8. A tailor bought two pieces of cloth, the shorter piece containing 24 yards; 5 eighths the number of yards in the shorter piece is 20 yards less than the number of yards in the longer piece; how many yards in both pieces?

9. If 7 tenths of an acre of land yield 28 bushels of wheat, what will 1 acre yield? what will 3 acres yield?

10. 16 is 4 fifths of what number?

ANALYSIS. 16 is 4 fifths of 5 times 1 fourth of 16; 1 fourth of 16 is 4, and 5 times 4 is 20. Therefore, 16 is 4 fifths of 20.

11. 25 is 5 eighths of what number?
12. 14 is 7 twelfths of what number?
13. 9 is 3 tenths of what number?
14. 12 is 4 fifteenths of what number?
15. 20 is 2 sevenths of what number?
16. 18 is 6 elevenths of what number?
17. 21 is 3 halves of what number?
18. 72 is 9 eighths of what number?
19. 40 is 10 elevenths of what number?
20. 36 is 12 twentieths of what number?
21. 42 is 7 fifths of what number?

22. 5 sixths of 24 is 2 thirds of what number?

ANALYSIS. 5 sixths of 24 is 2 thirds of 3 times 1 half of 5 times 1 sixth of 24; 1 sixth of 24 is 4, and 5 times 4 is 20; 1 half of 20 is 10, and 3 times 10 is 30. Therefore, & sixths of 24 is 2 thirds of 30.

23. 3 fourths of 16 is 6 sevenths of what number? 24. 4 fifths of 30 is 8 elevenths of what number? 25. 6 fourths of 28 is 7 ninths of what number? 26. 9 twelfths of 60 is 5 thirds of what number? 27. 8 ninths of 18 is 1 fourth of what number? 28. 11 fifteenths of 45 is 3 halves of what num ber.

29. 6 tenths of 100 is 5 twelfths of what number? 30. 3 twentieths of 80 is 2 sixteenths of what number?

31. 9 eighths of 64 is 8 fifths of what number? 32. Of a certain farm, 36 acres are woodland, and 5 sixths of the woodland is 3 fifths of the number of acres of cleared land; how many acres of cleared land, and how many acres does the farm contain?

33. Mr. Smith gave 5 sevenths of all the money he had for a horse; he then paid 12 dollars for a saddle and bridle, which was 3 fourths of all the money he had left; how much money had he at first?

34. A person, being asked his age, answered that if he were twice as old, 1 third of his age would be 20 years; how old was he?

43. A FRACTION is one or more of the equal parts of a unit. Fractions are expressed by figures in the following manner, viz.:

129

,

eleven twelfths.

one seventh.

13,

one eighth.

, one tenth.

209

thirteen twentieths.

41, four and 1 seventh.

9ğ, nine and 5 eighths, &c.

1. The number below the short horizontal line is called the denominator.

2. The number above the line is called the numerator.

3. The denominator shows into how many parts the whole thing is divided.

4. The numerator shows how many of these parts are taken or used.

5. A proper fraction is one whose numerator is less than the denominator; its value is less than a unit.

6. An improper fraction is one whose numerator is equal to, or greater, than the denominator; its value is equal to, or greater, than a unit.

7. A mixed number is a whole number joined with a fraction.

8. What kind of a fraction is ? What is the 4 called? What does it show?

9. In the fraction, what is the 3 called? What does it show?

10. Into how many equal parts must a thing be divided to produce the fraction? how many of these parts must be taken?

11. What kind of a fraction is ? Why? 12. What kind of a number is 63 ?

13. How would you obtain

14. How would you obtain

15. How many times in 6?

Why?

of any thing?

of any thing?

ANALYSIS. Since in 1 there are 4 times, or, in 6 there are 6 times, or 2. Therefore there are 24 times in 6.

16. How many times 17. How many times 18. How many times 19. How many times 20. How many times 21. How many times 22. How many times 23. How many times

in 4? in 8? in 9? in 12?
in 3? in 5? in 7? in 8?
in 2? in 4? in 5? in 7?
in 5? in 6? in 7? in 9?
in 3? in 4? in 6? in 7?
in 33? in 43? in 71⁄2?
in 24? in 53 ? in 61⁄2 ?
in 5? in 7? in 8?

24. In 12 how many thirds?
25. In 7 how many fifths?
26. In 10g how many eighths?
27. In 9 how many twelfths?
28. In 15 how many fourths?

29. Reduce 203 to an improper fraction. 30. Reduce 87 to an improper fraction. 31. Reduce 711 to an improper fraction. 32. Reduce 83 to an improper fraction. 33. Reduce 25 to an improper fraction. 34. How do you reduce a whole number to a fraction having a required denominator?

35. How do you change a mixed number to an improper fraction?

44. 1. In 16 how many times 1 ?

ANALYSIS. Since equal 1, 16 are as many times 1 as are contained times in 16; are contained in 10, 4 times. Therefore 16 are 4 times 1, or 4.

2. In 25 how many times 1?

6

3. In 42 how many times 1?
4. In 2 how many times 1?
5. In 120 how many times 1?
6. In how many times 1?
7. In 100 how many times 1?

8. How many times 1 in 24? in? in ? 9. How many times 1 in 32? in 45? in 70? 10. How many times 1 in 60? in 48? in 14? 11. How many times 1 in 125? in 150? in 146? 12. How many times 1 in 116? in 205? in 125? 13. How many times 1 in 20? in 102? in 42? 14. How many times 1 in 8? in ? in 100?

30

11

12

15. How many times 1 in 8? in ? in 2? 16. How do you reduce an improper fraction to a whole or mixed number?

20

17. Reduce to an equivalent whole number. 18. Reduce 104 to an equivalent mixed number. 19. Reduce 84 to an equivalent mixed number. 20. Reduce to an equivalent mixed number. 21. Express the value of 120 in a whole number. 22. Express the value of 288 in a mixed number. 23. Express the value of 95 in a mixed number.

60

45. 1. In of 1, how many sixths?

ANALYSIS. Since in 1 there are 8, in of 1, there are 2 times of §; } of § is , and 2 times are 1. Therefore, &c.

10. In of 1

11. In

1/2

how many twenty-fifths? of 1 how many sixtieths?

12. In of 1 how many eighteenths?