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Fractions, Decimals and Percentages

FoundationChallengeAQAEdexcelOCR

Master fractions, decimals and percentages for GCSE Maths with structured, exam-style practice. This Foundation resource covers converting between fractions, decimals and percentages and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Percentages are out of 100, so 25% = 0.25 = ¼.

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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.

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Topic overview

Fractions, decimals and percentages are three ways of writing the same proportion. Being able to move between them quickly is essential, because questions often mix the forms deliberately.

A fraction becomes a decimal by dividing the numerator by the denominator. A decimal becomes a percentage by multiplying by \(100\), and a percentage becomes a decimal by dividing by \(100\).

A small set of equivalents is worth knowing by heart: a half is \(0.5\) and 50 percent, a quarter is \(0.25\) and 25 percent, a fifth is \(0.2\) and 20 percent, and a tenth is \(0.1\) and 10 percent. Recognising these instantly saves time in ordering and comparison questions.

Revision notes

Converting between the forms

Fraction to decimal: divide the top by the bottom. Decimal to percentage: multiply by \(100\). Percentage to fraction: write it over \(100\) and simplify.

So \(\frac{3}{8} = 3 \div 8 = 0.375 = 37.5\%\), and \(45\% = \frac{45}{100} = \frac{9}{20}\).

Ordering mixed forms

Convert everything to the same form first, and decimals are usually easiest because they compare digit by digit.

To order \(\frac{2}{5}\), \(0.35\) and \(38\%\), convert to \(0.4\), \(0.35\) and \(0.38\), giving the order \(0.35\), \(38\%\), \(\frac{2}{5}\).

Equivalents worth memorising

Learn the common set: \(\frac{1}{2} = 0.5 = 50\%\), \(\frac{1}{4} = 0.25 = 25\%\), \(\frac{3}{4} = 0.75 = 75\%\), \(\frac{1}{5} = 0.2 = 20\%\), \(\frac{1}{10} = 0.1 = 10\%\), \(\frac{1}{3} = 0.333\ldots = 33.3\%\).

These appear constantly, and recognising them removes the need to calculate.

Key points

  • Divide the numerator by the denominator to get a decimal.
  • Multiply a decimal by 100 to get a percentage.
  • Divide a percentage by 100 to get a decimal.
  • Write a percentage over 100 to get a fraction, then simplify.
  • Convert to a common form before ordering.
  • Learn the common equivalents by heart.

Worked examples

Example 1

Write \(\frac{7}{20}\) as a decimal and a percentage.

Working

\[7 \div 20 = 0.35\]divide the numerator by the denominator
\[0.35 \times 100 = 35\%\]multiply the decimal by 100

Example 2

Write \(24\%\) as a fraction in its simplest form.

Working

\[\frac{24}{100}\]write the percentage over 100
\[= \frac{6}{25}\]divide top and bottom by 4

Example 3

Put \(0.62\), \(\frac{3}{5}\) and \(65\%\) in ascending order.

Working

\[\frac{3}{5} = 0.6 \text{ and } 65\% = 0.65\]convert everything to decimals
\[0.6 < 0.62 < 0.65\]compare the decimals
\[\frac{3}{5},\ 0.62,\ 65\%\]write the original forms in order

Common mistakes

  • Multiplying a percentage by 100 instead of dividing.

    45% is 0.45, not 4500. Dividing converts a percentage to a decimal.

  • Comparing fractions by their numerators.

    3/5 is larger than 5/9 even though 3 is smaller than 5. Convert before comparing.

  • Writing 0.4 as 4%.

    Multiply by 100 to get 40%. Losing the place value is a very common slip.

  • Leaving a fraction unsimplified.

    24/100 should be given as 6/25 when the simplest form is asked for.

Exam tips

  • Convert everything to decimals when ordering, since they compare most easily.
  • Learn the common equivalents so you do not have to calculate them.
  • Give the answer in the form the question asks for, not the form you worked in.
  • Simplify any fraction in a final answer.

Key terms

Equivalent
Different forms representing the same value.
Percentage
A proportion expressed out of 100.
Ascending order
Arranged from smallest to largest.
Simplest form
A fraction written with the smallest possible whole numbers.

Related topics

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