Percentages

Percentages

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

For example if the number 5050 has the percent sign after it, 50%50%, this means 5050 out of 100100.

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

Example: Calculate 25%25% of 200200

Remembering the handy tips above, we know that to find 25%25% divide by 44.

200÷4=50200div 4 = textcolor{blue}{50}

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Example 1: Finding the Percentage of an Amount

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

Example: Calculate 15%15% of 4040

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

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

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

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

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

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

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

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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 £180pounds 180. The price increased by 20%20%.

What is the new price after the increase?

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

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

10%=£180÷10=£1810% = pounds 180 div 10 = textcolor{green}{pounds 18}

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

20%=£18+£18=£36textcolor{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%20% to the original price.

New price =£180+£36=£216=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%35%. The original cost of a pack of apples is £1.40pounds 1.40.

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

[2 marks]

First, split 35%35% up into chunks.

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

10%=£1.40÷10=£0.14textcolor{green}{10%} = pounds 1.40 div 10 = textcolor{green}{pounds 0.14}

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

Combine the values found to make up 35%35%.

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

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

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

£1.40−£0.49=£0.91pounds 1.40 – textcolor{red}{pounds 0.49} = pounds 0.91 or 91p91text{p}

Question 2: Calculate

a) 75%75% of 8484

b) 50%50% of 4545

[2 marks]

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

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

Next find 25%25% of 8484.

84÷4=2184 div 4 = textcolor{orange}{21}

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

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

b) 50%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%50%, divide the value by 22.

50%=45÷2=22.5textcolor{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: 55 shaded squares.

Next count how many squares there are in total: 2525 squares.

Then form a fraction using these values.

525dfrac{5}{25} squares are shaded.

Using knowledge of equivalent fractions, we can find a fraction that has a denominator of 100100 to find this fraction as a percentage.

5×425×4=20100dfrac{5 textcolor{red}{times 4}}{25 textcolor{red}{times 4}} = dfrac{20}{100}

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