12.04 Identify fractions in areas

Can you recognise the number of equal parts and what fraction that makes?

Examples

Example 1

Here is a shape divided into parts, use it to answer the following questions.

a

This shape has ⬚ equal parts.

Worked Solution

Create a strategy

Count the number of smaller parts.

Apply the idea

This shape has 3 equal parts.

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b

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

Worked Solution

Create a strategy

Write each part as a fraction: \,\,\dfrac{\text{Number of shaded parts}}{\text{ Total number of parts}}

Apply the idea

Each part looks like this shaded part.

We have 3 parts and we only want 1 of them.

Each part is \dfrac{1}{3} of the whole.

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When we divide shapes into equal parts, we have seen how the parts can be described using fractions. We can also use this to describe the area of part of our shape.

We can divide shapes up into parts and describe these parts as fractions. We can also use this to describe the area of a part of our shape.

Examples

Example 2

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.

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