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berer), because it shows the number of parts contained in the fraction; while the lower figure, which is the divisor, is called the denominator (or namer) because it points out the name or value of the parts expressed by the numerator. The numerator and denominator are called the terms of the fraction. Both terms taken together represent the quotient in the division. Thus, 1 divided by 5, gives for quotient :

1. What is a fraction? What is meant by a half of a thing, or number? How is it represented ? [Answer orally or by the blackboard.] What is a third ? two-thirds ? How represented ? A fifth ? three-fifths ? an eighteenth ? five eighteenths ? an eleventh ? a thirteenth? twelve thirteenths? Where is the numerator placed ? Why so called? Where is the denominator placed? Why so called ? What does the hori. zontal line express? Which is the divisor ? the dividend ? the quotient?

2. What is the į of 2 beads ? [Use the frame.] One is what part of two ? Ans. One is the half of two. Two times one are how many times two ? How many halves make a whole one? Three are how many times two ? Ans. Once 2 and a { of two. Four are how many times two ? 5? Ans. Two times two and a half of 2. Six are how many times 2? 7 how many times 2 ? 8 ? 9? 10 ? 11 ? 12 ? 15 ? 16 ? 25 ? 26 ? 37 ? 38 ? 85 ? 93? 77 ? 50 ? 100 ? 102 ? 116 ? 105 ? 107 ? 117 ? 128 ? 125 ? 145 ?

3. One is what part of 3? Ans. One is a third of 3. Two is what part of 3? Ans. Two is two-thirds of 3. Three times one are how many times 3 ? How many thirds make a whole one ? Five are how many times 3? Ans. Once three and two-thirds of 3. What is a third of any thing? [See definition above.] What is two-thirds ? Six are how many times 3? 7 how many times 3 ? 8 ? 9? 10 ? 11 ? 12 ? 13? 17 ? 24 ? 26 ? 29 ? 30 ? 33 ? 34 ? 35 ?

4. How many fourths make a whole one? What part of 4 is 1 ? Ans. One is the fourth part of 4 ? What part of 4 is 2 ? 3? What do you understand by & ? ? ? 5 are how many times 4? 6 how many times 4? 7? 8?* 9? 10 ? 11 ? 13 ? 14 ? 15 ? 16 ? 17 ? 18 ? 19 ? 20 ?

5. How many fifths make a whole one ? One is what part of 5 ? 2 what part of 5 ?

3? 4 ? Six are how

many

times 5? 7 how many times 5 ? 8? 9? 10 ? [Show, by the frame, that every ten or ty, consists of ? fives.] Eleven how many

are

times 5 ? 12 ? 13? 24 ? 45 ? 49? 58 ? 60? 78 ? 84 ? 100 ? 120 ? 133 ? (13ty+3=26X5+3) 94 ? 86 ? 74 ?

6. How many sixes make a whole one? One is what part of 6? Two what part of six ? 3? 4? 5? 7 how many times 6? 8 how many times 6? 9? 10 ? 11 ? 12? 13 ? 14 ? 15 ? 16 ? 17 ? 18? 19 ? 20 ? 24? 27 ? 29 ? 30 ? 35 ? 39 ? 36 ? 44 ? 56 ? 60 ? 63 ? 75 ? 120 ? 122 ? 123 ? 129 ? 144 ? 157 ? 132 ? 135 ? 244 ? 7. One is what part of 7 ? 2 are what part? 3? 5? 8

how many times 7? 9 how many times ? 10 ? 15 ? 28 ? 22? 34 ? 46 ? 78 ? 84 ? 93 ? 97 ? 144 ? 138 ? 8. Two is what part of 8? 3 what part? 5? 6? 7? 9

many times 8? 10 how many times ? 11 ? 13? 15 ? 16 ? 19 ? 22 ? 25 ? 43 ? 37 ? 34 ? 47 ? 54 ? 72 ? 83? 84? 93 ? 96 ? 120 ? 135 ? 144 ? 147 ? 139 ?

9. One is what part of 9? 4 is what part? 5? 6? how

many times 9? 11 how many times ? 13 ? 15 ? 16 ? 19? 22 ? 25 ? 43 ? 37 ? 34 ? 47 ? 54? 72 ? 83? 84 ? 93? 96 ? 120 ? 135 ? 144 ? 147 ? 139 ?

10. Three is what part of 10? 4 what part? 7? 8? 9? 11 are how many times 10? 12 how many times ? 13 ? 15? 65 ? 142 ? 364? 567 ? 278 ?

are how

10 are

SECTION II. — Practical Questions. 1. If a yard of cloth be worth 3 dollars, and it be cut into 3 equal pieces, what will one of the pieces be worth ? that is, what will } of a yard be worth? What will į of a yard be worth? See Example 3, in last section.

2. If a barrel of fish cost 3 dollars, what part of a barrel can you buy for 1 dollar ? How many barrels for 7 dollars ? for 9 dollars? 10 ? 12? 25 ? 27 ? 35 ? 29 ? 38 ?

3. If two bushels of wheat will buy a yard of cloth, what part of a yard will 1 bushel buy? How many yards will 4 bushels buy? 5 bushels ? 7 ? 18 ? 34 ? 26 ? 57 ? 139 ?

4. If a pound of rice cost 4 cents, what part of a pound will 1 cent buy? 2 cents ? 3 cents? How much for 5 cents ? 8 cents ? 9 ? 11 ? 12 ? 13 ? 14 ? 24 ? 32 ? 65 ? 96 ? 87 ? 54 ? 72 ? 93 ?

5. If a barrel of four cost 5 dollars, what part of a barrel

can be bought for 1 dollar ? 3 dollars ? How many barrels for 10 dollars ? For 12 dollars ? 15 ? 18 ? 24 ? 27 ? 39 ? 96 ? 152 ? 274 ? 385 ?

6. If a barrel of beef cost 6 dollars, what would i of it be worth ? ? & ? ? How much could be bought for 7 dollars ? For 9 dollars ? 10 ? 12 ? 15 ? 17 ? 23 ? 24 ? 27 ? 35 ? 32 ? 36 ? 43 ? 54 ? 65 ? 97? 84 ? 156 ? 132 ?

7. At seven dollars for a barrel of flour, how much could be bought for 1 dollar ? For 5 dollars ? How much would + of a barrel be worth ? $? How much for 8 dollars ? 9 dollars ? 15 ? 18? 23 ? 27 ? 28 ? 29 ? 35 ? 46 ? 65 ? 53 ? 57 ? 81 ? 63 ? 97 ? 78 ? 83 ?

8. If sugar be 8 cents a pound, how much could be bought for 1 cent ? For 3 cents ? 4 cents ? 5 ? 7 ? 9 ? 11? 12 ? 15 ? 17 ? 18? 19 ? 22 ? 35 ? 36 ? 37 ? 38 ? 45 ? 54 ? 72 ? 63 ? 87 ? 65 ? 56 ? 66 ? 77 ? 49 ? 59 ? 37 ? 26 ?

9. When wheat is 9 shillings a bushel, how much can be bought for 1 shilling? 2 shillings? 5? 6? 7? 8? 10? 15 ? 37 ? 24 ? 25 ? 56 ? 62 ? 73 ? 82 ? 95 ? 36 ? 44 ? 57 ? 29 ? 93 ?

10. If sugar is 10 dollars a hundred weight, how much can be bought for 3 dollars ? 7 dollars ? 9? 14 ? 17 ? 36 ? 45 ? 27 ? 30 ? 46 ? 54 ? 82? 194 (19ty and 4) ? 277 ? 567 ? 394 ? 846 ? 732 ? 589 ?

11. If you had 45 dollars, how many barrels of flour could you buy at 5 dollars a barrel ? At 9 dollars ? At 6 ? 4? 7 ? 11 ? 8 ? 3?

12. For 59 cents how many pounds of meat can be bought, at 6 cents a pound? At 8 cents ? At 7 ? 5? 9? 11 ? 10 ? 13?

13. How many hours would it take you to travel 75 miles, if you go 3 miles an hour ? 5 miles ? 7 ? 10 ? 25 ? 16 ? 24 ? 14 ? 13 ? 18 ? 22 ?

14. If you had 81 pounds of butter that you wished to put into boxes that would contain 9 pounds each, how many boxes would it take?

15. At 30 dollars for 5 barrels of flour, how much for 1 barrel ? For 4 barrels ? For 6 ? 9 ? 13 ? 15 ? 20 ? 24 ?

16. At 75 dollars for 15 barrels of flour, how much for 1 barrel ? For 7 ? 9? 24 ? 32 ?

17. If 6 horses consume 48 quarts of oats in a day, how many quarts will serve 8 horses the same time? 5 horses ? 9 ? 24 ? 15 ? 7 ? 22 ?

18. If 3 horses consume 27 quarts of oats a day, how much will 8 horses consume per day? 2 horses 2 9 ? 14 ? 18 ? 25 ? 28 ? 35 ? 42 ?

SECTION III. - Fractions of Numbers exceeding Unity, con

tinued. 1. Two times 2 beads and į of two beads how many ? [Use frame, and repeat the word beads in this and the following examples, till the class attain a clear idea of the nature of the numbers, but no longer.] 3 times 2 beads and 1 of 2 beads ? 4 times 2 and 1 of 2? 5 times 2 and 1 of 2? 6 times 2 and 1 of 2 ? 9 times 2 and 1 of 2 ?

2. Three times 3 [beads, if necessary] and of 3, how many ? 4 times 3 and { of 3? 5 times 3 and of 3? 6 times 3 and j of 3? 7 times 3 and į of 3? 8 times 3 and

of 3? 9 times 3 and ß of 3 ? 17 times 3 and } of 3 ? 19 times 3 and } of 3? 25 times 3 and f of 3? 72 times 3 and } of 3 ?

3. Three times 4 beads, if necessary) and 4 of 4, how many ? 5 times 4 and 4 of 4? 7 times 4 and of 4? 9 times 4 and is of 4? 12 times 4 and of 4? 13 times 4 and of 4 ? 16 times 4 and is of 4? 35 times 4 and is of 4? 27 times 4 and i of 4?

4. Four times 5 and of 5, how many ? 6 times 5 and of 5? 7 times 5 and of 5 ? 9 times 5 and of 5 ? 16 times 5 and all of 5 ? 19 times 5 and of 5 ? 37 times 5 and of 5 ? 95 times 5 and şof 5 ?

5. Seven times 6 and of 6, how many ? 8 times 6 and [ of 6 ? 9 times 6 and of 6? 15 times 6 and 5 of 6 ? 25 times 6 and å of 6 ? 49 times 6 and á of 6 ? 27 times 6 and g of 6 ? 32 times 6 and of 6 ?

6. Six times 7 and 4 of 7, how many ? 7 times 7 and of 7? 9 times 7 and of 7 ? 8 times 7 and of 7 ? 12 times Tıand of 7 ? 14 times 7 and of 7? 19 times 7 and of 7 ? 43 times 7 and of 7 ? 84 times 7 and of 7 ?

7. Five times 8 and 3 of 8, how many ? 9 times 8 and 3

of 8? 42 times 8 and { of 8? 73 times 8 and 3 of 8? 95 times 8 and g of 8? 47 times 8 and of 8 ? 69 times 8 and i of 8 ?

8. Nine times 9 and 3 of 9, how many ? 18 times 9 and

of 9? 37 times 9 and sof 9 ? 25 times 9 and 5 of 9? 27 times 9 and í of 9 ? 99 times 9 and į of 9? 67 times 9 and 3 of 9?

9. Eight times 10 and 1 of 10, how many ? 17 times 10 and is of 10 ? 14 times 15 and 15 of 15 ? 17 times 25 and

of 25 ? 16 times 34 and 3 of 34 ? 18 times 23 and 2 of 23? 25 times 19 and 15 of 19 ? 36 times 24 and 2 of 24?

10. Eleven times 7 and 4 of 7, how many ? 18 times 9 and of 9 ? 37 times 9 and of 9 ? 15 times 14 and of 14? 16 times 18 and is of 18? 35 times 24 and 2 of 24 ? 27 times 36 and 36 of 36? 28 times 19 and is of 19? 27 times 15 and 4 of 15 ?

SECTION IV.- Practical Questions. 1. If a yard of cloth cost 4 dollars, what will 45 yards cost ? 84 yards ? 73 ? 151? 197 ?

2. If sugar cost 6 dollars a hundred weight, what will 83 hundred weight cost? 5 hundred weight ? 94 ? 154 ? 241 ? 263?

3. If a man pay at the rate of 7 dollars a week for his board, how much will he have to pay for 7 weeks? 84 weeks? 154 ? 249 ? 494?

4. If nutmegs are 10 cents an ounce, what must be paid for 6 ounces? 976 ounces? 2476?7210 ? 8570 ?

5. At 6 dollars for a barrel of flour, what will 93 barrels cost ? 112 barrels ? 131 ? 183 ? 15% ?

6. If butter is 7 dollars a firkin, how much will 18 firkins cost ? 124 firkins ? 199 ? 45% ?

7. If a man travel at the rate of 24 miles a day, how far will he travel in 19.4 days? In 25 days?

8. If a pound of currant jelly cost 40 cents, what will be the cost of 16% pounds ? 530 pounds? 70 pounds ?

9. If a yard of bocking cost 75 cents, what will 335 yards cost ?

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