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Operations with Fractions

Adding and Subtracting Fractions

When adding and subtracting fractions , the first thing to check is if the denominators are the same.

Adding and Subtracting Fractions with Like Denominators

If the denominators are the same, then it's pretty easy: just add or subtract the numerators, and write the result over the same denominator.

For example,

2 7 + 4 7 = 6 7

Adding and Subtracting Fractions with Unlike Denominators

If the denominators are not the same, then you have to use equivalent fractions which do have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators.

For example,

3 4 + 5 3 = 3 × 3 4 × 3 + 5 × 4 3 × 4 = 9 12 + 20 12 = 29 12

Multiplying and Dividing with Fractions

Multiplying a Fraction by a Fraction

To multiply two fractions, just multiply the numerators to get the numerator of the product, and multiply the denominators to get the denominator of the product.

a b c d = a c b d

For example,

4 3 5 7 = 4 5 3 7 = 20 21

Multiplying a Fraction by an Integer

To multiply a fraction by a whole number, remember that any integer n can be written as the fraction n 1 .

For example,

6 3 13 = 6 1 3 13 = 6 3 1 13 = 18 13

Dividing by a Fraction

To divide by a fraction , multiply by the reciprocal of the fraction.

For example,

Divide 2 3 by 4 5 .

2 3 ÷ 4 5 = 2 3 4 5 = 10 12 = 5 6

See also: Multiplying a Fraction by a Fraction , Multiplying a Fraction by an Integer and Dividing by a Fraction