SECTION THIRD.

LESSON I.

REMARK. When any thing is divided into two equal parts, one of the parts is called one half of the thing; so when any number is divided into two equal parts, one of these parts is called one half of the number.

1. If an apple is worth two cents, what is one half of it worth?

Ans. It is worth one half of two cents.

2. What is one half of two cents?

Ans. One half of two cents is one cent.

3. Why? Ans. Because, if we divide two cents into two equal parts, one of the parts is one cent.

4. How many halves of an apple make a whole apple?

5. How many halves of a pear make a whole pear? 6. Are two halves of a dollar equal to a whole dollar?

Ans. Yes. Two halves of any thing make the whole of that thing.

7. If you can buy a pear for two cents,

of it can you buy for one cent? 8. One is what part of two? Ans. One is one half of two.

what part

9. If you can buy one pear for two cents, how many pears can you buy for three cents?

10. Three are how many times two?

Ans. Once two and one half of two.

11. If you can buy one yard of cloth for two dollars, how many yards can you buy for four dollars?

12. Four are how many times two?

13. Two is what part of four?

14. Six are how many times two? 15. Five are how many times two?

Ans. Two times two and one half of two.

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?

4

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 hali, 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.