Add Fractions and Mixed Numbers

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Adding Fractions

Fractions with the same denominators are added by placing the sum of the numerators over the common denominator.  After adding, write the sum in simplest form.

Example

Add

First we add the numerators and the denominators stays the same

Now we write the sum in simplest form

What If They Do Not Have Common Denominators?

You can find the common denominator: The common denominator is the least common multiple (LCM) of the denominators. You can then rewrite each fraction as an equivalent fraction with that LCM.

Example

Solve:

The multiples for each denominator are

4: 4, 8, 12, 16

3: 3, 6, 9, 12, 15

Therefore the least common multiple (LCM) equals 12, then we can rewrite the fractions using the LCM

Since the denominators are the same we can add numerators and simplify

Adding Mixed Numbers

The sum of a whole number and a fraction is a mixed number.

To add mixed numbers, add the fractions, then add the whole numbers.  Remember to reduce the sum to simplest form.

Example

Solve:

Add the fractions

then add the whole numbers.

3 + 1 = 4

Remember to reduce the sum to simplest form

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Remember that you may need to find the LCM of the fractions in order to add them.

Example

Solve:

Rewrite the fractions using the lowest common denominator

Add the fractions and whole numbers

Write the improper fraction as a mixed number

Add whole numbers