# 5.06 Equivalent fractions

Lesson

Can you  identify the size of a fraction from a diagram  ?

### Examples

#### Example 1

Below is a fraction bar.

What is the fraction of the coloured piece?

A
\dfrac{2}{3}
B
\dfrac{3}{4}
C
\dfrac{1}{4}
D
\dfrac{1}{3}
Worked Solution
Create a strategy

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

Apply the idea

There is 1 shaded part and 3 total parts in the fraction bar. So the fraction is \dfrac{1}{3}.

The correct option is D.

Idea summary

When writing fractions using fraction bars:

• The denominator shows the number of equal parts the whole is divided into.
• The numerator shows how many parts are shaded.

## Equivalent fractions

This video looks at equivalent fractions up to one whole.

### Examples

#### Example 2

Fill in the blank to find an equivalent fraction to \dfrac{3}{6}:\dfrac{3}{6}=\dfrac{1}{⬚}

Worked Solution
Create a strategy

To find the equivalent fraction, divide the denominator by the same number as the numerator.

Apply the idea

Notice that 3\div 3=1 in the numerator. Since we divided the top number by 3, we need to divide the bottom number by 3 as well.

So, we have:\dfrac{3}{6}=\dfrac{1}{2}

Idea summary

To find an equivalent fraction, we can divide the numerator and denominator by the same number.

## Create equivalent fractions

This video shows us how to create an equivalent fraction.

### Examples

#### Example 3

Fill in the blank to find an equivalent fraction to \dfrac{5}{8}:\dfrac{5}{8}=\dfrac{50}{⬚}

Worked Solution
Create a strategy

To find the equivalent fraction, multiply the denominator by the same number as the numerator.

Apply the idea

Notice that 5\times 10=50 on the numerator. Since we multiply the top number by 10, we need to multiply the bottom number by 10 as well.

So, we have:\dfrac{5}{8}=\dfrac{50}{80}

Idea summary

To find an equivalent fraction, we can multiply the numerator and denominator by the same number.

## Equivalent fractions with mixed numbers

This video shows us how to handle equivalent fractions with mixed numbers.

### Examples

#### Example 4

Complete the table with the improper fractions that are equivalent in value to 2 \dfrac{1}{6}.

Worked Solution
Create a strategy

To find the improper fraction, multiply the whole number by the denominator, then add the numerator.

To find an equivalent fraction, multiply both the numerator and the denominator by the same number.

Apply the idea

First we convert 2 \dfrac{1}{6} to an improper fraction:

To complete the equivalent fraction in the table, we need to multiply the numerator by 3 since 6 \times 3 =18.

Completing the table, we have:

Idea summary

To find an equivalent fraction for a mixed number, first convert the mixed number to an improper fraction, then multiply (or divide) both the numerator and the denominator by the same number.

### Outcomes

#### VCMNA211

Compare fractions with related denominators and locate and represent them on a number line