Percentages

Percentages

The word percent means “out of \bold{\textcolor{darkturquoise}{100}}“ and this is a good way for your child to think of percentages.

For example if the number 50 has the percent sign after it, 50\%, this means 50 out of 100.

Percentage of an Amount

As with fractions, your child may be asked to find the percentage of a given amount. This could be in the context of a discount off an item of clothing or the proportion of a journey to school.

Some helpful tips for your child to remember when finding the percentage of an amount are:

  • Divide by \textcolor{red}{2} to find \textcolor{red}{50\%}
  • Divide by \textcolor{red}{4} to find \textcolor{red}{25\%}
  • Divide by \textcolor{red}{10} to find \textcolor{red}{10\%}

Example: Calculate 25\% of 200

Remembering the handy tips above, we know that to find 25\% divide by 4.

200\div 4 = \textcolor{blue}{50}

Example 1: Finding the Percentage of an Amount

The building blocks can be used to find other percentages that aren’t just 50\%,\,\,25\% and 10\%.

Example: Calculate 15\% of 40

For this question, let’s split the percentage amount we need to more manageable chunks.

\textcolor{red}{15\%} = \textcolor{green}{10\%} + \textcolor{purple}{5\%}

From the building blocks above, we can find \textcolor{green}{10\%} then we can use the fact that \textcolor{green}{10\%} is double \textcolor{purple}{5\%}.

\textcolor{green}{10\%} = 40 \div 10 = \textcolor{green}{4}

\textcolor{purple}{5\%} = \textcolor{green}{4} \div 2 = \textcolor{purple}{2}

So, we can now put the two values together to find \textcolor{red}{15\%}.

\textcolor{red}{15\%} = \textcolor{green}{4} + \textcolor{purple}{2} = \textcolor{red}{6}

Example 2: Percentage Increase

In order to find a percentage increase or decrease, find the percentage as normal then either add or subtract it from the original value.

Example: The original price of a table was \pounds 180. The price increased by 20\%.

What is the new price after the increase?

As with previous examples, find 20\% of the original price.

\textcolor{red}{20\%} = \textcolor{green}{10\%} + \textcolor{green}{10\%}

10\% = \pounds 180 \div 10 = \textcolor{green}{\pounds 18}

Then to find \textcolor{red}{20\%}:

\textcolor{red}{20\%} = \textcolor{green}{\pounds 18} + \textcolor{green}{\pounds 18} = \textcolor{red}{\pounds 36}

However, the question hasn’t been answered yet as we now need to add on the extra 20\% to the original price.

New price =\pounds 180 + \textcolor{red}{\pounds 36} = \pounds 216

Now we have done everything the question has asked of us.

Percentages Example Questions

Question 1: At the shop all packs of apples are discounted by 35\%. The original cost of a pack of apples is \pounds 1.40.

What is price of a pack of apples after the discount has been applied?

[2 marks]

First, split 35\% up into chunks.

\textcolor{red}{35\%} = \textcolor{green}{10\%} + \textcolor{green}{10\%} + \textcolor{green}{10\%} + \textcolor{purple}{5\%}

\textcolor{green}{10\%} = \pounds 1.40 \div 10 = \textcolor{green}{\pounds 0.14}

\textcolor{purple}{5\%} = \pounds 0.14 \div 2 = \textcolor{purple}{\pounds 0.07}

Combine the values found to make up 35\%.

\textcolor{red}{35\%} = \textcolor{green}{\pounds 0.14} + \textcolor{green}{\pounds 0.14} + \textcolor{green}{\pounds 0.14} + \textcolor{purple}{\pounds 0.07}

\textcolor{red}{35\%} = \textcolor{red}{\pounds 0.49}

Finally to find the new price after the discount, subtract the discount from the original value.

\pounds 1.40 - \textcolor{red}{\pounds 0.49} = \pounds 0.91 or 91\text{p}

Question 2: Calculate

a) 75\% of 84

b) 50\% of 45

[2 marks]

a) First, split up 75\% into building blocks we can easily calculate.

\textcolor{red}{75\%} = \textcolor{orange}{25\%} + \textcolor{orange}{25\%} + \textcolor{orange}{25\%}

Next find 25\% of 84.

84 \div 4 = \textcolor{orange}{21}

So, we need three blocks of \textcolor{orange}{25\%}.

\textcolor{red}{75\%} = \textcolor{orange}{21} + \textcolor{orange}{21} + \textcolor{orange}{21} = \textcolor{red}{63}

b) 50\% was one of the original building blocks so, we don’t need to split it up. From the rules we know to find 50\%, divide the value by 2.

\textcolor{red}{50\%} = 45 \div 2 = \textcolor{red}{22.5}

Question 3: What percentage of squares in the grid are shaded?

[2 marks]

First, count how many squares are shaded: 5 shaded squares.

Next count how many squares there are in total: 25 squares.

Then form a fraction using these values.

\dfrac{5}{25} squares are shaded.

Using knowledge of equivalent fractions, we can find a fraction that has a denominator of 100 to find this fraction as a percentage.

\dfrac{5 \textcolor{red}{\times 4}}{25 \textcolor{red}{\times 4}} = \dfrac{20}{100}

So, as a percentage 20\% of the grid is shaded.