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Percentages of Amounts

Percentages of Amounts Revision

Percentages of Amounts

Percent means “out of 100” and is denoted by the \% sign. e.g. 40\% means 40 percent which is 40 out of 100.

Percentages can be written as fractions or decimals:  40\% = \dfrac{40}{100} = 0.4

 

Learning Objectives:

After this topic students will be able to:

  • Calculate a percentage of an amount
  • Write a number as a percentage of another
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Percentage of an Amount Examples

 

Example 1: Calculate \textcolor{#10a6f3}{15 \%} of \textcolor{#10a6f3}{70}.

Convert \textcolor{#10a6f3}{15\%} to a decimal:

15\%=\textcolor{#10a6f3}{0.15}

Multiply \textcolor{#10a6f3}{70} by this decimal:

0.15 \times 70 = \textcolor{#10a6f3}{10.5}

 

Example 2: Calculate \textcolor{#10a6f3}{46\%} of \textcolor{#10a6f3}{160}.

Convert \textcolor{#10a6f3}{46\%} to a decimal:

46\%=\textcolor{#10a6f3}{0.46}

Multiply \textcolor{#10a6f3}{160} by this decimal:

0.46\times 160 = \textcolor{#10a6f3}{73.6}

 

Example 3: Calculate \textcolor{#10a6f3}{98.5\%} of \textcolor{#10a6f3}{520}.

Convert \textcolor{#10a6f3}{98.5\%} to a decimal:

98.5\%=\textcolor{#10a6f3}{0.985}

Multiply \textcolor{#10a6f3}{520} by this decimal:

0.985\times 520= \textcolor{#10a6f3}{512.2}

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Number as a Percentage of Another Examples

Example 1:  A cinema screen has \textcolor{#10a6f3}{150} seats. \textcolor{#10a6f3}{81} of the seats have been taken.

What percentage of seats have been taken?

 

Here, we need to calculate 81 as a percentage of 150.

Divide the first number by the second number:

81 \div 150 = \textcolor{#10a6f3}{0.54}

Convert this into a percentage by multiplying by 100:

0.54 \times 100 = \textcolor{#10a6f3}{54\%}

 

Example 2:  A music shop has \textcolor{#10a6f3}{200} CDs to sell. \textcolor{#10a6f3}{142} of these are sold.

What percentage of CDs have been sold?

 

Here, we need to calculate 142 as a percentage of 200.

Divide the first number by the second number:

142 \div 200 = \textcolor{#10a6f3}{0.71}

Convert this into a percentage by multiplying by 100:

0.71 \times 100 = \textcolor{#10a6f3}{71\%}

 

Example 3:  An office has \textcolor{#10a6f3}{20} computers. \textcolor{#10a6f3}{3} of these are broken.

What percentage of computers work?

 

Here, we need to calculate 20 - 3 = 17 as a percentage of 20.

Divide the first number by the second number:

17 \div 20 = \textcolor{#10a6f3}{0.85}

Convert this into a percentage by multiplying by 100:

0.85 \times 100 = \textcolor{#10a6f3}{85\%}

Percentages of Amounts Example Questions

Question 1: There are 240 cars in a car park. 80\% of these leave. How many cars are left in the car park?

If 80\% leave, we know that 20\% are remaining. We then need to convert 20\% to a decimal:

20\% = 0.2

Then multiply the original amount by this decimal:

0.2 \times 240 = 48

So there are 48 cars remaining.

Question 2: There are 400 different books for sale in a book shop. 220 of these are non-fiction. What percentage of books are non-fiction?

Here, we need to calculate 220 as a percentage of 400.

Divide the first number by the second number:

220 \div 400 = \textcolor{purple}{0.55}

Convert this into a percentage by multiplying by 100:

0.55 \times 100 = \textcolor{purple}{55\%}

Question 3: A hospital has 880 beds for patients. 790 of these are occupied. What percentage of beds are free?

Here, we need to calculate 880 - 790 = 90 as a percentage of 880.

Divide the first number by the second number:

90 \div 880 = \textcolor{purple}{0.102}

Convert this into a percentage by multiplying by 100:

0.102 \times 100 = \textcolor{purple}{10.2\%}

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