DIVISION OF FRACTIONS.

181. To divide a fraction by an integer.

1. If of an orange is divided equally between 2 girls, what part of the orange will each girl have? How much is #+2?

2. A man divided of an acre into 3 equal lots. How large was each? How much is

÷ 3?

3. If a horse ate & of a bushel of oats in 4 days, how much did he eat each day? How much is & + 4?

4. In dividing a fraction by an integer, what part of the fraction is divided?

5. If $ is divided equally between 2 boys, what part of a dollar will each boy get? How much is

÷ 2? 6. When 3 pounds of sugar can be bought for $1, what is the price per pound? How much is ÷ 3?

7. If of a ship is owned equally by 5 men, what part of the ship is owned by each? How much is ÷ 5?

8. In what other way, besides dividing the numerator, can a fraction be divided by an integer? State both ways in which a fraction may be divided by an integer.

9. If 3 dozen oranges can be bought for $%, what do they cost per dozen?

10. If of a pound of tea is divided equally among 3 persons, what part of a pound will each receive?

11. If of a bushel of walnuts fills 4 bags of equal size, what part of a bushel does each bag hold?

12. Mrs. Jay filled 5 tumblers with 19 of a gallon of jelly. How much did each tumbler hold?

13. Divide by 2; by 2; by 3; by 4; 19 by 5. 14. Divide by 2; 7 by 3; # by 4; 4 by 5; 7 by 6.

15. If 3 yards of cloth cost $14, what does 1 yard cost? 16. When 5 bushels of potatoes cost $43, what does a bushel cost?

17. If 3 dozen oranges cost $ §, what does 1 dozen cost? 18. If 4 brooms are worth $, how much are they worth apiece?

19. When I can buy 4 dozen eggs for $1, 8 what is the price per dozen?

20. If 5 yards of gingham sell for $4, what is the price per yard?

21. If 6 pounds of tea are worth $15, what is a pound. worth?

22. When 5 bushels of wheat sell for $41, what is the price per bushel?

23. James earned $63 in 6 days. What were his daily wages?

24. A boy divided 6 dozen marbles equally among his 5 sisters. How many did each receive?

182. It is apparent from the solution of the above examples that:

A fraction may be divided by an integer by dividing the numerator or multiplying the denominator of the fraction by the integer.

118=47. 47÷4=47=218.

Or,

4)113
218.

EXPLANATION.-The mixed number may be reduced to an improper fraction, and the division performed as before.

Or, the number may be divided without being reduced to an improper fraction. Thus, 4 is contained in 113 2 times, and a remainder of 33, or 15; and 15 divided by 4 equals 15. Hence the result is 218.

25. The cost of 5 tickets from Troy, N.Y., to Bethlehem, N.H., was $404. How much did each cost?

26. The rain interfered with a laborer's working 31 working days in 2 weeks. How many days did he work on an average per week?

27. A farmer forgot the price which he received for his butter per pound, but he knew that he received $2 for 8 pounds. At that rate, what did he receive per pound?

28. An estate of $39563 was divided equally among 5 heirs. What sum did each receive?

29. The earnings of 5 men for 10 days were $87. What were the average earnings of each per day?

30. If a man can reap a field in 10 days, in what time can 12 men reap it?

31. If a locomotive runs 142 miles in 6 hours, what is the average rate of speed per hour?

32. A field containing 125 square rods was divided into 10 lots of equal size. How large were the lots?

184. To divide an integer by a fraction.

1. How many tenths of a dollar are there in a dollar? 2. At $each, how many quires of paper can be bought for $1? For $2? For $3? For $4?

3. When butter is worth $1 per pound, how many pounds can be bought for $1? For $2? For $3? 4. How many penknives, at $ apiece, can be bought for $1? For $2? How many at $3 apiece can be bought for $2?

For $4?

5. If a boy spends of an hour in going to school, in how many days will he spend 3 hours? 6 hours? 9 hours?

6. A man gave his daughter $ & a month to spend as she pleased. In how many months would he give her $9?

7. The retail price of one kind of molasses is $ per gallon. How many gallons can be bought for $8?

8. A young man spends of each day in work and recreation. In what time will he spend 12 days in this way?

9. How many times is contained in 5? In 9? In 12?

WRITTEN EXERCISES.

185. 1. Divide 5 by %, or find how many times is contained in 5.

3 5x7 5÷ 3 Or,

=

=

= 11.

5=35; 35+4 11.

=

EXPLANATION. Since is contained in 17 times, it is contained in 5, 5 times 7 times, or 35 times, and in 5 of 35 times, or 11 since in 5 there are 35, is contained in 35 11 times.

1. Cancellation can often be used advantageously.

is contained

times. Or,

2. Mixed numbers may be reduced to improper fractions.

28. Divide 24 by 54.

-

EXPLANATION. By changing the dividend and divisor to 7ths, the division is performed as in simple division.

39 )168(4

38. When cloth is $.103 per yard, how many yards can. be bought for $3.36?

39. My lot has a frontage on the street of 385 feet. How many rods is it in front, 16 feet being a rod?

40. A cheap kind of flour sells for $35 per barrel. How many barrels can be bought for $763 ?

41. A farmer bought a wagon for $68, paying for it in apples at $13 per barrel. How many barrels did he give for it?

42. Boots are commonly sold in cases containing 12 pairs. If a dealer paid $ 99 for a quantity of boots at $23 a pair, how many cases did he purchase?