# 8.09 Area models 2

Lesson

## Introduction

Introduction to the lesson

## Ideas

Let's review how to use an  area model to represent a fraction  .

### Examples

#### Example 1

Which of the following shows \dfrac{2}{6} of the area shaded?

A
B
Worked Solution
Create a strategy

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

Apply the idea

The fraction \dfrac{2}{6} is asking for two parts of the shape to be shaded. So 2 out of 6 parts should be shaded. This means that the correct answer is Option A.

Idea summary

For an area model to represent a fraction:

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

## Fractions of shapes

Let's look at representing fractions as areas of shapes.

### Examples

#### Example 2

What fraction is shown here?

Worked Solution
Create a strategy

We want to use a fraction to say how much of the shape is shaded. A fraction is written as:

\dfrac{\text{number of shaded parts}}{\text{total number of parts}}

Apply the idea

There are 6 shaded parts and 7 total parts.\text{Fraction}=\dfrac{6}{7}

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