Fractions · GCSE Maths

Equivalent fractions and simplifying

Equivalent fractions have the same value: 2/5 = 4/10 = 6/15. Multiply or divide the top and bottom by the same number.
To simplify, divide the numerator and denominator by their highest common factor: 18/24 = 3/4 (dividing by 6).

An improper fraction has a numerator bigger than its denominator: 11/4 = 2 3/4 (11 ÷ 4 = 2 remainder 3).
To convert a mixed number: 3 1/2 = (3 × 2 + 1)/2 = 7/2.

Make the denominators the same first: 2/3 + 1/4 = 8/12 + 3/12 = 11/12.
For mixed numbers, convert to improper fractions (or add the whole numbers and fractions separately).

Multiply the numerators and multiply the denominators: 3/4 × 2/5 = 6/20 = 3/10.
To divide, keep the first fraction, change ÷ to ×, and flip the second: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Always convert mixed numbers to improper fractions before multiplying or dividing.

To find 3/5 of 40, divide by the denominator and multiply by the numerator: 40 ÷ 5 × 3 = 24.
To write one quantity as a fraction of another, put the first over the second and simplify: 15 out of 60 = 15/60 = 1/4.

Numerator: The top number of a fraction.
Denominator: The bottom number of a fraction.
Equivalent fractions: Fractions that have the same value, such as 1/2 and 3/6.
Simplest form: A fraction whose numerator and denominator have no common factor except 1.
Improper fraction: A fraction whose numerator is larger than its denominator.
Mixed number: A whole number and a fraction together, such as 2 3/4.
Reciprocal: One divided by a number; the reciprocal of 4/5 is 5/4.