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# Adding and Subtracting Fractions with Unlike Denominators

When adding and subtracting fractions with unlike denominators, you will need to use equivalent fractions that have a common denominator. You do this by finding the least common multiple (LCM) of the two denominators. The LCM is the smallest number that both denominators will divide into. Once you have your common denominator, you can create equivalent fractions and then add or subtract normally.

## An example of adding fractions with unlike denominators

$\frac{1}{11}+\frac{2}{3}$

Our denominators are 3 and 11, which are relatively prime (share no common factors), so the LCM is $3×11=33$ . Next, we need to find fractions with 33 in the denominator that are equivalent to $\frac{1}{11}$ and $\frac{2}{3}$ . To do this, first, you multiply both the numerator and denominator of $\frac{1}{11}$ by 3. Then you multiply both the numerator and denominator of $\frac{2}{3}$ by 11.

$\left(\frac{1}{11}×\frac{3}{3}\right)+\left(\frac{2}{3}×\frac{11}{11}\right)=\frac{3}{33}+\frac{22}{33}$

Now that we have like denominators, we can add the fractions above as $\frac{3}{33}+\frac{22}{33}$ and get the answer:

$\frac{25}{33}$

Since 25 and 33 share no common factors, then our answer is already in the lowest terms.

Fractions

## Get help learning about adding and subtracting fractions with unlike denominators

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