The Lesson

Fractions can be added. Imagine you wanted to add 1/5 (one-fifth) and 3/5 (three-fifths).

How to Add Fractions

It is easy to add fractions when the bottom numbers (called the denominators) are the same. It is slightly trickier to add fractions when the bottom numbers are different.

A Real Example of How to Add Fractions with the Same Denominator

Question

Add the fractions below.

Step-by-Step:

1

Add the top numbers (called the numerators) of both fractions.
1 + 3 = 4
Place the answer above their common denominator.

2

Simplify the fraction if possible. (The fraction in our example is already as simple as possible).

Answer:

1/5 (one-fifth) plus 3/5 (three-fifths) equals 4/5 (four-fifths).
1/5 + 3/5 = 4/5

How to Add Fractions with Different Denominators

Question

Add the fractions below.
In this example, the bottom numbers (the denominators) are different. Before our fractions can be added, we must make the denominators the same. In other words, we must find a common denominator for both fractions. The common denominator can be found using one of the methods below:

Lesson Slides

The slider below shows how to add ½ and ⅓ using the common denominator method.

Top Tip

It's All About the Denominators

The secret to adding fractions is making the denominators the same. Once you've done that, it's simple.

Note

Least Common Denominators and Least Common Multiples

The least common denominator method relies on finding the least common multiple of the denominators of the fractions. For our example used in the least common denominator method, the denominators are 2 and 3. List the multiples of 2 and 3:

Multiples of 2 = 2, 4, 6, 8, 10...

Multiples of 3 = 3, 6, 9, 12, 15...

The least common denominator is the lowest number that appears in both lists,:

Multiples of 2 = 2, 4, 6 , 8, 10...

Multiples of 3 = 3, 6 , 9, 12, 15...

The least common denominator of 2 and 3 is 6.