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8.03 Convert between fractions, decimals and percentages

Lesson

Are you ready?

Let's review how to write  fractions as percentages  .

Examples

Example 1

Express the fraction \dfrac{5}{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{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:

FractionDecimalPercentage
\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.TenthsHundredths
0.60

We can simplify this decimal by writing it as 0.6.

FractionDecimalPercentage
\dfrac{60}{100}0.660\%
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.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

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