22. Reduce to sixths; to eighths; to tenths.

23. Reduce to 10ths; to 20ths; to 30ths.

24. Reduce to 12ths; to 20ths; to 36ths. 25. Reduce and to 12ths.

26. Reduce,, and ğ to 40ths.

27. Reduce,, 1 to 24ths.

NOTE. When fractions have the same denominator they are said to have a common denominator.

28. Reduce and to a common denominator.

ANALYSIS.-A common denominator of halves and fifths is tenths; equals, and equals.

and

to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.
to a common denominator.

29. Reduce
30. Reduce and
31. Reduce and
32. Reduce and
33. Reduce and 3
34. Reduce and
35. Reduce and
36. Reduce and
37. Reduce and
38. Reduce,,
and
39. Reduce , and
40. Reduce, },
1 and
41. Reduce,, and
42. Reduce, 4,
2, and
43. Reduce,, and
44. Reduce,, and

3' 5'

to a common denominator.

5.

FRACTIONS TO LOWER TERMS.

1. How many fourths in?

ANALYSIS. Since equals, there are as many 4ths in as is contained times in, or .

Since equals 3, by what do we divide both numerator and denominator of to produce?

NOTE. To reduce a fraction to lower terms, divide both numerator and denominator by a number that will divide each.

11. By what may we divide both numerator and denominator of ?8? 10?

12. Reduce to thirds; 19 to 5ths.

13. Reduce to 3ds; to 4ths.

14. Reduce to 6ths; 0 to 4ths.

12

8

18. Reduce 1 to 4ths; 18 to 10ths; to 5ths.

NOTE.-When a fraction cannot be reduced to one having a less de

nominator, it is said to be in its lowest terms.

19. Reduce and § to their lowest terms.

26. Reduce and 35 to their lowest terms. 27. Reduce and to their lowest terms. 28. Reduce 18 and 15 to their lowest terms.

6.

COMPOUND FRACTIONS.

A compound fraction is a fraction of a fraction; as, of

of .

1. What is of } ?

ANALYSIS. Since equals, of } is { of %, or .

7. If I had of a dollar and spent of it, how much did

I spend?

8. A man sells

9. How much is

of

14

of his corn; how much does he sell? of of an inch?

10. A man earned of a dollar and his son as much;

20. A boy had

of a dollar and spent of it; how much

did he spend?

21. If a boy has of a pie and gives away of it, how much does he give away?

22. If Amos has of a dollar and spends of it, how much does he spend?

23. If I give away of of my money, how much do I give away?

24. A boy had 40 cents: he spent of of it; how much did he spend ?

25. A horse cost 120 dollars, and a cow cost of as much; how much did the cow cost?

26. A gentleman who owned of a farm sold of his share; how much of the farm did he sell?

27. George had of a bushel of chestnuts: he shared them equally among 6 of his playmates; what part of a bushel did each get?

28. William had of a dollar, and shared it with 3 brothwhat part of a dollar did each get?

ers;

ADDITION OF FRACTIONS.

1. What is the sum of

of a pie and of a pie?

2. What is the sum of 3

3. What is the sum of

of a dollar and 2 of a dollar? of a dollar and

4. What is the sum of 3 of an orange and

of a dollar?

of an orange?

5. How much is of a peck, g of a peck, and § of a

40. What is the sum of 23 and 11?

SOLUTION 1.-2 equals ; 1 equals ; equals 12, and equals 12; plus 11⁄2 equals 12, or 311.

SOLUTION 2.-2 plus 1 are 3; equals 12, and equals 1; 11⁄2 plus are; hence 23 plus 1 equals 311.

NOTE.-In solution 2 the whole numbers and the fractions are added separately.

51. I paid of a dollar for a hen and of a dollar for a duck; how much did I pay for both?

52. If a book cost of a dollar and a slate of a dollar, how much do both cost?

53. If I pay of a dollar for a dinner and 3 of a dollar for car-fare, how much do I pay for both?