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17. How many are 9 times ? 15 times 7? 18. How many are 23 times ? 49 times 19. What cost 8 boxes of strawberries, at dollar per box?

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of a

20. What cost 25 yards of sheeting, at 75 of a dollar per yard?

21. If it costs 13 of a dollar to build a rod of wall, what will it cost to build 20 rods?

22. If a boy runs of a rod in 1 second, how many rods, at the same rate, will he run in 15 seconds?

23. If a locomotive runs of a mile in 1 minute, how far will it run in 75 minutes?

24. If 2 bushels of apples cost of a dollar, what will 1 bushel cost?

Solution. One bushel will cost 1 half as much as 2 bushels; 1 half of § of a dollar is of a dollar; therefore, if 2 bushels cost of a dollar, 1 bushel will cost of a dollar.

NOTE. To find of a number is the same as to divide the number by 2. It is just as evident that of is, as it is that of 6 cents is 3 cents. Hence, dividing the numerator of a fraction by any number, is dividing the fraction by the same number.

25. If a boy walks 3 miles in of an hour, how long will it take him to walk 1 mile?

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26. What is of § ? Ans. § ÷ 3 27. If 4 men can reap of an acre of rye in an hour, how much can 1 man reap in the same time? 28. If a boy can run of a mile in 3 minutes, how far can he run in 1 minute?

29. What is 1 dozen of eggs worth, if 7 dozen are worth of a dollar?

30. What is of 1? Ans. 1÷7

31. What is

32. What is

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33. Hannah divided one third of a pie equally be tween 2 children; what part of the whole pie did she give to each child?

Solution. One third equals , and

of

is ;

of the

that is, of is ; and therefore she gave whole pie to each.

NOTE. Multiplying the denominator by 2 makes twice as many parts in the unit, and therefore each part is only one half as great; hence, multiplying the denominator by any number, divides the fraction by the same number.

34. Three fifths of a barrel of flour were divided equally among 4 poor families; what part of a barrel did each receive?

35. If of a bushel of chestnuts are divided equally among 5 boys, what part of a bushel does each receive?

36. What is 1 sixth of §? 1 eighth of ?
37. What is 1 ninth of ğ? 1 twelfth of 1?
38. Mary having a nice large pineapple, gave

of it to Sarah, to Fanny,

to Laura, and kept

the rest herself; what part of the pineapple did she

give away? What part did she keep?

39. What is+â+â .?

40. What is 11-7? 11-4? + 41. What is +&++15?

42. What is 8

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23

LESSON II.

1. ONE half is equal to how many sixths? Solution. Since & make a whole one, of a whole one will be of &, which is &; therefore, etc.

2. One third of an apple is equal to how many sixths of an apple?

3. James gave of a pear to William, to George, and kept the rest himself; how much did he give away? How much did he keep?

NOTE. Change the fraction to sixths. Before fractions that have different denominators can be added together, or before one can be subtracted from another, it is necessary to change them to other fractions that have like denominators.

4.

what? 1--what?

5. A man gave of a dollar to one of his workmen, and 3 of a dollar to another; how many fourths of a dollar did he give to both? How many dollars?

6. are how many ? How many times 1 ? NOTE. Read the first question in Ex. 6 as follows: One half and three fourths are how many fourths? Read all similar examples in like manner.

7. A man gave of a barrel of apples to one of his neighbors, and of a barrel to another; did he give more to one than to the other?

8. and are how many? How many times 1 ? 9. Henry gave of an orange to his brother John, to his sister Marion, and kept the rest himself. With this division the selfish John was dissatisfied, saying that Henry had given more to Marion than to him. No, John, said Marion, Henry has given just as much to you as to me. Now which was right, John or Marion? What part of the orange did Henry keep for himself?

10. is how many? 11. }+&+}

how many? How many times 1? 12. Samuel worked of a day for Mr. Adams, and of a day for Mr. Daniels. Mr. Adams paid Samuel 50 cents. Now, at the same rate, what should Mr. Daniels pay him? How much, at that rate, will Samuel earn in a day? What part of a dollar?

13. are how many ?

14. A boy wished to give of a pear to his sister, and to his brother; and in order to do this most conveniently, he first cut the pear into 6 equal pieces; how many pieces did he give to each? How many pieces had he remaining?

15. Samuel gave of a dollar to one poor boy, and of a dollar to another; what part of a dollar did he give away? How much more to one boy than to the other?

16. What is + Į? ƒ— 4 ?

17. James had a box of strawberries, and said he would give of them to Addie, to Willie, and the rest to Georgie, if he could tell how to divide them. Georgie won; how did he divide them?

18. Harriet having 3 quarts of cherries, said she would give of a quart to Mary, of a quart to Martha, and the rest to any one of the company who would most quickly tell how to divide them. Would you have won had you been there, and how would you divide them?

19. are how many? 3 are how many? 20. how many ? 3

=

what?

21. A man having 2 bushels of wheat to give to 3 of his workmen, wished to give of a bushel to the first, 3 of a bushel to the second, and the rest to the third; how much should he give to the third?

22. are how many? are how many? 23. A farmer had a horse, a cow, and a sheep. The horse would eat of a ton of hay in a month, the cow, and the sheep; how much would they all eat? How much more would the horse eat than the sheep? How much less would the sheep eat than the

cow?

24.

are how many? are how many? 25. A man gave of a ton of coal to B, and 2 of a ton to C; to which did he give the most? How much?

How much to both?

26. A little girl having a pound of figs, gave of them to one schoolmate, to another, and kept the rest; what part of the pound did she give away? What part did she keep?

27. are how many?

are how many?

28. A spendthrift having received a fortune, squandered of it the first month, and of it the next month, after receiving it; what part of it had he then remaining?

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23. Reduce and to equivalent fractions having a common denominator.

24. Reduce and so that they shall have the least common denominator.

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28. Reduce, 3, and 4, so that they shall have the

least common denominator.

29. Reduce, 75, and 24. 30. Reduce 3, 3, and 4. 31. Add together and . 32. Add together and .

and .
and

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