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How to add fractions with unlike denominators

Following on from our last blog on adding fractions with like denominators, adding fractions with unlike denominators is a little more complicated.

Improper fractions, or fractions with unlike denominators, may look a bit difficult. However, once you make the denominators the same, the addition is easy.

Let’s use an example:
fractions with unlike denominators 

Find the least common multiple

First, we need to find the Least Common Multiple (LCM) for the denominators. Basically, we need to find a common multiple that they share.

The common multiples of 4 are 4, 8, 12, etc.

The common multiples of 12 are 12, 24, 36, etc.

Now we need to find the first common value. For most students new to this, it’s easiest to sketch it out on a number line:
fractions finding least common multiple 
The least common multiple is (1, 3) = 12.

Multiply the numerator and denominator to get like denominators

Now, you’ll need to multiply the entire fraction to make the denominator become the least common multiple. In our example, this is what that looks like:
multiply the fractions 
Important: you multiply both the top and the bottom by the same amount to keep the value of the fraction the same.

multiply top and bottom of fractions

Add the numerators

Now the denominators (the bottom numbers) are the same. This means we can add the numerators (the top numbers):
adding numerators in fractions

Simplifying fractions

Finally, let’s simplify the fraction.

Think about the Greatest Common Factor: the highest number that divides evenly into both the numerator and the denominator.

8 divides into 1, 2, 4, 8

12 divides into 1, 2, 4, 6, 12

The Greatest Common Factor is 4. 8/4 = 2, and 12/4 = 3:
simplifying fractions 
So the answer is:
adding fractions with unlike denominators 
If you are looking for worksheets to practice adding fractions with unlike denominators, why not try out our grade 5 fractions worksheets.