Topics
6. Percentages
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Australia
Year 5

6.01 Fractions out of 100

Lesson
Practice

Are you ready?

Do you recall how we can write fractions different ways, using  equivalent fractions  ?

Examples

Example 1

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 to find the equivalent fraction.

Apply the idea
A fraction bar divided into 3 parts with 1 shaded part.

The fraction \dfrac{1}{3} looks like this where 1 out of 3 parts are shaded.

We want to write this as a fraction out of 6. Dividing into 6 parts would look like the image below with 2 shaded parts:

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

So we can say that:

\dfrac{1}{3}=\dfrac{2}{6}

Idea summary

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

Percentages from fractions

We can express, or write, fractions as percentages, by thinking of them with 100 as the denominator. Let's see how to express a fraction as a percentage.

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Examples

Example 2

What percentage of the figure is shaded blue?

A 10 by 10 square grid with 68 squares shaded out of 100 squares.
Worked Solution
Create a strategy

Find the fraction shaded then convert to a percentage.

Apply the idea

68 out of 100\ squares in the grid are shaded. We can express this as the fraction \dfrac{68}{100}.

\displaystyle \text{Percentage}\displaystyle =\displaystyle \dfrac{68}{100}\times 100\%Multiply by 100\%
\displaystyle =\displaystyle 68\%Cancel out the 100s
Idea summary

We can convert any fraction into a percentage by finding its equivalent fraction that has a denominator of 100. After this, we can write the value in the numerator followed by the \% symbol to represent the percentage.

Percentages back to fractions

We may need to write a percentage as a fraction, so this video shows you how to do that.

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Examples

Example 3

Express 55\% as a fraction.

Worked Solution
Create a strategy

To write a percentage as a fraction divide by 100.

Apply the idea
\displaystyle 55\%\displaystyle =\displaystyle \frac{55}{100}Divide by 100
Idea summary

We can convert any fraction into a percentage by finding its equivalent fraction that has a denominator of 100.

Percentages and fractions with different denominators

What if we have a fraction that doesn't have 100 as its denominator? Let's see how we can express that as a percentage.

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Examples

Example 4

Express the fraction \dfrac{10}{25} as a percentage.

Worked Solution
Create a strategy

Find the equivalent fraction that has a denominator of 100.

Apply the idea

To get a denominator of 100, we need to multiply 25 by 4 since 25\times 4=100. But if we multiply the denominator by 4 we must also multiply the numerator by 4.

\displaystyle \frac{10}{25}\displaystyle =\displaystyle \frac{10}{25}\times \dfrac{4}{4}Multiply the top and bottom by 4
\displaystyle =\displaystyle \frac{40}{100}Perform the multiplications
\displaystyle =\displaystyle 40\%Write as a percentage
Idea summary

A shaded diagram, a fraction and a percentage can all be used to represent the same value.

A table of the same value as a diagram, a fraction and a percentage. Ask your teacher for more information.

If our denominator is not 100, we can find an equivalent fraction with 100 as the denominator, and then express it as a percentage.

Outcomes

AC9M5N04

recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents

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