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Adding Fractions

FoundationHigherAQAEdexcelOCR

This free Foundation and Higher GCSE Maths worksheet on adding fractions helps you revise adding and subtracting fractions. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Always convert to a common denominator before adding or subtracting.

Free downloads

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

Adding and subtracting fractions requires the parts being combined to be the same size. Thirds and quarters cannot simply be added, because the pieces are different.

The fix is a common denominator. You rewrite both fractions so they share a bottom number, add or subtract the numerators, and leave the denominator alone. The lowest common multiple of the two denominators is the tidiest choice, though any common multiple works.

Mixed numbers add a step. Either convert both to improper fractions first, or add the whole numbers and the fractional parts separately. The improper-fraction route is safer when subtracting, because it avoids the awkward case where the second fraction is larger than the first.

Revision notes

Finding a common denominator

Find a number both denominators divide into, then scale each fraction so its denominator matches. Whatever you multiply the bottom by, you must multiply the top by too.

For \(\frac{2}{3} + \frac{1}{4}\), the lowest common multiple of \(3\) and \(4\) is \(12\). So \(\frac{2}{3} = \frac{8}{12}\) and \(\frac{1}{4} = \frac{3}{12}\), giving \(\frac{11}{12}\).

Adding the numerators only

Once the denominators match, add or subtract the numerators and keep the denominator unchanged. The denominator tells you the size of the pieces, and that size has not altered.

Adding the denominators is the classic error: \(\frac{1}{4} + \frac{1}{4}\) is \(\frac{2}{4}\), which simplifies to \(\frac{1}{2}\), not \(\frac{2}{8}\).

Mixed numbers

Convert to improper fractions by multiplying the whole number by the denominator and adding the numerator. So \(2\frac{1}{3}\) becomes \(\frac{7}{3}\).

Work with improper fractions throughout, then convert back at the end if the question asks for a mixed number. Simplify the final answer.

Key points

  • Fractions can only be added when the denominators match.
  • Use the lowest common multiple of the denominators.
  • Whatever you multiply the denominator by, multiply the numerator by too.
  • Add or subtract only the numerators.
  • Convert mixed numbers to improper fractions first.
  • Simplify the final answer.

Worked examples

Example 1

Work out \(\frac{2}{5} + \frac{1}{3}\).

Working

\[\text{LCM of } 5 \text{ and } 3 = 15\]find a common denominator
\[\frac{6}{15} + \frac{5}{15}\]scale both fractions to fifteenths
\[= \frac{11}{15}\]add the numerators only

Example 2

Work out \(\frac{5}{6} - \frac{1}{4}\).

Working

\[\text{LCM of } 6 \text{ and } 4 = 12\]find the lowest common denominator
\[\frac{10}{12} - \frac{3}{12}\]rewrite both with denominator 12
\[= \frac{7}{12}\]subtract the numerators

Example 3

Work out \(2\frac{1}{2} + 1\frac{2}{3}\).

Working

\[\frac{5}{2} + \frac{5}{3}\]convert both to improper fractions
\[\frac{15}{6} + \frac{10}{6} = \frac{25}{6}\]use a common denominator of 6 and add
\[= 4\frac{1}{6}\]convert back to a mixed number

Common mistakes

  • Adding the denominators as well as the numerators.

    One quarter plus one quarter is two quarters, not two eighths. The denominator shows the size of the pieces and does not change.

  • Scaling only the denominator.

    Turning 2/3 into ninths means multiplying top and bottom by 3, giving 6/9, not 2/9.

  • Subtracting mixed numbers part by part.

    In 3¼ − 1½ the fractional part goes negative. Converting to improper fractions avoids this entirely.

  • Leaving the answer unsimplified.

    6/8 should be given as 3/4. Marks for the final answer often require the simplest form.

Exam tips

  • Write the common denominator down before doing any arithmetic.
  • Show the scaled fractions as a separate line to earn method marks.
  • Convert mixed numbers to improper fractions before subtracting.
  • Always check whether the final fraction can be simplified.

Key terms

Numerator
The number on the top of a fraction.
Denominator
The number on the bottom, showing how many equal parts make a whole.
Common denominator
A shared bottom number that allows fractions to be added or subtracted.
Improper fraction
A fraction whose numerator is larger than its denominator.

Related topics

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