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Ex. 1. If a ton of coal costs 9 dollars, what will a ton cost?

Suggestion.-Since a whole ton costs

9 dollars, 1 half a ton will cost 1 half of

Operation.
2)9

Ans. 4 dolls.

9 dollars. Now 2 is contained in 9, 4 times and 1 over. Place the 1 over the divisor 2, and annex it to the quotient. (Art. 58.) 2. What will of a yard of cloth cost, at 36 shillings per yard?

3)36

Suggestion.-First find what 1 third First Operation. of a yard will cost, then 2 thirds. That is, divide the given number by the denominator 3, then multiply the quotient by the numerator 2.

12

2

Ans. 24 shil.

Or, we may first multiply the given Second Operation number by the numerator, then di

vide the product by the denominator. The answer is the same as before.

36

2

3)72

Ans. 24 shil.

3. If an acre of land costs 30 dollars, what will of an acre cost?

4. What will of a barrel of flour cost, at 40 shillings per barrel?

5. What will of a hogshead of molasses cost, at 37 dollars per hogshead?

6. What will of a barrel of apples cost, at 28 shillings per barrel?

7. Multiply 48 by 2. 8. Multiply 35 by 4. 9. Multiply 54 by . 10. Multiply 49 by 4. 11. Multiply 64 by .

12. Multiply 56 by . 13. Multiply 72 by 4. 14. Multiply 120 by §. 15. Multiply 168 by 7. 16. Multiply 243 by 1.

Multiplying a whole number by a mixed number. 17. What will 5 yards of cloth cost, at 18 shillings per yard?

Suggestion. Since 1 yard costs. 18 shillings, 5 yards will cost 5 times as much. We first multiply 18 shillings by 5, then by, and

2)18 cost of 1 yd.

51

90 cost of 5 yds.
9" of yd.
"ofyd.

add the products together. Hence, Ans. 99s. “of 52 yds. 84. To multiply a whole number by a mixed number Multiply first by the whole number, then by the fraction, and add the products together. (Art. 83.)

18. Multiply 26 by 21.
19. Multiply 30 by 21.
20. Multiply 36 by 34.
21. Multiply 45 by 43.
22. Multiply 42 by 51.
23. Multiply 36 by 31

24. Multiply 56 by 74.
31. Multiply 41 rods by 54.
32. Multiply 68 rods by 16.

Ans. 65.

25. Multiply 75 by 24. 26. Multiply 63 by 44. 27. Multiply 100 by 53. 28. Multiply 165 by 74. 29. Multiply 180 by 85. 30. Multiply 192 by 97. Ans. 225 rods.

33. What cost 21 acres of land, at 35 dollars per acre?

34. What cost 344 hundred weight of indigo, at 47 dollars per hundred ?

35. What cost 633 tons of iron, at 96 dollars per ton?

Dividing a whole number by a fraction.

Ex. 1. How many apples at a cent apiece, can you buy for 5 cents?

Analysis. If a cent will buy 1 apple, 5 cents will buy as many apples, as a cent is contained times in 5 cents; that is, as many as there are halves in 5 whole ones.

QUEST.--84. How do you multiply a whole number by a mixed number?

Now in 1 cent there are 2 halves, therefore in 5 cents there are 5 times 2, which are 10 halves; and 1 half is contained in 10 halves, 10 times. Ans. 10 apples.

2. How many plums, at of a cent apiece, can you buy for 8 cents?

Analysis. Reasoning as before, you can buy as many plums as of a cent are contained times in 8 cents. Now

in 1 cent there are 3 thirds, therefore in 8 cents there are 8 times 3, which are 24 thirds, and 2 thirds are contained in 24 thirds, 12 times. Ans. 12 plums. Hence,

85. To divide a whole number by a fraction.

Multiply the given number by the denominator, and divide the result by the numerator.

OBS. When the numerator is 1, it is unnecessary to divide by it; for it is plain that dividing by 1 does not alter the value of

number.

3. Divide 17 by .

17

We multiply the 17 by the denominator Operation. 2; and since dividing by 1 does not alter the value of a number, we do not divide by it.

4. Divide 19 by .

Multiply the 19 by 3, and divide the product by 2. Place the remainder 1 over the divisor, and annex it to the 28.

2

34 Ans

Operation.

19

3

2)57

28 Ans

[blocks in formation]

QUEST.-85. How do you divide a whole number by a fraction? (bs. When the numerator is 1, is it necessary to divide by it? Why not?

Dividing a whole number by a mixed number. Ex. 1. How many lemons, at 5 cents apiece, can you buy for 22 cents?

Analysis. Since 5 cents will buy 1 lemou, 22 cents will buy as many lemons, as 5 cents are contained times in 22 cents. Now in 5 cents there are 11 halves, and in 22 cents there are 44 halves; but 11 halves are contained in 44 halves, 4 times. Ans. 4 lemons.

Operation.
5122

2 2

11 )44

Suggestion. We change the divisor to halves by multiplying the whole number by the denominator 2, and adding the numerator, we have 11 halves; then reducing the dividend to halves by multiplying it by 2, we have 44 halves. Now 11 is contained in 44, 4 times. Hence, 86. To divide a whole number by a mixed number.

Ans. 4 lemons.

Multiply the whole number in the divisor by the denominator, and to the product add the numerator. Then multiply the dividend by the same denominator, and divide as in whole numbers.

Note.--For further illustrations of the principles of fractions see Practical Arithmetic, Section VI. It is incompatible with the design of the present work to treat of fractions more exten sively than is necessary to enable the pupil to understand the operations in Reduction.

EXAMPLES.

Operation. 44)15

2. How many times is 43 contained in 15 ? Suggestion. Multiplying the 4 and 15 by 3, reduces them to thirds. Now it is plain we can divide thirds by thirds as well as we can divide one whole number by another; for the divisor is of the same name or denomination as the dividend.

3 3

14 45

Ans. 3.

QUEST.-86. How do you divide a whole number by a mixed numbor ?

3. Divide 18 by 1. 4. Divide 20 by 31. 5. Divide 25 by 53.

6. Divide 37 by 64.

7. Divide 46 by 74.

8. Divide 60 by 51. 9. Divide 75 by 84. 10. Divide 100 by 108.

EXAMPLES FOR PRACTICE.

1. How many apples can you buy for 4 cents, if you paya cent apiece?

2. How many peaches can you buy for 6 cents, if you pay of a cent apiece?

3. How many yards of tape can Sarah buy for 8 cents, if she pays of a cent a yard?

4. How many yards of ribbon can Harriet buy for 9 shillings, at of a shilling per yard?

5. How many pounds of tea, at of a dollar a pound, can be bought for 6 dollars?

6. How many yards of calico, at of a dollar per yard, can you buy for 3 dollars?

7. At of a penny apiece, how many marbles can George buy for 14 pence?

8. At of a dollar a bushel, how many

can a man buy for 6 dollars?

bushels of corn

9. At of a dollar a yard, how many yards of silk can a lady buy for 15 dollars?

10. At of a dollar apiece, how many lambs can a drover buy for 27 dollars?

11. In 1 rod there are 5 yards: how many rods are there in 88 yards?

12. In 1 rod there are 16 feet: how many there in 132 feet?

rods are

13. How many yards of cloth, at 5 dollars per yard, can be bought for 100 dollars?

14. How many cows, at 12 dollars apiece, can be bought for 125 dollars?

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