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# Adding Fractions with Unlike Denominators

## The Algorithm and Why It Works

Let’s think about the problem of adding and . When we divide the pizza portion corresponding to into three equal pieces, each of the three pieces represents one sixth of the pizza. The model shows that and are equivalent fractions. In the same way, when the pizza portion representing is divided into two equal pieces, both pieces represent one sixth of the pizza. This shows that and are equivalent fractions.

To do this step without using the pizza models, we replace each fraction by an equivalent fraction so that the two fractions have the same denominators.

We can easily add these equivalent fractions because they have like denominators.

When you multiply both numerator and denominator of a fraction by the same number, the result is an equivalent fraction.

Example 1

Find using equivalent fractions with the same denominator.

Solution

First, find equivalent fractions for both and that have the same denominator. Multiply both the numerator and denominator of by 5 (the denominator of ) .

So is equivalent to. Now multiply both the numerator and denominator of by 3 (the denominator of ) .

So is equivalent to. Now we can add the equivalent fractions.