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Percentages of Amounts

FoundationHigherAQAEdexcelOCR

Master percentages of amounts for GCSE Maths with structured, exam-style practice. This Foundation and Higher resource covers finding percentages of an amount and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Find 10% by dividing by 10, then build up the percentage you need.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Finding a percentage of an amount is one of the most useful skills in the whole GCSE, because it underpins interest, discounts, VAT, wages and almost every real-life money question.

There are two reliable methods. The non-calculator approach builds the percentage from parts you can find easily, such as 10 percent, 5 percent and 1 percent. The calculator approach uses a multiplier: convert the percentage to a decimal and multiply once.

Both give the same answer, so choose the one that suits the question. Foundation papers often want the building-block method shown clearly, while Higher papers usually reward the faster multiplier approach, especially when several percentage steps follow one another.

Revision notes

The building-block method

Start from 10 percent, which is the amount divided by 10. From there, 5 percent is half of 10 percent and 1 percent is the amount divided by 100.

To find 35 percent of \(£80\): 10 percent is \(£8\), so 30 percent is \(£24\); 5 percent is \(£4\); adding gives \(£28\). Showing these parts earns method marks even if the final addition slips.

The multiplier method

Divide the percentage by 100 to get a decimal, then multiply. For 35 percent the multiplier is \(0.35\), so \(0.35 \times 80 = 28\).

This is far quicker for awkward percentages such as 17.5 percent or 3 percent, and it is essential once you meet repeated percentage change, where you multiply by the same number several times.

Increases and decreases

To increase by a percentage, add it to 100 percent before converting. A 20 percent increase uses a multiplier of \(1.2\); a 20 percent decrease uses \(0.8\).

This single step replaces finding the percentage and then adding or subtracting it, and it is much less error-prone in multi-stage questions.

Key points

  • 10 percent is the amount divided by 10.
  • 1 percent is the amount divided by 100.
  • The multiplier is the percentage divided by 100.
  • To increase by \(p\) percent, multiply by \(1 + \frac{p}{100}\).
  • To decrease by \(p\) percent, multiply by \(1 - \frac{p}{100}\).
  • Both methods give the same answer, so pick whichever suits the numbers.

Worked examples

Example 1

Find 15 percent of \(£240\) without a calculator.

Working

\[10\% = 240 \div 10 = 24\]start by finding 10 percent
\[5\% = 24 \div 2 = 12\]halve 10 percent to get 5 percent
\[24 + 12 = £36\]add the parts together

Example 2

Use a multiplier to find 68 percent of \(£350\).

Working

\[68 \div 100 = 0.68\]convert the percentage to a decimal multiplier
\[0.68 \times 350\]multiply the amount by the multiplier
\[= £238\]work out the answer

Example 3

A coat costs \(£64\) and is reduced by 25 percent. Find the sale price.

Working

\[100\% - 25\% = 75\%\]a 25 percent decrease leaves 75 percent
\[0.75 \times 64\]use 0.75 as the multiplier
\[= £48\]work out the sale price

Common mistakes

  • Using 0.5 as the multiplier for 5 percent.

    5 percent is 5 ÷ 100 = 0.05. Using 0.5 finds 50 percent instead, ten times too much.

  • Finding the decrease but forgetting to subtract it.

    If a question asks for the sale price, the percentage found must still be taken off the original amount, unless you used the 0.75-style multiplier.

  • Adding percentages of different amounts together.

    10 percent of £50 and 10 percent of £80 are not the same, so the parts must come from the same starting amount.

  • Rounding money to more than 2 decimal places.

    Money answers should be given to the nearest penny, so £23.456 is written as £23.46.

Exam tips

  • Show the 10 percent and 1 percent steps in non-calculator questions to secure method marks.
  • Use a single multiplier when a percentage change is applied more than once.
  • Write money answers to 2 decimal places with the pound sign.
  • Check the direction of the answer: an increase must be larger than the original.

Key terms

Percentage
A proportion expressed out of 100.
Multiplier
The decimal you multiply by to apply a percentage, such as 0.85 for a 15 percent decrease.
Percentage increase
Adding a proportion of the original amount to itself.
Original amount
The starting value before any percentage change is applied.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.