Add Fractions and Mixed Numbers


Add Fractions and Mixed Numbers


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



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