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72. Principle.-The least common denominator of several fractions is the least common multiple of their denominators.

WRITTEN EXERCISES.

16. Reduce, 1, and to their common denominator.

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Find the L. C. M. of the given denominators.

Divide this by each denominator and multiply both terms of the fraction by the quotient.

NOTE.-Reduce mixed numbers to improper fractions, and all to their lowest terms before finding the least common denominator.

Reduce to their least common denominator

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ADDITION OF FRACTIONS.

ORAL EXERCISES.

73.—1. Find the sum of 2 thirds and 5 thirds.
2. Find the sum of 2 sixths and 3 sixths.
3. Find the sum of 3, 4, and .

4. Find the sum of and .

f, f, and .

and §.

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74. Principle.-To add fractions they must be reduced to a

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Reducing the fractions to 24ths, we have = 14, 1 = 14, and 7 = 11. Since the fractions now have a common denominator, we add their numerators: 16 twenty-fourths + 18 twenty-fourths + 21 twenty-fourths, equal 55 twenty-fourths, or, or 24.

RULE.

Reduce the fractions to a common denominator, then add their numerators, and write the sum over the common denominator. NOTE.-Always reduce the result to its lowest terms.

Find the sum—

22. Of,, and §.

23. Of 4, §, and 7.

3.

24. Of,, and .
25. Of, 3, and 14.

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13

15

PROCESS.

2912,

Ans.

The sum of and is 1.

The sum of 13 and 15 is 28.

The sum of 28 and 1 is 29.

41. Find the sum of 8, 10%, and 14.
42. Find the sum of 102, 2047, and 9015.
43. Find the sum of 221, 343, 424, and 604.
44. Find the sum of 621, 871, 75, and 112.
45. Find the sum of 67, 4, 6003, and 5027.

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6. from. 4.
10.
& from .

from . 14.

18. 736 from .

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76. Principle. To subtract fractions they must be reduced to a common denominator.

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fractions now have a common denominator, we subtract their numerators: 35 fortieths 12 fortieths equals 23 fortieths, or 3.

RULE.

Reduce the fractions to a common denominator, subtract their numerators, and write the result over the common denominator. NOTE.-Always reduce the result to its lowest terms.

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We cannot subtract & from 3; we take 1 from 21, which added to equal 13, or 10; from 10 leaves, and 8 from 20 leaves 12. Hence the required result is 125.

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PRACTICAL PROBLEMS

In Addition and Subtraction of Fractions.

1. A bought 16 tons of coal, and B bought 83 tons; how much did they both buy, and how much more did A buy than B?

2. The first of three farms contains 119 acres, the second 975 acres, and the third 2165 acres; how many acres in the three farms?

3. A teacher's salary per month is $135,7%, and his expenses average $517; how much does he save per month?

4. My agent charged me $110 for traveling expenses and $104 for boarding; his sales amounted in cash to $1000; how much should he return to me?

5. A merchant sold $5000 worth of goods in four months: the first month he sold $9704 worth, the second $1002 worth, and the third $1260,7 worth; how much did he sell the fourth month?

6. A farmer raised 800 bushels of wheat, corn, and rye; how much wheat did he raise, if there were 108 bushels of rye and 257 bushels of corn?

7. A miller had 250 bushels of wheat: after buying 3163 bushels he sold 4267 bushels; how much less had he than he had at first?

8. A had $20454, then lost $1204, then gained $316, after which he lost $5283; how much remained?

9. The sides of a field are 421 rods, 635 rods, 70151⁄2 rods, 534 rods, and 37 rods, respectively; what is the distance around the field?

10. A man went to a store with $500: he paid $75 for a reaper, $344 for a stove, and $125 for a wagon; how much money had he remaining?

11. If I pay my grocer $183, my coal-dealer $271⁄2, and my tailor $221, how much will I have left out of four twentydollar bills?

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