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Expressing as a Fraction or Percentage

FoundationChallengeAQAEdexcelOCR

Practise expressing as a fraction or percentage with this free Foundation GCSE Maths worksheet from Virtus Academy. You'll work through expressing one quantity as a fraction or percentage of another, building confidence for your exam, and every question comes with worked solutions in the mark scheme. Suitable for AQA, Edexcel and OCR. Write the part over the whole, then multiply by 100 for a percentage.

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Topic overview

Expressing one quantity as a fraction or percentage of another shows how big the part is relative to the whole. The structure is always the same: the part goes on top and the whole goes on the bottom.

Once written as a fraction, multiplying by \(100\) converts it to a percentage. So \(12\) out of \(40\) is \(\frac{12}{40}\), which is \(0.3\), which is 30 percent.

The difficulty is identifying the whole. In a question about \(12\) girls in a class of \(40\), the whole is \(40\). If instead you are told there are \(12\) girls and \(28\) boys, the whole is \(12 + 28 = 40\), and using \(28\) as the denominator gives a wrong answer that looks plausible.

Revision notes

Part over whole

Write the part as the numerator and the total as the denominator, then simplify.

For \(15\) out of \(60\): \(\frac{15}{60} = \frac{1}{4}\). Both numbers must be in the same units, so convert first if one is in centimetres and the other in metres.

Converting to a percentage

Divide the part by the whole and multiply by \(100\).

So \(\frac{15}{60} \times 100 = 25\%\). Rounding to one decimal place is usually acceptable unless the question specifies otherwise.

Identifying the whole

The whole is the total of everything, which sometimes has to be worked out first.

With \(9\) red and \(21\) blue counters, the whole is \(30\), so red counters are \(\frac{9}{30} = 30\%\). Using \(21\) as the denominator would be wrong.

Key points

  • The part goes on top, the whole on the bottom.
  • Multiply by 100 to convert a fraction to a percentage.
  • Work out the total first if it is not given.
  • Both quantities must be in the same units.
  • Simplify fractions in the final answer.
  • A part of a whole is always less than 100 percent.

Worked examples

Example 1

Express \(18\) as a fraction of \(45\) in its simplest form.

Working

\[\frac{18}{45}\]write the part over the whole
\[= \frac{2}{5}\]divide both by 9 to simplify

Example 2

A test is marked out of \(80\) and a student scores \(68\). Find the percentage.

Working

\[\frac{68}{80}\]write the score over the total
\[68 \div 80 = 0.85\]convert to a decimal
\[= 85\%\]multiply by 100

Example 3

A bag has \(7\) red and \(13\) green counters. What percentage are red?

Working

\[7 + 13 = 20\]work out the total number of counters
\[\frac{7}{20} \times 100\]write the part over the whole and convert
\[= 35\%\]state the percentage

Common mistakes

  • Using the wrong quantity as the whole.

    With 7 red and 13 green, the denominator is 20, not 13.

  • Putting the whole on top.

    The part is always the numerator, or the answer exceeds 100 percent.

  • Comparing quantities in different units.

    40cm out of 2m must be 40 out of 200, not 40 out of 2.

  • Leaving the fraction unsimplified.

    18/45 should be given as 2/5 when the simplest form is asked for.

Exam tips

  • Work out the total before writing the fraction.
  • Check both quantities are in the same units.
  • Sense-check that the percentage is below 100.
  • Simplify the fraction in your final answer.

Key terms

Part
The quantity being expressed as a share of the whole.
Whole
The total amount, used as the denominator.
Simplest form
A fraction with the smallest possible whole numbers.
Percentage
A proportion expressed out of 100.

Related topics

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