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Ratio

FoundationHigherAQAEdexcelOCR

Get to grips with ratio using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on simplifying and sharing in a ratio, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Divide the total by the number of parts to find the value of one part.

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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

A ratio compares two or more quantities, showing how much of one there is relative to another. The ratio \(3 : 2\) means three parts of the first for every two of the second.

Ratios simplify like fractions, by dividing every part by a common factor. So \(12 : 18\) becomes \(2 : 3\), and the relationship is unchanged even though the numbers are smaller.

The most common task is sharing an amount in a given ratio. Add the parts to find the total number of parts, divide the amount by that total to find one part, then multiply up. Working out the value of one part first keeps the method reliable whatever the numbers.

Revision notes

Simplifying ratios

Divide every part by their highest common factor.

For \(20 : 30\), both divide by \(10\), giving \(2 : 3\). The parts must be in the same units first, so \(50\)cm to \(2\)m becomes \(50 : 200\), which simplifies to \(1 : 4\).

Sharing in a ratio

Add the parts, divide the total amount by that number, then multiply each share.

Sharing \(£60\) in the ratio \(2 : 3\): there are \(5\) parts, so one part is \(£12\), giving shares of \(£24\) and \(£36\). Check the shares add back to the original total.

Ratios in the form 1 : n

Divide both parts by the first number to write a ratio starting with \(1\).

For \(4 : 10\), divide both by \(4\) to get \(1 : 2.5\). The second number may not be a whole number, and that is perfectly acceptable.

Key points

  • A ratio compares quantities part by part.
  • Simplify by dividing by the highest common factor.
  • Convert to the same units before simplifying.
  • Add the parts to find the total number of parts.
  • Divide the amount by the total to find one part.
  • Check the shares add back to the original amount.

Worked examples

Example 1

Simplify the ratio \(24 : 36\).

Working

\[\text{HCF of } 24 \text{ and } 36 = 12\]find the highest common factor
\[2 : 3\]divide both parts by 12

Example 2

Share \(£80\) in the ratio \(3 : 5\).

Working

\[3 + 5 = 8 \text{ parts}\]add the parts
\[80 \div 8 = £10\]find the value of one part
\[£30 \text{ and } £50\]multiply up, checking they total £80

Example 3

Write \(5 : 20\) in the form \(1 : n\).

Working

\[5 \div 5 = 1\]divide both parts by the first number
\[20 \div 5 = 4\]divide the second part too
\[1 : 4\]write the ratio

Common mistakes

  • Dividing the amount by one part of the ratio.

    Divide by the total number of parts, not by 3 or 5 individually.

  • Simplifying without converting units.

    50cm to 2m is 50 : 200, not 50 : 2. Convert first.

  • Giving one share and stopping.

    The question usually wants both shares, and they should total the original amount.

  • Reversing the order of the ratio.

    The order matters: 3 : 5 is not the same as 5 : 3.

Exam tips

  • Always find the value of one part before calculating shares.
  • Check your shares add back to the original total.
  • Convert to common units before simplifying.
  • Keep the parts in the order given in the question.

Key terms

Ratio
A comparison of two or more quantities.
Part
One unit of a ratio.
Simplify
To divide all parts by a common factor.
Share
To divide an amount according to a ratio.

Related topics

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