16. If two dollars will buy one barrel of apples, how many barrels will five dollars buy?

17. If two dollars will buy a bushel of wheat, how many bushels will seven dollars buy?

18. Eight are how many times two? 19. Nine are how many times two? 20. Ten are how many times two?

REMARK. When any thing or any number is divided into three equal parts, one of these parts is called one third of the thing or one third of the number; two of the parts are two thirds of the thing or of the number. 21. How many thirds of an apple make a whole Apple?

22. If a load of wood is worth three dollars, and if it is divided into three equal parts, what will one of the parts be worth; that is, what will one third of the load be worth?

23. What is one third of three dollars?

24. Suppose the load to be divided as before, what will two of the parts be worth; that is, what will two thirds of the load be worth?

25. What is two thirds of three?

26. If a barrel of apples is worth three dollars, what part of a barrel will one dollar buy? What part of a barrel will two dollars buy?

27. One is what part of three? Ans. One is one third of three. 28. Two is what part of three ?

Ans. Two is two times one third of three; that is, two is two thirds of three.

29. If you can buy a pound of tea for three shillings, how much can you buy for four shillings? How much for five shillings? For six shillings?

30. Four are how many times three? Ans. Once three and one third of three. 31. Five are how many times three! 32. Six are how many times three?

33. If apples are worth three dollars a barrel, how many barrels can you buy for seven dollars? How many for eight dollars?

34. What is meant by one third of any thing?

Ans. One third of any thing is one of the three equal parts into which that thing is divided. See Remark after Example 20.

35. What is meant by two thirds of any thing? 36. Nine are how many times three?

37. Ten are how many times three?

LESSON II.

1. WHAT is meant by one fourth of a thing? Ans. One of the four equal parts into which the thing is divided.

2. What is meant by two fourths, or three fourths, of any thing or of any number?

3. If a cake is worth 4 cents, and it is cut into 4 equal parts, what is 1 of the parts worth; that is, what is 1 fourth of the cake worth? What are 2 fourths of it worth? What are 3 fourths of it worth?

4. If you can buy a cord of wood for 4 dollars, what part of a cord can you buy for 1 dollar? What part for 2 dollars? For 3 dollars?

5. What part of four is one? Ans. One is one fourth of four. 6. What part of four is two?

Ans. Two fourths, or one half, of four.

7. What part of four is three?

Ans. Three fourths of four.

8. How many fourths make a whole one?

9. If you can buy a yard of cloth for four dollars, how much can you buy for 5 dollars? How much for 6 dollars? For 7 dollars?

10. Five are how many times four?

Ans. Once 4 and one fourth of 4.

11. Six are how many times 4?

Ans. Once 4 and two fourths of 4; or, once 4 and one half of 4.

12. Seven are how many times 4? Ans. Once 4 and three fourths of 4.

13. Eight are how many times 4?

14. If 4 barrels of apples will buy 1 ton of coal, how many tons will 9 barrels buy? How many tons will 10 barrels buy? How many tons will 11 barrels buy? 15. Twelve are how many times 4? 16. Thirteen are how many times 4? 17. Fourteen are how many times 4? 18. Fifteen are how many times 4? 19. Sixteen are how many times 4? 20. What is one fourth of 4? Ans. One fourth of 4 is 1.

21. Why? Ans. Because, if we divide 4 into four equal parts, one of the parts is 1.

22. What is two fourths, or one half, of 4.

23. What is three fourths of 4?

24. If one half of an apple costs 1 cent, what will the whole apple cost?

Solution. Since one half of the apple costs 1 cent, two halves, or the whole apple, will cost two times 1 cent, which are 2 cents.

25. If one half of a barrel of flour is worth 4 dollars, what is a whole barrel worth? Why?

26. If one third of a melon is worth 4 cents, what are two thirds of it worth? What is the whole melon worth?

27. If one fourth of a pie costs 5 cents, what will two fourths, or one halı, of the pie cost? What will three fourths of it cost? What the whole pie? 28. What is one half of 6 apples?

Ans. Three apples.

29. Why? Ans. Because, if 6 apples are divided into two equal parts, each part is 3 apples.

30. What is one half of 8 cents? Why?
31. What is one half of 12 oranges? Why?
32. What is one half of 10?

Why?

33. What is one third of 6 apples?

Ans. Two apples.

34. Why? Ans. Because, if 6 apples are divided into three equal parts, each part is 2 apples.

35. What is one third of 12 lemons? Why? 36. What is two thirds of 12 lemons? Why? 37. What is one third of 15 dollars?

thirds of 15 dollars?

What is two

38. What is one third of 21? Two thirds of 21 ?

39. What is one half of 3 apples?

Ans. One apple and one half of another apple.

40. What is one half of 5 apples?

Ans. Two apples and one half of an apple. 41. What is one half of 7 apples?

42. What is one half of 9 pears?

43. What is one third of 4 oranges? Two thirds? 44. What is one fourth of 16 miles?

45. What is two fourths, or one half, of 16 miles ? 46. What is three fourths of 16 miles?

47. What is one fifth of 15 dollars?

48. What is two fifths of 15 dollars? Three fifths? 49. What is meant by one fifth, two fifths, etc., of my number? See Remark after Ex. 20, page 49.

50. Mary had two fifths of a dollar, and her mother gave her another fifth; what part of a dollar had she then?

51. Henry had four fifths of a dollar, but he spent two fifths of a dollar for fruit; what part of a dollar has he now?

52. How many fifths make a whole one?

53. A boy spent one fifth of all his money on Monday, and two fifths on Tuesday; what part of his money did he spend in these two days? What part had he then remaining?

LESSON III.

REMARK. The following lines represent a yardstick, marked off or divided into halves, fourths, and eighths of a yard.

leighth. 1 eighth. 1 eighth. 1 eighth. 1 eighth. 1 eighth. 1 eighth. 1eighth 1. One half equals how many fourths? Ans. Two. 2. One fourth equals how many eighths?

3. One half equals how many eighths?

4. If you cut an apple into halves, and then cut each half into two equal pieces, into how many pieces will the apple be cut? What part of the whole apple is one of these small pieces?

5. One half of an apple is equal to how many times one fourth of an apple?

6. How many fourths of an orange are equal to one half of an orange?

REMARK. The following lines represent a yardstick divided into thirds and sixths of a yard.

One third.

One third.

One third.

One sixth. One sixth. One sixth. One sixth. One sixth. One sixth,

7 One third equals how many sixths?

8. If you cut a cake into thirds, and then cut each third into two equal parts, into how many equal parts will the cake be cut? Each of the small picces will be what part of the whole cake?

9. One third of a cake is how many times one sixth of the same cake?

10. If you cut a pie into halves, and then cut each half into three equal parts, what part of the pie will one of these small pieces be?