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.
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