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How to Add Fractions (Mathematics Lesson)

Adding Fractions

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

An Example Question

What is the answer to adding the fractions below?

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

Step 2
Simplify the fraction if possible. (The fraction in our example is already as simple as possible.)

How to Add Fractions with Different Denominators

An Example Question

What is the answer to adding 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:

The Common Denominator Method

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

The Least Common Denominator Method

The slider below shows how to add ½ and ⅓ using the least common denominator method.
Interactive Test
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Here's a second test on adding fractions.
Here's a third test on adding fractions.
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

What Is a Fraction?

What Is a Fraction?

A fraction is a part of a whole number.

Fractions consist of a numerator and a denominator.

There are three different types of fractions:

What's in a Name?

"Fraction" comes from the Latin "fractus", meaning "broken". The whole is "broken" into parts.

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:



The least common denominator is the lowest number that appears in both lists, in this case 6: