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Number · Foundation & Higher

Fractions

Fractions represent parts of a whole. You need to add, subtract, multiply and divide fractions, and convert between fractions, decimals and percentages.

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Key facts to remember

  • 1To add or subtract fractions, find a common denominator first.
  • 2To multiply fractions: multiply numerators together and denominators together.
  • 3To divide by a fraction: flip it (find the reciprocal) and multiply.
  • 4A mixed number like 2½ = 5/2 as an improper fraction.
  • 5Always simplify your answer by dividing by the highest common factor (HCF).
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Formulas

Add/Subtract
a/b ± c/d = (ad ± bc) / bd

Find common denominator first

Multiply
a/b × c/d = ac / bd
Divide
a/b ÷ c/d = a/b × d/c = ad / bc

Flip the second fraction

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Worked examples

Example 1

Work out 2/3 + 3/4

Working

  1. Find the LCM of 3 and 4 → LCM = 12
  2. 2/3 = 8/12 and 3/4 = 9/12
  3. 8/12 + 9/12 = 17/12
  4. Convert to mixed number: 1 5/12
Answer1 5/12
Example 2

Work out 3½ ÷ 7/8

Working

  1. Convert 3½ to an improper fraction: 7/2
  2. Flip 7/8 to get 8/7
  3. 7/2 × 8/7 = 56/14
  4. Simplify: 56 ÷ 14 = 4
Answer4
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Common mistakes

✗Adding denominators instead of finding a common denominator (e.g. writing 1/2 + 1/3 = 2/5).
✗Forgetting to flip when dividing — you flip the second fraction, not the first.
✗Not simplifying the final answer.
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Exam tips

✓Show your common denominator working — examiners award method marks even if your final answer is wrong.
✓Convert mixed numbers to improper fractions before multiplying or dividing.

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