Topics
4. Fractions
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AustraliaNSW
Stage 3

4.09 Equivalent fractions

Lesson
Practice
Lesson

Are you ready?

Can you identify the size of a  fraction using a model  ? Let's do a practice problem to review.

Examples

Example 1

Which of the following shows \dfrac{1}{10} of the area of the shape shaded?

A
A rectangle divided into 10 equal parts. 2 parts are shaded.
B
A rectangle divided into 11 equal parts. 1 part is shaded.
C
A rectangle divided into 10 equal parts. 1 parts are shaded.
D
A rectangle divided into 9 equal parts. 1 part is shaded.
Worked Solution
Create a strategy

The numerator tells us how many parts should be shaded. The denominator tells us how many parts to divide the shape into.

Apply the idea

The fraction \dfrac{1}{10} is asking for one part of the shape to be shaded out of 10 total parts. The shape in option C has 10 total parts with 1 shaded part.

The answer is option C.

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.

Tenths and hundredths equivalent fractions

Equivalent fractions are fractions that have the same value, even though they might look different. This video will explain more.

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Examples

Example 2

Write \dfrac{7}{10} as an equivalent fraction out of 100:

\dfrac{7}{10}\, = \,\dfrac{⬚}{100}

Worked Solution
Create a strategy

Multiply the numerator and denominator by 10.

Apply the idea
\displaystyle \dfrac{7}{10}\displaystyle =\displaystyle \dfrac{7 \times 10}{10 \times 10}Multiply the numerator and denominator by 10
\displaystyle =\displaystyle \dfrac{70}{100}
Idea summary

Equivalent fractions represent the same size, but have different numerators and denominators.

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

Equivalent fractions in fraction families

This video looks at equivalent fractions in fraction families.

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Examples

Example 3

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

\dfrac{1}{3}= \dfrac{⬚}{6}

Worked Solution
Create a strategy

Use fraction area models.

Apply the idea

On the left of the equals sign we have \dfrac{1}{3} which looks like this:

A rectangle divided into 3 equal parts with 1 shaded part.

1 out of the 3 squares are shaded. We want to write this as a fraction of 6. Dividing the model into 6 parts would look like this:

A rectangle divided into 6 equal parts with 2 parts shaded.

We can see that 2 out of 6 parts are shaded to get the same area. So:

\displaystyle \frac{1}{3}\displaystyle =\displaystyle \frac{2}{6}
Reflect and check

We also could have multiplied the numerator and denominator by 2 since 3\times 2=6.

\displaystyle \dfrac{1}{3}\displaystyle =\displaystyle \dfrac{1 \times 2}{3 \times 2}Multiply the numerator and denominator by 2
\displaystyle =\displaystyle \dfrac{2}{6}

Equivalent Fractions for whole numbers

This video looks at equivalent fractions to whole numbers.

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Examples

Example 4

Fill in the blank to find an equivalent fraction to 5:

5= \dfrac{⬚}{2}

Worked Solution
Create a strategy

Write 5 as a fraction and then multiply the numerator and denominator to find the equivalent fraction.

Apply the idea

5 as a fraction is \dfrac{5}{1}.

But we want a denominator of 2. So we need to multiply the denominator and the numerator by 2.

\displaystyle \dfrac{5}{1}\displaystyle =\displaystyle \dfrac{5 \times 2}{1 \times 2}Multiply by 2
\displaystyle =\displaystyle \dfrac{10}{2}

5=\dfrac{10}{2}

Idea summary

Equivalent fractions look different but have the same value.

You need to multiply or divide both the numerator and the denominator of a fraction by the same number to work out the equivalent fraction.

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