# 5.09 Add and subtract fractions with models

Lesson

Let's review how to  identify a fraction  using a model.

### Examples

#### Example 1

What fraction of the square is shaded blue?

Worked Solution
Create a strategy

Write the fraction as: \,\, \dfrac{\text{Number of shaded parts}}{\text{Total number of parts}}.

Apply the idea

There are 9 squares shaded blue and 16 squares in total.

So, the fraction shaded blue is \,\dfrac{9}{16}.

Idea summary

When a fraction is represented in an area model:

• To find the numerator of the fraction, count the number of parts shaded.

• To find the denominator, count the total number of parts.

## Adding fractions using area models

This video shows how to add fractions using an area model.

### Examples

#### Example 2

In the image below, \dfrac{1}{2} has been shaded red and \dfrac{1}{4} has been shaded blue.

a

Write the addition that describes the image.

Worked Solution
Create a strategy

Apply the idea

\text{Red}+\text{Blue}=\dfrac{1}{2}+\dfrac{1}{4}

b

What is the total fraction shaded?

Worked Solution
Create a strategy

Count how many parts are shaded and how many parts there are in total.

Apply the idea

The total number of squares in the image is 4.

So the total fraction shaded is \dfrac{3}{4}.

Idea summary

Area models can help us see the parts of fractions that are being added or subtracted.

## Subtract fractions using area models

This video shows how to subtract fractions using an area model.

### Examples

#### Example 3

The image below shows \dfrac{1}{3} of the rectangle shaded.

a

What is the equivalent fraction in fifteenths?

\dfrac{1}{3}=\dfrac{⬚}{15}

Worked Solution
Create a strategy

To find the numerator of the fraction, count the number of parts shaded.

Apply the idea

There are 15 squares in total and 5 of them are shaded.

So the images also shows \dfrac{5}{15} of a rectangle shaded.

\dfrac{1}{3}=\dfrac{5}{15}

b

We now want to take away \dfrac{4}{15}.

What is the answer to \dfrac{1}{3}-\dfrac{4}{15}?

Worked Solution
Create a strategy

Use the equivalent fraction we found in part (a).

Apply the idea
Reflect and check

We can also count the number of shaded squared left after 4 are taken away.

In the image, 4 squares are shaded lighter to suggest that they are being taken away. Then we would only have 1 shaded square left out of 15.

So again: \dfrac{1}{3}-\dfrac{4}{15}=\dfrac{1}{15}

Idea summary

Area models can help us see the parts of fractions that are being added or subtracted.

## Add and subtract fractions on number lines

We can also use number lines to add and subtract fractions.

### Examples

#### Example 4

We want to calculate the sum \dfrac{1}{2}+\dfrac{3}{8}.

a

Complete the statement to make an equivalent fraction for \dfrac{1}{2}.

\dfrac{1}{2}=\dfrac{⬚}{8}

Worked Solution
Create a strategy

Use this a fraction wall showing halves and eighths.

Apply the idea

By looking on the fraction wall, we can see that there are 4 eighths in 1 half.

So the complete statement is:

\dfrac{1}{2}=\dfrac{4}{8}

b

Plot \dfrac{4}{8} on the number line.

Worked Solution
Apply the idea

To plot \dfrac{4}{8}, we want to start at zero and jump right four spaces. So we have:

c

Choose the image below that represents the addition \dfrac{1}{2}+\dfrac{3}{8}.

A
B
C
D
Worked Solution
Create a strategy

Use the equivalent fraction found in part (a).

Remember when adding an amount on a number line we move to the right.

Apply the idea

We have found that \dfrac{1}{2}+\dfrac{3}{8} is the same as \dfrac{4}{8}+\dfrac{3}{8}.

So we should start at \dfrac{4}{8} then jump right 3 eighths.

The correct answer is option B.

Idea summary

We can use area models to change fractions to their equivalent fraction so the denominators are the same.

We can add and subtract fractions by moving right and left on the number line.

### Outcomes

#### VCMNA212

Solve problems involving addition and subtraction of fractions with the same or related denominators