# How to Add Fractions with Like Denominators

- Math Lessons >
- Adding Like Fractions

### Overview of Adding Like Fractions:

### How to Add Like Fractions

Before we get started, let’s brush up on what like fractions are. When two fractions have the same denominators, we call them like fractions. The good news is adding like fractions is as easy as pie!

Let’s take an example. Look at this whole pepperoni pizza cut into 8 equal parts.

If Jake ate *3***8** and Amanda ate *2***8** of the pizza, how much pizza did they eat altogether?

Jake ate 3 out of the 8 slices.

*3***8**

Amanda ate 2 out of the 8 slices.

*2***8**

The pizza they ate all-together would be:

*3***8** + *2***8** = *5***8**.

So, Jake and Amanda ate 5 out of the 8 slices or *5***8** of the pizza altogether.

### Adding Fractions Using a Number Line

Let’s take another example and learn to add like fractions using a number line.

Linda walked *4***9** of a mile to reach the library. She walked *3***9** of a mile to reach the park. How many miles did Linda walk altogether?

Here, the two fractions refer to the same whole 9. So, we divide the number line into 9 equal parts as shown.

Now, let’s draw hops to represent the distance covered by Linda.

The first hop depicts *4***9** of a mile, and rest of the hops show *3***9** of a mile. The endpoint *7***9** denotes the total distance covered or the sum of the two fractions.

Framing a fraction-addition equation for the model, we get:

*4***9** + *3***9** = *7***9**.

So, Linda walked *7***9** of a mile in all.

### Adding Like Fractions - Step by Step

Now that we have learnt to add like fractions with the help of real-life examples, let’s explore like-fraction addition presented as math problems!

Recollect these two points whenever you add like fractions.

✯ While adding like fractions, we don’t add the denominators. We simply retain them.

✯ We add only the top numbers and write the sum over the common denominator.

Now, let’s try this: *5***13** + *7***13**.

Combining the numerators: *5 + 7***13**.

Adding the numerators: *12***13**.

So we have, *5***13** + *7***13** = *12***13**.

### Simplifying the Sum - An Added Step

Here’s an example with an added step. Let’s work it out.

*6***15** + *3***15**

= *6 + 3***15** [Combining the numerators]

= *9***15** [Adding the top numbers]

And now comes the added step. The fraction *9***15** can be reduced further. That is to say, it can be simplified to the lowest terms. To reduce it,

Factor the numerator and denominator: *9***15** = *3 x 3***3 x 5**.

Cancel the common factors if any: .

Thus, *6***15** + *3***15** = *3***5**.

Now that we know the steps, let’s implement them to add three fractions.

### How to Add Three Like Fractions

Adding three fractions doesn’t make much of a difference in the steps involved. Let’s look at an example.

Example

Find *7***34** + *6***34** + *4***34**.

*7***34** + *6***34** + *4***34**

[Expression given]

= *7 + 6 + 4***34**

[Combining the numerators]

= *17***34**

[Adding numbers on the numerator]

= *17***2 x 17**

[Factoring the denominator]

= *1***2**

[Simplifying]

So, we have *7***34** + *6***34** + *4***34** = *1***2**.

### It’s Your Turn Now!

1) Find the sum of the fractions represented by the models.

The addends represented by the models are *3***7** and *2***7**.

The sum of the fractions is *3***7** + *2***7** = *5***7**.

2) Sarah cut a cake into 12 equal pieces. She gave away *3***12** of the cake to her friends. She let her family have *4***12** of it. How much cake did Sarah give away in all?

To friends: *3***12** of the cake.

To family: *4***12** of the cake.

The quantity of cake given away in all: *3***12** + *4***12** = *7***12**.

3) Our city recorded a rainfall of *1***5** of an inch in the morning. It registered a rainfall of *2***5** of an inch at night. Draw a number line to represent the scenario and find the total rainfall.

The number line model that represents the given scenario is:

The addition equation is *1***5** + *2***5** = *3***5**.

So, the total rainfall the city saw is *3***5** of an inch.

4) Add:

i) *1***4** + *3***4** = 1

ii) *3***6** + *2***6** = *5***6**

iii) *3***18** + *5***18** + *4***18** = *2***3**

iv) *5***16** + *2***16** + *8***16** = *15***16**

### The Lesson in Short

Fractions with the same denominators are called like fractions.

To add like fractions:

✯ Combine the numerators.

✯ Add the numbers on the numerator.

✯ Simplify or reduce the sum to its lowest terms, if required.

Excel in the process by practicing our free printable Adding Like Fractions worksheets.