Adding Fractions with Unlike Denominators

Contributor: Rachel Lewis. Lesson ID: 12777

Can you picture adding fractions with unlike denominators? Don't be "blue;" after you've "red" this lesson, you will learn to picture those fractions and easily add them in a fraction of the time!

categories

Arithmetic, Fractions and Operations

subject
Math
learning style
Visual
personality style
Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

Audio:

You know that ½ + ½ = 1.

  • What is ½ + ¼?
  • Do you know how to add fractions with unlike denominators?

Fractions show part of a whole.

The top number is the numerator. The bottom number is the denominator.

To add fractions, we have to look at the denominator first. If the denominator in the two fractions is the same number, we can simply add the numerators and keep the denominator the same.

  • What happens if the denominators of the two fractions are different?

Look at the two fractions below:

fraction diagram

  • Do you see how the blue and red sections are different sizes?

We can't add two fractions with different denominators. So, we have to find a common denominator to make them the same.

Follow these steps to add fractions with unlike denominators:

Step 1: Find a common denominator.

In the model above, the first box is divided into two parts. The second box is divided into four parts.

We can use our picture to create like units for each fraction:

fraction diagram

Divide the first box into four parts like the second box. Divide the second box into two parts like the first box.

Now, we can count the shaded units.

Out of the eight parts in the first box, four parts are shaded. Our fraction is 48.

Out of the eight parts in the second box, two parts are shaded. Our fraction is 28.

Step 2: Add the numerators.

4 + 2 = 6

Step 3: Keep the denominator the same.

Our answer is 68.

Step 4: Simplify.

Six and eight can be divided by two, so we can simplify this fraction:

  6 → ÷ 2 → 3
  8 → ÷ 2 → 4

 

Now, we will go over another strategy to add fractions with unlike denominators.

This strategy will use the Lowest Common Multiple (LCM) to find common denominators.

Look at the fractions below:

  1 + 1
  3 6

 

They have unlike denominators so they cannot be added yet.

Step 1: Find a common denominator.

First, we will list the multiples for each denominator.

Remember that multiples are the numbers you get when you multiply a given number by each whole number, or skip counting.

Multiples of 3:

3, 6, 9, 12, 15, 18

Multiples of 6:

6, 12, 18, 24, 30, 36

Next, notice any common multiples:

common multiples

3 and 6 both have the common multiples of 6 and 12.

However, 6 is the lowest, so it is the LCM and will become our common denominator.

Let's change 1/3 into a fraction with the denominator of 6.

We know 3 x 2 will give us 6. Then, multiply the top and the bottom of the fraction by the same number, which in this case is 2:

multiply by 2

Next, change 1/6 into a fraction with the denominator of 6.

Wait! This fraction already has a denominator of 6, so all we have to do is multiply the top and bottom by 1:

multiply by 1

Step 2: Add the numerators.

2 + 1 = 3

Step 3: Keep the denominator the same.

Our answer is 3⁄6.

Step 4: Simplify.

Three and six can be divided by three, so we can simplify this fraction:

  3 → ÷ 3 → 1
  6 → ÷ 3 → 2

The denominator shows you the number of equal parts in a whole. You can't add two fractions if they have different denominators.

That's why it is important to find the least common denominator before you add fractions together.

For more practice, go to the Got It? section!

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