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ADDITION OF VULGAR FRACTIONS.

CASE I.

To add fractions having common denominators. RULE. Add the numerators all together, divide the sum by the common denominator, the quotient is the answer.

Add

Examples.

9 10 6 5 11 12 14

15′ 15 15 15 15 15' together.

15

the numerators 9+10+6+5+11+12+1467

67-1547 Ans.

CASE II.

To add fractions having different denominators. -RULE.-Find a common denominator by case 5th (in Reduction,) use it as a dividend; use each given denominator as a divisor; divide, and multiply the quotients by the several numerators, and the sum of all the products is the numerator to the common denominator, and is the fraction required.

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To add mixed numbers whose fractions have common denominators.

RULE. Add the fractions as in case 1st, and the whole numbers as in Simple Addition; then add the sum of the fractions to the whole number.

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whole num. 104+111+96+80 = 391

num. of frac. 2+16+14+16=48÷20=

20

230

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2. Required to add 14, 1518 7 together.

13

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To add mixed numbers whose fractions have different denominators.

RULE. Add the fractions as in case second, and the whole numbers as in simple addition; then add the sum of the fractions, to the sum of the whole numbers, and it is done.

Examples.

1. Add 125, 16, 17, 16, and 19% together. Whole num. 12 + 16 +17 +16+ 1980.

8 6

Sum of the fractions. 3,1%

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2. Add 21%, 67, 127, and 14121 together.

Ans. 14277 73

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CASE V.

To add fractions of several denominations, such as parts of cuts.; parts of grs. ; parts of lbs. &c.

RULE. Find the value of each separate fraction by case tenth in reduction, and add the several sums together as in compound addition..

Examples.

1. Add a cwt. of a qr. and § of a lb. together.

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RULE. Subtract the least numerator from the largest, and the remainder placed over the common denominator will be the difference required.

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CASE II.

To subtract a simple fraction, or a mixed number, from a whole number.

RULE.-Subtract the numerator of the fraction from its denominator, and put the denominator of the fraction under the remainder; and carry one to be deducted from the whole number.

Examples.

1. It is required to subtract

12

from 12.
-=113 Ans.
2. It is required to subtract 274 from 32.

Ans. 4

3. What is the difference between 122 and 21?

10

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To subtract fractions having different denominators. RULE. Reduce the fractions to a common denominator, by case 5th, in Reduction; and the difference of the numerators is the difference requir

ed.

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CASE IV.

To distinguish the largest of any two fractions, &c.

RULE. Reduce them to a common denominator,, (by case 5th in Reduction,) and the one that has the largest numerator is the largest fraction...

Example.

1. Which is the greatest fraction or To 11? reduced to a common denom. is equal to 2 reduced to a common denom. is equal to

10

54

60

181-18

Ans.

60

Therefore

13

is the largest fraction.

CASE V..

To subtract a mixed number from a mixed number, when the fraction which is to be subtracted is greater than the one which it is to be taken from.

RULE. Reduce the fractions to a common denominator; then subtract the numerator of the greater from the common denominator, and to the remainder add the least numerator; and the sum of them must be set over the common denominator; and carry one to the whole number, and subtract the whole number as in simple subtraction..

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Examples

12

1. It is required to take 8 from 123.

19

reduced to a common denom. is equal to

"

reduced to a common denom. is equal to

72

72

114

57

114

125 less by 82 = 394.

8- = 3.99 Ans..

114.

114.

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