A fraction is increased when the numerator is made larger; for the larger the numerator, the more fractional parts there are taken. Thus, & are greater than . A fraction is increased when the denominator is made smaller; for the smaller the denominator, the fewer are the number of parts into which the unit is divided. Thus, is greater than .

A fraction is made smaller when the numerator is made smaller, or when the denominator is made greater 1. Into how many parts is the unit divided when the denominator of the fraction is 2?

2. What is meant by of an apple? ANS. One of the two equal parts into which an apple (unit) is divided.

3. How many halves make a whole? Why? Because the unit is divided into two equal parts to make halves, and the two equal parts taken together must make the unit, or whole.

4. Which is the greater, or? Why? Because is one of the two equal parts, while is one of the three equal parts, into which a unit is divided.

5. How many thirds are there in one?

6. How many thirds are there in two? ANS. One contains, therefore 2 will contain ÷ +

7. How do you cut an apple so as to obtain ? ANS. I cut an apple into 3 equal pieces, then 2 of the pieces are of the apple.

8. How many fourths in 1? in 2? in 4?

9. What do you mean by ? ANS. One of the four equal parts into which a unit is divided.

10. What do you mean by ? ANS. Three of the four equal parts into which a unit is divided.

11. Into how many parts is the unit divided when the denominator is 4?

12. are how many times the fourth of one? ANS. Three times the fourth one.

13. If a class consists of 10 pupils, how many pupils are there in one half of the class? in one fifth of the class? in four fifths of the class?

14. What is one half of 10? 14? 18? 24?

15. What are five halves of 10? 14? 18? 24?

16. If 5 is one half of some number, what are 2 halves of the same number? 7 halves? 9 halves? 12 halves?

17. If 5 is one half of some number, how many halves of the same number are 15? 25? 45? 55? 18. If 15 are three halves of some number, how many halves of the same number are 20? 30? 40? 50? 19. Which is greater, or ? Why?

20. How many fifths in one? in two? in seven? 21. What do you mean by of an orange?

22. are how many times the fifth of one?

23. How do you cut a yard of cloth so as to obtain of it?

24. If an arithmetic costs 15 cents, what is of the cost of the book? what are of the cost of the book? 25. What is one third of 18? 27? 33? 42?

26. What are four thirds of 18? 27? 33? 42?

27. If 6 nuts are one third of the number of nuts that Charley has, what are two thirds of his nuts? How many nuts has he?

28. If 6 is one third of some number, how many thirds of the same number are 24? 48? 60? 72?

29. If 24 are four thirds of some number, how many thirds of the same number are 30? 42? 54? 66? 30. Which is the greater, or ? Why?

31. How many sixths in one? in two? in eight? 32. What do you mean by ? & are how many

times the sixth of one?

33. How would you obtain of a pine-apple?

34. If a sleigh cost 32 dollars, what is of the cost of the sleigh? what are 2 of the cost of the sleigh? of the cost?

35. What are five fourths of 24? 36? 48? 52? 36. James has 9 cents, which is one fourth as much money as Edwin has; what is 3 fourths of Edwin's money? how much money has he?

37. If 3 is one fourth of some number, how many fourths of the same number are 18? 24? 27? 3? 6?

38. If 18 are 6 fourths of some number, how many fourths of the same number are 15? 33? 39? 45?

39. How many sevenths in one? in five? in nine? 40. What do you mean by ? are how many times the seventh of one?

41. Five gentlemen agreed to furnish a family of poor children with clothes and books, in order that they might attend school; the expense was 35 dollars, which they shared equally; what part of the money, and how much, did each pay?

42. What are seven fifths of 15? 20? 25? 45?

43. If 6 is one fifth of 30, what are four fifths of the same number? 6 fifths? 8 fifths? 12 fifths? 16 fifths?

44. Twelve melons are 4 fifths of the number of melons in my garden; how many times one fifth of my melons are 18 melons? 21 melons? 27 melons? 36 melons?

45. A market-man carried 42 ears of green corn to market, which were 6 fifths of the number of ears carried the day before; required 3 fifths of the number of ears carried the day before; 8 fifths of the number; 11 fifths; 13 fifths.

46. How many eighths in one?

47. What do you mean by g? & are how many times the eighth of one?

48. I have 32 oranges to divide equally among 8 boys; what number of oranges can I give to each boy? 49. A gentleman has 66 acres of land in 6 fields of equal size; how many acres in 5 of the fields?

50. What are 8 sixths of 48? 60? 72? 84? 51. An angler being asked how many fish he had caught that morning, replied, that 18 were 3 sixths of the number taken; how many had he caught?

52. If 32 are 8 sixths of some number, how many sixths of the same number are 28? 36? 44? 52?

53. Lucy has 12 cherries, which are 4 sixths of the number she has eaten; what are 3 sixths of the number of cherries she has eaten? how many has she eaten?

54. How many ninths in one? in seven? in eleven? 55. What do you mean by ?

56. If 20 dollars are paid for 10 sevenths of a ton of hay, what is the price per ton?

57. What are 9 sevenths of 21? 35? 49? 56? 63? 58. Eighteen scholars are 2 sevenths of the number in the school; how many sevenths of the number are 36? 72? 81? 108?

59. A company of children went out to gather pondlilies, and, upon returning, found that 63 were 9 sevenths of the number gathered; how many did the little girl receive that had 2 sevenths of the lilies for her share? how many did they gather?

60. How many tenths in one? in eight? in twelve? 61. If an acre of land will produce 24 bushels of corn, how much will 7 eighths of an acre produce?

62. What are 9 eighths of 48? 64? 96? 112?

63. Sixty-three credit marks are 9 eighths of the highest number of marks given to any boy; how many eighths of the number of marks does the boy receive who gets 49? how many eighths has the scholar that has 56?

64. If 49 are 7 ninths of some number, what are 9 ninths of the same number? 11 ninths? 14 ninths?

65. If 21 are 3 elevenths of some number, how many elevenths of the same number are 49? 63? 77 ? 91?

66. What is a fraction?

67. How are the numbers of a common fraction written?

68. What is the lower number called? What does it show?

69. What is the upper number called? What does it show?

70. How is a fraction made greater? How is a fraction made smaller?

SECTION XX.

ANS. 2. Why? Be

1. What part of 2 is 1?
cause 1 must be the half of 2 times 1.
2. What part of 3 is 1? is 2?

3. What part of 4 is 1? is 2? is 3?
4. What part of 5 is 1? is 2? is 3? is 4?
5. How many are 3 times the half of 2 ?

6. If 2 pounds of sugar cost 14 cents, what will 1 pound cost? 6 pounds? 8 pounds? 12 pounds?

7. If 3 pairs of shoes cost 6 dollars, what is the cost of 1 pair? 8 pairs? SOLUTION. If 3 pairs of shoes cost 6 dollars, 1 pair will cost a third of 6 dollars, or 2 dollars; 8 pairs will cost 8 times 2 dollars, or 16 dollars. ANS. 16 dollars.

8. What are 10 times the half of 14? what are 9 times the third of 6?

9. If 4 cords of wood cost 24 dollars, what will 12 cords cost?

10. What are 9 times the fourth of 24?

11. How many bushels of oats will 9 horses eat in a month, if 6 horses eat 30 bushels in the same time? 12. How many are 8 times the sixth of 30?

13. If 8 cows are worth 160 dollars, how much are 7 of them worth?

14. What part of 8 is 1? is 7? is 5?

15. How many panes of glass are there in a window of your school-room? what part of the whole will 4 panes be?

16. How many scholars are reciting in your class? what part of the class are 4 scholars? 6 scholars? 10 scholars?