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Number · Foundation & Higher

Percentages

Percentages mean "out of 100". You need to find percentages of amounts, convert between fractions/decimals/percentages, and use percentage multipliers.

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Key facts to remember

  • 1To find x% of an amount: multiply by x/100 (or the decimal equivalent).
  • 2Percentage → Decimal: divide by 100 (e.g. 35% = 0.35).
  • 3Decimal → Percentage: multiply by 100.
  • 4Fraction → Percentage: divide numerator by denominator, then × 100.
  • 5A multiplier for an increase of 15% is 1.15; a decrease of 15% is 0.85.
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Formulas

Percentage of an amount
(Percentage ÷ 100) × Amount
Percentage multiplier (increase)
1 + (percentage ÷ 100)
Percentage multiplier (decrease)
1 − (percentage ÷ 100)
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Worked examples

Example 1

Find 35% of £240

Working

  1. 35% = 0.35
  2. 0.35 × 240 = 84
Answer£84
Example 2

Increase £360 by 22%

Working

  1. Multiplier = 1 + 0.22 = 1.22
  2. 1.22 × 360 = £439.20
Answer£439.20
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Common mistakes

✗Finding 10% and then trying to build up incorrectly (e.g. 35% ≠ 30% + 5% done wrong).
✗Using the wrong multiplier for a decrease (using 1.15 instead of 0.85 for a 15% decrease).
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Exam tips

✓Use the multiplier method — it's faster and less error-prone than building up from 10%.
✓Always re-read whether the question says "of the original" or "of the new value".

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