GCSE Maths: Number Skills Revision Guide

Fractions

To add or subtract fractions, first find a common denominator. To multiply fractions, multiply the numerators and denominators separately. To divide by a fraction, multiply by its reciprocal (flip it upside down).

Percentages

To find a percentage of an amount, convert the percentage to a decimal and multiply, e.g. 15% of 80 = 0.15 × 80 = 12. For percentage change, use: (change ÷ original) × 100. For compound interest, multiply repeatedly by (1 + rate) for each time period.

Standard form

Standard form writes very large or very small numbers as A × 10ⁿ, where 1 ≤ A < 10. For example, 45,000 = 4.5 × 10⁴, and 0.00032 = 3.2 × 10^-4.

Indices (powers)

Key index laws: multiplying powers of the same base adds the indices (a^m × aⁿ = a^m+n); dividing subtracts them (a^m ÷ aⁿ = a^m-n); a negative index means a reciprocal (a^-n = 1/aⁿ); and a fractional index means a root (a^1/2 = √a).

Common mistakes

• Forgetting to find a common denominator before adding or subtracting fractions.
• Confusing percentage change with just finding a percentage of the original amount.
• Writing standard form with A outside the range 1 to 10.