quality for which $484 has been paid ? 10. D. A. Fraser boue^ht of H. P. Bezanson half a dozen linen collars Qi $0.25 each; 8 dress shirts @ $1.15 each; half a dozen cuffs (« $0.80 each ; 2 neckties at $(),()5 each; 1 fur hat (a $2.75, and 1 silk handkerchief (n $1.20. Make out receipted bill for the above, filling" in date unc place at which you write. I ' 88 EXAMINATION PAPER. NO. 6. EXAMINATION PAPER. No. 6. (TiMI. : 1 Ihu K. \'aLI K OV l.Al II QlKSTION, 10.) 1. V\nd the product of the sum and ditTerence o^ lliirty- six thousand and nineteen and one thousand and one. 2. Divide r„S()(;H«)(WiS.i by iHu^. 3. The minuend in an exercise in subtraction is 1001086 and the remainder 112'J. What is tlie subtra- hend ? 4. When $l(M).r)0 is divided amoni,'- '2") persons, what IS the share of each ? 5. If 17 oran^-es are worth H7 apples, for how many apples can I exchange HHO orani^^es? 6. Make out the bill for the followincf, supplying* place and date: 7 yards of Scotch tweed, («! $1.8."); 5 yards of blue pilot, ((7' $15. ();"); 9 yards Canadian tweed, (i^ $I.ir); 11 yards Oxford g-ray,' (a> $().<)(), and 27 yards silk bindings @ $0.18. 7. A boy worked for a farmer 10 days, receivingf $0.85 the Hrst day, with an increase of $0.05 each day. What was the amount of his earnings and the aver.'ii^e for each day? 8. If 8G yards of lawn cost $H. 28 what will 97 yards cost? 9. When 4 dozen pairs of g^loves are boug-ht for $55. ()H, how many pairs can be boui^ht for $()8.s0? 10. The sum of thr'^e numbers is 400. The first two are equal, and the third is equal to the sum of the first and second. What are the numbers? ANSWERS. Exercise I.— (Pa^^e 9).— 1. Seven. 2. Eleven. 3. Seventeen. 4. TsveiUy-six. 6. Thirty-threi'. 6. I'orty-ei^ht. 7. Fifty-nine. 8. Sixty-six. 9. Seventy. 10. Kij4:hty-fhree. 11. Ninety-nine. 12. One luiiidrecl twenty-five. 13. One humlred sixtv-ei^ht. 14. One huiuli-ecl thirty. 15. One hinulred seventeen. 16. One luMuh'ni ti'ii. 17. One lunulii-il seven. 18. Four hundred forty-four. 19. Seven hundred nine. 20. Nine hundred eleven. 21. HO. 22. '.»1. 23. lOr,. 24. 240. 25. H77. 26. . 18. .'ii^-s. 19. 29'). 20. 239. 21. 9H9. 22. 7H9. 23. 999. 24. h5M. 25. 35. 26. 42. 27. 51. 28. 51. 29. 40. 30. 44. Exercise III.— (Pa^e 12).— 1. 95 cents. 2. 157 apples. 3. 29 egK^s. 4. 13'.) dollars. 5. 59 days. 6. 122davs. 7. 184 days. 8. 219 sheep. 9. 398 feet. 10. 648 yards. 11.190. 12.998. Exercise IV. (a).— (Page 10).— 1. Three hundred ten. 2. Nine hundred six. 3. Three thousand, one hundred seventy-two. 4. Four thousand, eij^ht hundred seventy-seven. 5. Ei_i;ht thousand, nineteen. 6. Seven thousand, thirty-three. 7. Seven thousand, five hundred six. 8. I'our thousand, four hundred four. 9. Nino thousand, five. 10. Otu! tlK^usatul, one. 1 1. Thirty-two thousand, seven hundred forty-eight* 12. Twi'lve thousand, four hundred nine. 13. l-'ifty-eij^-hl thousand, six hundred four. 14. Forty-seven thousand, eighty. 16. Ninety thousand, six hundred thirty. 16. Seventy thousand, two hundred six. 17. Eighty-six thousand, five. 18. Six hundred twenty-three thousand, seven hundred fifleec 19. One hundred four thousand, four hundred one. 20. Three hundred eight thousand, thirty. 2 1. Seven hundred sixty thousand, twenty-five. 22. Nine hundred thousand, eight hundred forty-three. 23. Seven hundred ten thousand, six. 24. One hundred ninety thousand, one hundred ninety. (89) 4 ! 90 2. S. 4. 5. 6. 7. 8. 9. JlO. 11. 12. 13. 14. 15. 16. 17. 18. 4. 10. 15. 4. 8. 12. 15. 3. n. 18. 25. 4. 11. 17. 23. 28. 3. 8. ANSWERS. Exercise IV. (b).— (Pa^e 10).— 1. Eight thousand, eighteen. Seven hundred one thousand, three. Six hundred fifty thousand, ten. Six hundred thousand, seven hundred. Eight hundred thousand, one hundred nineteen. Seven million, sixteen thousand, one hundred thirty. Seven million, one hundred thousand, eight hundred. Six million, one hundred thirty thousand, forty-nine. Nine million, nine. Eight million, three hundred seventy-two thousand, six hundred ninety-four. One million, twenty-thousand, three hundred four. Sfventy million, eight hundred six thousand, nine hundred ten. One billion, one hundred eleven million, one hundred eleven tlunisand, one hundred eleven. Nine billion, niiu'tecn. Thrt^e c|uatlrillion, two hundred trillion, seventy billion, five hun- tlrt'd million, seven huiulred thousand. Six trillion, four hundred seventy-three billion, eight hundred fifty-one iiiillit>n, nine hundred twenty-seven thous Mid, three hundred sixt v-four. One billii>n, three hundred million, thirteen thousand, thirteen. Seven quadrillion, ouc trillion, ten billion, two hundred million, five ttjousand, fifty. Exercise V. (a).— (Page ir.).— 1. 200. 2. 81 «. 7H2(). 6. lo;')?. 6. <"'ioi. 7. ^(Mi*;. 8. 'limrt. f)->u {). 11. 2u)\\)\. 12. nrAmi 13. sooooh. h;}0()11. 3. 34<)2. 9. 70411). 14. 200202. Exercise V. (b).— (Page 17).— 1. l(')871)lt. 2. .5013. 3. 3014004. 7000770. 5. oOr.OOOl"). 6. 4720('.O001. 7. 807005403. O0'.)00',l00. 9. 2r20110r>(>. 10. 32041 I35IO. 11. 40720004000f:. oh070i;o.".o(). 14. ooioooinoooioioo. 000000000000000!>. 16. 20100001000001(H): (). Exercise Vi. — (Page 10).— Last result in each: ;i(i. 4. 4s. 5. «')0. 6. 72. 7. H4. 8. Oti. 9. 70. 12. 82. 13. 01. 14. 04. 15. 78. 16. 81. 83. 19. 100. 20. 102. 21. 03. 22. lor.. 23. 144. Exercise Vil. (a).— (Page 21).— 1. 127. 2. 248. 238. 5. 204. 6. 20r.. 7. 200. 8. 21)4. 9. 223. 318. 12. 322. 13. 1880. 14. 1002. 16. 1002. 16. 13<18. 2172. 18. 2412. 19. 2.300. 20. 2015. 21. 10708. 22. 20162, 10317. 24. 220()0. 25. 30830. 26. 32486. 27. 27073. 23772. 29. 421117. 30. 401364. 31. 308803. 32. 33r)04o. Exercise VII. (b)— (Page 22).— 1. 3232615. 2. 1418401. 1037095. 4. 1858593. 5. 9679924. 6. 8474700. 7. 17034545. 13818628. 9. 19659421568. 10. 29974430849089766. 1. 1 2. 2 . 24. 108. in 10. 1 ', 120. 1 /. 86. 24. 132. 3. 171. 10 • » 1 i ANSWERS. 91 Exercise VIII — (Page 28).— 1. 399. 2. 2253. 3. 8901. 4. 20580. 5. 41562. 6. 29159. 7. 22226. 8. 96451. 9. 168733. 10. 51668. 11. 59935. 12. 422812. 13. 169302. 14. 224168. 15. 8784625. 16. 8853680. 17. 23640275. 18. 10938567. 19. 1584267081. 20. 8938285777563134. Exercise IX.— (Page 25).— 1. 440 pages. 2. 365 days. 3. 691 dollars. 4. 356 sheep. 6. 984 miles. 6. 316 trees. 7. 235.32 trees. 8. 11174 dollars. 9. 23533 cattle. 10. 86854. 11. mm. 12. 114751. 13. 363542. 14. 109078. 15. 321263. 16. 4833239. Exercise X.— (Page 29).— 1. 42862. 2. 62862. 3. 80684. 4. 124268. 5. '.)3069. 6. 159306. 7. 273390. 8. 249360. 9. 16H608. 10. 210936. 11. 2HH pens. 12. 168 pupils. 13. 1648 doll.irs. 14. 1648 cents. 15. 1288 apples. 16. 1()2H pa^t-s. 17. 3208 pages. Exercise XI.— (Page 31).--1. 192648. 2. 147852. 3 174592. 4. 9. 14. 19. 24. 29. 34. 39. dA 3. 8. 13. 18. 23. 3. 8. 12. 16. 20. 24. 3. 8. 12. 16. 20. 23. 26. 29. 183470. 24o490. 300430. 305778. 3iJ9037. 545202. 770264. 483732. 70430H. 6. 185187. 10. 187000. 1 98240 499494. 490434. 319740. 5754HH. 834105. 447372. 15. 20. 25. 30. 35. 40. 45. 6 223.'>54. 11. 204H31. 16. 281.^71. 21. 237224. 26. 051002. 31. 415968. 36. 2330!)6. 41. 372680. 46. 753990. 7. 25.3917. 8. 12. 190700. 17. 408282. 22. 2r.90H4. 27. 205770. 32. OoOOO't. 37. 507405. 42. 051370. 47. 871023. 212418. 13. 185H45. 18. 40H758. 23. 499982. 28. 320810. 33. 00259;>. 38. 744444. 43. 917r,64. 48. 1015884. Exercise XII. (a).— (Page 32).— 0.55410. 4. 03 '751. 5. 325248. 9. 84r)94. 10. 47iHiH). 14. 022102. 15 0H830H. 487448. 142413. 184704. 097320. 19. 503S44. 20. 052152 24. 505342. 1. 294470. 6. 40174S. 11. 20,")M»;i». 16. 395208. , 21. 540580 2. 400259. 7. 2.04524. 12. .'il83076. 10. 341003038, H. lHr,r,4O9O0. 14. 017992037. 15. 3HH430208. 18. 3185474050. 19. 332K32.',750. 4098341772. 22. 1442042432. 23. 250939l;M. 0893535210. 26. 481300102504. Exercise XIII.— (Page 34).— 1. 28040892. 2. 20519744. 52440300. 4. 31707812. 5. 3090330O. 6. 34247200. 7. 54887430. 38880520. 9. 60418118. 10. 00205120. 11. I85040.o0. 27953254. 13. 20748300. 14. 87745800. 15. 64488700. 620880000. 17. 49146300. 18. 690317800. 19. 58074156280. 100147000000. 21. 24379565760. 22. 73336003600. 491133254481. 24. 565234946856. 25. 247976790000. 454925422100. 27. 720014500072. 28. 10275245280a 60643205616. 30. 5650259200. IMAGE EVALUATION TEST TARGET (MT-3) 7 // &?^ :/ 1.0 I.I If lig' 12.0 IL25 i 1.4 1.8 1.6 V] *^ S / // y /A Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, NY. 14580 (716) 872-4503 # [V JV >^ ■-^ "ds" 6"^ 4f> rv^ 'ii^ -T" I Va 92 ANSWERS. > '} 5. 11. 16. 4. 9. 14. 19. 3. 7. 11 15. Exercise XIV (Page 35).— 1. 312. 2. 510. 8. 2910. 4. 5432. 8640. 6. 3024. 7. 1224. 8. G2G40. 9. 76544. 10. 13650. 34687."). 12. 420;60. 13. 66528. 14. 4992. 16. 56560000. 512000. 17. 57600. 18. 42000. 19. 11022480. 20. 3734368. Exercise XV.— (Page 35).— 1. 20928. 2. 24705. 3. 118144. 130365. 5. 2558H8. 6. 165732. 7 531 h28. 8. 700.3296. 9. 4. 10. 15. 20. 25. 30. 3. /. 11. 18. 4. 10. 16. 22 27. 32. 37. 4. 10. 15. 20. 25. 30 12. 6096303. 17. 5041872. 13 18. )32119C, 2342844 6675944. 10. 7229568. H. 5039694. 14570640. 15 7776648. 16. 7632922. 47332176. 20- 85548816. Exercise XVI (Page 36).— 1. 759 apples. 2. 2250 yards. 270704 bricks. 4. 49'.^80 yards. 5- 1214.52 pounds. 6" lf;278.feet. 43904 oianges. 8. 1370940 people. 9. 380160 feet. 10. $405. 65766 men. 12. $200070. 13. 4641 bushels. 14. 135464 stalks. 260064 checks. 16. 561996 steps. 17. $6080. Examination Paper No. I. - (Page 37)-l. Two thousand nine; thirt}-one thousand, thirteen ; seventy million, six thousand, forty. 13900; 10050004; 19806000. 3. 193444. 4. 5625753. 5. 160 marbles. 6. 14 4 panes. 7. 1700 cents. 8. 126 miles. $11180. 10. $603. Exercise XVIII.- (Page 39).— i. 1342. 2. 1613. 3. 2352. 5314. 5. 40425. 6. 20226. 7. 63053. 8. 343.^3. 9. 361361. 12. 506143. 13. 722451. 14. 567104 17. 504717. 22. 433246. 27. 71160;*. 32. 705300. Exercise XIX.— (Page 40).— 1. 31 bushels. 2. 23 marbles. 31 cents. 4. 142 pounds. 5. 1520 j'ards. 6. 33 marbles. 153 apples. 8. 33 eggs. 9- 16 marbles. 10- 21 buttons. 133. 12. 3. 13. 162. 14 2504. 15. 1244. 16. 3272. 17. $5013. 8545. 19. $2065. 20. $4670. Exercise XX,- (Page 43).— 1. 5851. 2 3665. 3. 4845. 2562. 5. 6036. 6. 5546. 7. 4536. 8. 2557. 9. 3758. 55286. 11. 54545. 12. 12458. 13. 57647. 14. 37857. 15. 17. 45048. 18. 27488. 19. 33^88. 20. 39934. 21 23. 53528. 24. 469. 25. 297538. 26. 389623. 416250. 452232. 613313. 531230. 707630. 11. 16. 21. 26. 31. 305240. 54271'^. 222 16(.. 814064. 700110. 18. 401244. 23. 142314. 28. 801126. 19. 420443. 24. 206040. 29. 3403. » 69365. 17946. 399042. 72804. 91078. 25666. 8798. 28. 024568. 29. 77664. 30. 33. 233628. 34. 1382 47. 35- 38. 347985. 39. 311869. 40. Exercise XXI (Page 44).— 1. 34673 6824. 5. 53431. 6- 59712. 7. 4136. 18223. 11. 40996. 12. 59833. 13 207144. 16. 622666. 17. 425235. 1. 168995. 97377. 36. 148760. 2. 3.5914. 8. 8727. 9 242174. 14. 317673. 18. 170679. 19. 626996. 77. 304909. 3. 57964. 24772. 409264. 21. 317266. 22. 598799. 23. 480826. 24. 77924. 21267. 26. 93192. 27. 34568. 28. 97994. 29. 79998. 469992. ANSWERS. 9S Exercise XXII.— (Page 44).- 1 39 marbles. 2. $302. 3. 749 years. 4. $392oA. 5. $64. 6. 109 sections. 7. 10371. 8. $4. 9. 61413. 10. 85024. H. $606. 12. $288. 13. Halifax 1812. 14. 4810. 15. 4669. Exercise XXIIl (Page 46).— 1. 4784. 2. 125. 3. 7041. 4. 28441. 5. 83412. 6- 35217. 7. 2096. 8- 417. 9. 803. 10. 1610. 11. 1. 12. 117782. 13. 37913. 14. 5639. 15. 1018. 16. 46275. 17. 15671054. 18. 8966098. 19. 264115. 20. 19123. Exercise XXIV. (a).— (Page 47).— 1. 163. 2. 6432. 3. 29. 4. 2640. 5. 5015472. 6. 61325. 7. 84H3. 8. 665856. 9. 11517. 10. 46. 11. 47. 12. 15. 13. 10392. 14. 4580. 15. 4580. 16. 57. 17. 155. 18. 900. 19. 79291. 20- 76569. 21. 43. 22. 3554. 23. 3467462. 24- 2745887. 25. 921584. Exercise XXiV. (b).— (Page 48).— 1. 5204736082. 2. 4910088. 3. 56'».s<)'.)9. 4. 174414. 5. 6552. 6. 39501. 7. 3909632. 8. 31007. 9. 300 and 222. 10- 1032834 and 433058. 11.75308643. 12.88450739. Exercise XXV.— (Page 49).— 1. 1785 days. 2. 1376 men. 3. $429. 4. $30. 5. $1912. 6. $1254. 7- 30199. 8 $56. 9. »222. 10. $1855. 11. $158. 12. 144 days. 13. 816 days. 14- Gain $81. 15. 876204 letters. 16- $1200. 17- Lost $228. 18. 221 miles. 19. 975 miles. 20- $2.84. Examination Paper No. 3.— (Page 51).— 1. 58567. 2. 66.5007241128. 3- 998998. 4. 51. 5. 69825. 6. Ninety-six, four. 7. 1112 yards. 8- 240647202. 9. 162008. 10. Gain $19. Exercise XXVil (Page 55).— 1. 2413. 2- 1203. 3. 1788. 4. 1435. 5. 26696. 6. 24636. 7. 24325. 8. 13436. 9 24752. 12. 142543. 13. 208145. 14. 142786. 17. 144322. 18. 192978. 19. 33618. 22. 167863. 23. 122423. 24- 25241. 27. 23142. 28 14262^. 29- 32257|. 32. 63673. 33. 51452|. 34. 124868|. 11. 298071. 16. 123228 21. 141612. 26. 343651 . 31. 145484|. 36. 14224,V- 37. 33141. 38. 67517. 39. 63741i*ff. 10. 153237. 15. 194383. 20. 42247^. 25. 122334. 30. 51592^. 35. 25691 rV 40. 69743tV Exercise XXVIII (Page 56).— 1. .32421. 2. 416226. ' 3. 273819. 4. 371926. 6. 312114. 6. 236821. 7. 377188. 8. 228394^. 9. 253541^. 10. 152263. U. 241875J. 12. 329218. 13. 212133. 14. 162144. 15. 145143f 16. 256436. 17. 168186. 18. 228977^. 19. 121424. 20. 142453. 21. 258268|. 22. 153564f. 28. 121413. 24. 141612. 25. 151424. 26. 145142^. 27. 196588f. 28. 1879«6|. 29. 17125|. SO. 121412. 31- 142442f. 32- 23860f. 33. 34622f. 34 22323. 35. 32325. 36 54245^. 37- 23242. 38. 32344. 39. 22314,9^. 40. 31335. 41. 52043/t. 42. 63206^7,. 48. 85276^. 44. 82998ji». I n I 94 ANSWERS. 'I 3. 8. 13. 18. 23. 28. 33. 38. 3. 7. 11. 15. 4. 10. 15. 3. 8. 13 18. 4. 9. 14. 19. 24. 29. 34. 3. 8. 13. 18. 23. 27. 31. 35. 2. 6. 10. 14. Exercise XXIX (Page56).-1. 380628^. 2. 1408U5. 151>005^. 190609i. 1 20053 f. 176899^ 69005|. 43033§. 98765^. 42254,%. 487655 . 7. 150873^. 12. 46929^. 17. 66045. 22. 725455. 27. 1787591. 32. 84802f. 37. J8070i\. 5. 140684f. 6. 199085|. 9. 116029. 10. 159908. H. 1849671. 14. 40634|. 15. 128609f 16. 82675^ 19. 122063. 20. 32004. 21 124000^. 24. 125950^. 25. 103040^. 26. 42014. 29. 189846f 30. 100003|. 31. 11600§. 34. 97212^. 35. 95238. 36. 88969| 39. 58344H. 40. 79299. Exercise XXX (Page 57).— 1. 31 stamps. 2. 205 barrels. $1269. 4. 1760 yards. 5. 867 bills. 6. 3570 pecks. 2884 barrels. 8. 1252bag-s. 9. 49 half dozens. 10- 11429 boxes. 6908 houses. 12. 1440 minutes. 13. 855 tents. 14- 7682. 1536 times. 16. 85129| square yards. 17. 378/2- dozens. Exercise XXXI (Pag-e 59).— 1. 2713 2. 2719. 3. 8309. 7. 89171^^. 8. 9008;^. 9. 7938||. 83744 1234 I298|n ^. 5. 6H04. 6 9876. 7. 8917?,^ 8. 9008;^. 11. 2234 ,V^. 12. 3917a'',. 13. 4436i|^. 14. 16. ll833S§t-. (Pagre60).-1. 872,V.. 2. 783//^- 5. 7173^?.. 6. 15421^;}^. 7. 16547U- 11. 198^*,°,. 12. 740MI 16. 542iVr?T. 17- •-•(;43-i^^|. '^m- 2 6. 3142. 7. 2311U. 8 11. I324|f 12. 2314^5 1342. 3. 1335AI 131.U/,T. 13. 1346Ui 3121644V 15. 2345H. 16. 4116^- 17. 2415if. 18. 141: iij. Exercise XXXII. 375SU\. 4. 30929 77s5^i. 9. 365.T,Vf,. 10. 1U5^V. !S. D. i\ '•1 f if I (I