Add Fractions and Mixed Numbers

**Add Fractions and Mixed Numbers**

**Adding Fractions **

**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 **

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

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