 # 8.08 Area models 1

Lesson

## Ideas

You may have already looked at representing fractions as fractions bars or points on the number line.

### Examples

#### Example 1

Here is a fraction bar.

Complete the statements below.

a

This fraction bar has equal parts.

Worked Solution
Create a strategy

Count the number of smaller rectangles that make up the whole bar.

Apply the idea

There are 5 rectangles inside the fraction bar.

This fraction bar has 5 equal parts.

b

Each part is \dfrac{⬚}{⬚} of the whole.

Worked Solution
Create a strategy

Each part looks like this:

We can write this fraction as:

Apply the idea

Each part is \dfrac{1}{5} of the whole.

Idea summary

When writing fractions:

• The number of equal parts the whole is divided into is the denominator (bottom number).

• The numerator (top number) is how many parts that are shaded, and so shows the value of the fraction.

## Fractions of shapes

With any model of a fraction, we use:

• the denominator (the bottom number of the fraction) to decide how many pieces to divide it into, and
• the numerator (the top number of the fraction) to shade the number of pieces.

Let's learn about fractions as areas of shapes.

### Examples

#### Example 2

Which of the following shows \dfrac{3}{4} of the area shaded?

A
B
Worked Solution
Create a strategy

The top part of the fraction (numerator) tells us how many parts should be shaded. The bottom part of the fraction (denominator) tells us how many parts to divide the shape into.

Apply the idea

The fraction \dfrac{3}{4} is asking for three parts of the shape to be shaded. So 3 out of 4 parts should be shaded. This means that the answer is Option B.

Idea summary
• The numerator (top number) is the number of parts shaded to represent the fraction.
• The denominator (bottom number) is the number of equal parts the shape is divided into.

### Outcomes

#### MA2-7NA

represents, models and compares commonly used fractions and decimals