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33. What is the value of of i of li of of 15?
34. What is the value of of 34 of of 29?

DIVISION.

CASE I.

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185. To divide a fraction by an integer.

1. Mr. Allen divided 3 fourths of a dollar equally between 3 boys. How much did each receive?

2. A man divided of an acre into 3 equal lots. How large were they?

3. If 7 yards of cloth were bought for $%, what was the cost per yard?

4. If 4 books cost $13, what is the cost of each?

5. Mr. Hurd put of his crop of wheat on 3 wagons. What part of his crop was on each wagon? How much is } :32

6. In dividing a fraction, what part of the fraction is divided ?

7. A gentleman divided } a barrel of flour equally between 2 people. What part of a barrel did each receive? How much is 1 : 2?

8. 3 boys spent altogether $1. If each spent the same amount, what part of a dollar did each spend? How much is į : 32

9. Mr. Smith divided 1 of his farm into 3 equal fields. What part of his farm did each field contain? How much is 1 :-3? How is the result obtained from the fraction 1?

10. In what other way, then, besides dividing the numerator may a fraction be divided ?

11. When a number is divided by 3 what part of it is found ? 12. When a fraction is divided by 7 what part of it is found? 13. What is { of 1? 4:3? } of ? = 5? 14. What is the value of $ = 2? Of 5 -- 3? Of 1 +9?

186. PRINCIPLE.Dividing the numerator or multiplying the denominator of a fraction by any number, divides the fraction by that number.

WRITTEN EXERCISES.

PROCESS.

1. Divide 14 by 6.

ANALYSIS.—Since dividing the nu14 =-6=146 = 1 옮

merator of a fraction divides the frac

tion, the fraction 14 may be divided by. Or,

6 by dividing the numerator by 6. Or, • 13 - 6=i=

Since multiplying the denominater

divides the fraction, the fraction may be divided by 6 by multiplying the denominator by 6. The result by both processes is 1.

RULE.—Divide the numerator or multiply the denominator by the given integer.

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Divide:

Divide:

15. 173 by 6.
16. 254 by 4.

Divide:

17. 38.5 by 8.
18. 24 ú by 9.

19. 361 by 10. 20. 251 by 7.

21. A man gave each of his 5 sons an equal share of of his estate. What part of the whole did each receive?

22. 8 men built of a mile of wall in 10 days. What part of a mile did each man build daily?

23. Mr. B. earned $35} by working 8 days. How much did he earn per day? 24. I paid $104 for 27 pounds of butter. · What did I

pay a pound?

25. A farmer realized $2331 for 21 bushels of clover seed. How much did he get per bushel?

26. Three men who have been partners in business gain $3216. If they share equally, what will be each one's part of the gain?

CASE 11. 187. To divide an integer by a fraction. 1. How many fourths are there in an apple? In 2 apples?

2. How many apples, at cent cach, can be bought for 2 cents ? For 3 cents? For 10 cents?

3. At $f a yard, how many yards of cloth can be bought for $1? For $2? For $3? For $10?

4. At $} an ounce, how many ounces of nutmegs can be bought for $2? How many at $z an ounce can be bought for $2?

5. If a man can mow 4 of a field per day, how long will it take him to mow the entire field? How long if he can mową per day?

6. At $j a bushel, how many bushels of lime can be bought for $5? At $3 a bushel how many bushels can be bought for $5?

7. When apples are worth of a cent apiece, how many can be bought for 12 cents? How many times is contained in 12?

8. How many pieces of cloth of a yard long can be cut from a piece 9 yards long? How many times is contained in 9?

9. How many times is a contained in 8? in 9?
10. What is the quotient when 8 is divided by ?? 10 by f?
11. What is the value of 10:1? 7= $?9:-4?

WRITTEN EXERCISES.

PROCESS.

12:

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1. Divide 12 by g.

ANALYSIS.— is contained in 12

7 times 12, or 84 times; and q, one. 유

i
12X7--14
iexz

sixth of 84 times, or 14 times. Or, Or,

Reducing 12 to sevenths, we have

84 sevenths. 6 sevenths are contained 12=84; 84:- =14 in 84 sevenths 14 times. X

RULE.Multiply the integer by the denominator of the fraction and divide the product by the numerator.

01,

X Reduce the dividend and the divisor to similar fractions, and divide the numerator of the dividend by the numerator of the divisor.

Divide:

Divide:

2. 18 by 4.
3. 64 by 8
4. 26 by 7.
5. 48 by 4.
6. 75 by 16.
7. 31 by z
8. 45 by 46.

Divide:

10. 72 by
11. 34 by.
12. 15 by 18.
13. 49 by 21
14. 91 by 4.
15. 64 by 19.
16. 54 by 23
17. 39 by 13

18. 51 by 27. 19. 69 by 4. 20. 70 by 11 21. 65 by 23. 22. 90 by 41 23. 36 by 13. 24. 39 by 1 25. 24 by 13

9. 39 by Ó.

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33. At $1 a yard, how many yards of cloth can be bought for $15?

34. When corn is worth $5 a bushel, how many bushels must a man sell to get money enough to pay $18 taxes?

35. A man invested $32 in peaches at $1% per basket. How many baskets did he purchase ?

36. What is the price of hay, when 34 tons sell for $37?

37. Mr. Shaw paid $6 for 14ş pounds of Java coffee. What did it cost him per pound? - 38. It requires 656 pounds of meat to supply 34 soldiers 31 weeks. How much does each soldier eat daily?

CASE III.

188. To divide a fraction by a fraction.

1. How many fourths are there in 1? How many fifths? eighths? tenths? fifteenths? twentieths?

2. How many pieces of cloth of a yard long, can be cut from a yard?

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