Fractions, Decimals and Percentages

GCSE Maths · Number

Three ways to show the same thing

Fractions, decimals and percentages are three ways of writing a proportion of something. Being able to convert between them is essential.

Add/subtract: make the denominators the same (common denominator), then add/subtract the numerators. 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
Multiply: multiply tops and bottoms: 2/3 × 4/5 = 8/15.
Divide: flip the second fraction and multiply (KFC – Keep, Flip, Change): 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Simplify by dividing top and bottom by their HCF.

Finding a percentage of an amount: e.g. 15% of 80 = 0.15 × 80 = 12.
Percentage increase/decrease: use a multiplier.
Increase by 20% → ×1.20. Decrease by 20% → ×0.80.
Example: £50 increased by 20% = 50 × 1.20 = £60.
Percentage change: (change ÷ original) × 100.
Reverse percentages: if a price after a 20% rise is £60, the original = 60 ÷ 1.20 = £50 (divide by the multiplier).

Interest earned on interest, using the multiplier repeatedly:

final amount = starting amount × (multiplier)^number of years

E.g. £200 at 5% for 3 years = 200 × 1.05³ ≈ £231.53.

A jacket costs £80 and is reduced by 25% in a sale. Find the sale price.

Adding fractions by adding tops and bottoms — you need a common denominator first.
Forgetting to flip when dividing fractions.
For reverse percentages, mistakenly taking the percentage off the final amount instead of dividing by the multiplier.

Learn the multiplier method — it handles increase, decrease, reverse and compound problems.
Always simplify fractions at the end.
For "percentage change", divide the change by the original amount.

Convert: fraction → decimal (divide), decimal → % (×100), % → fraction (over 100, simplify).
Fractions: common denominator to add/subtract; multiply tops & bottoms; divide = flip and multiply.
Percentages via multipliers: +20% → ×1.2, −20% → ×0.8; reverse % = divide by the multiplier; compound = multiplier^years.