Adding and Subtracting Fractions with Unlike Denominators:

Using the Area Model

MATH 8Ms. Stewart

Outcome: B5 Add and subtract fractions concretely, pictorially, and symbolically

B6 Add and subtract fractions mentally, when appropriate

For example:

How do you add fractions with unlike denominators?

We will be learning about how to solve this type of question by creating area models…

Quick (but important!) Review

This fraction represents one out of 3 equally sized parts of the whole

The denominator also names the size of the part, so we know that each of these parts is a third

Quick (but important!) Review

In order to add numbers together, we must use the same unit.

For example:4 apples + 3 bananas = ?

Common Denominator

Can we find a common unit for apples and bananas?

What about pieces of fruit?

4 pieces of fruit + 3 pieces of fruit =7 pieces of fruit

The same principle applies to fractions, in order to add fractions together, we need to have a common denominator (the same unit!)

Common Denominator

 

Using Area Models

From our models, it is clear to see that we cannot not add these fractions together yet, because the pieces represent different units.

Using Area Models

In order to add these two fractions we need to find a common denominator. To find a common denominator we are going to combine these two models:

First, we will equally divide our model of ½ into 5 equal parts

 

Now we have fractions of the same unit and can simply add!

Add up the area…

 

 

 

Your turn…