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{5}{25}	\displaystyle =	\displaystyle \frac{5}{25}\times \dfrac{4}{4}	Multiply the top and bottom by 4
	\displaystyle =	\displaystyle \frac{20}{100}	Perform the multiplications
	\displaystyle =	\displaystyle 20\%	Write as a percentage

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.

Convert decimals, fractions and percentages

This video looks at strategies to complete tables of equivalent values for fractions, decimals and percentages.

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Examples

Example 2

Convert between percentages, fractions and decimals to complete the table:

Fraction	Decimal	Percentage
\dfrac{60}{100}

Worked Solution

Create a strategy

To convert fractions and decimals to percentages multiply by 100\%. To convert between fractions and decimals use a place value table.

Apply the idea

First we can convert the fraction to a percentage:

\displaystyle \dfrac{60}{100}	\displaystyle =	\displaystyle \dfrac{60}{100} \times 100\%	Multiply by 100\%
	\displaystyle =	\displaystyle 60\%	Cancel out the 100s

The fraction \dfrac{60}{100} means 60 hundredths. So we can write it in a place value table to convert to a decimal:

Units	.	Tenths	Hundredths
0	.	6	0

We can simplify this decimal by writing it as 0.6.

Fraction	Decimal	Percentage
\dfrac{60}{100}	0.6	60\%

Idea summary

We can convert fractions and decimals to percentages by multiplying by 100\%.

Percentages and complements

This video looks at how 1 whole is 100\%, and how we can use that knowledge to find complements, that add together to make the whole.

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Examples

Example 3

What is the complement of 40\%?

Worked Solution

Create a strategy

Subtract 40\% from 100\%.

Apply the idea

To find the number that makes 100\% when added to 40\%, we can just subtract 40\% from 100\%.

\displaystyle 100\%-40\%	\displaystyle =	\displaystyle 60\%	Subtract 40\% from 100\%
	\displaystyle =	\displaystyle 60\%

Idea summary

1 whole is 100\%.

If you have a percentage such as 25\%, the complement to that is 75\% because it makes up the whole.

8.03 Convert between fractions, decimals and percentages

Ideas

Are you ready?

Examples

Example 1

Convert decimals, fractions and percentages

Examples

Example 2

Percentages and complements

Examples

Example 3

Outcomes

ACMNA131

What is Mathspace

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