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8.04 Common percents


Are you ready?

In previous lessons we learned how to  write fractions as percentages  . Let's practise this concept by looking to the following example.


Example 1

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

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

Common percentages

This video shows us how 10\% is 1 tenth, 25\% is 1 quarter and 50\% is 1 half and uses this to find 10\%,\,25\% and 50\% of values.

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Example 2

What is 50\% of 26?

Worked Solution
Create a strategy

Use the fact that 50\% means half and "of" means multiply.

Apply the idea
\displaystyle 50\% \text{ of }26\displaystyle =\displaystyle \dfrac{1}{2} \times 26Replace 50\% with \dfrac{1}{2} and "of" with \times
\displaystyle =\displaystyle 13Halve 26
Idea summary

When we need to find some common percentages, we can use these to help us:

10\%\dfrac{1}{10}\div 10
25\%\dfrac{1}{4}\div 4
50\%\dfrac{1}{2}\div 2

Multiples of 10%

Now that you have seen how to find 10\% of an amount, this video shows you how you can find multiples of 10\% of an amount, such as 20\% ,\, 30\% or 80\%.

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Example 3

What is 30\% of \$40?

Worked Solution
Create a strategy

Find the 10\% and multiply it by 3.

Apply the idea
\displaystyle 10\% \text{ of } \$40\displaystyle =\displaystyle 40 \div 10Rewrite as division
\displaystyle =\displaystyle 4 Cancel out the 0s
\displaystyle 30\% \text{ of } 40 \displaystyle =\displaystyle 4\times 3Multiply 10\% by 3
\displaystyle =\displaystyle \$12Include the units
Idea summary

To find a percentage of a quantity that is a multiple of 10\%, e.g. 20\% ,\, 30\%,\,40\%, we can first find 10\% and then multiply the result.



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