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Adding 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.

To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.

For example, suppose you want to add:

1 11 + 2 3

1/11 + 2/3

The LCM of 3 and 11 is 33 . So, we need to find fractions equivalent to 1 11 and 2 3 which have 33 in the denominator. Multiply the numerator and denominator of 1 11 by 3 , and multiply the numerator and denominator of 2 3 by 11 .

( 1 × 3 11 × 3 ) + ( 2 × 11 3 × 11 ) = 3 33 + 22 33

Now we have like denominators, and we can add as described above.

= 25 33

3/33 + 22/33 = 25/33

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