Fractions Calculator

A fraction shows part of a whole. The numerator (top number) tells how many parts you have, and the denominator (bottom number) shows how many equal parts make one whole.

There are three types of fraction you need to know for GCSE: proper, improper and mixed. The type depends on whether the numerator is smaller than, equal to or larger than the denominator.

Simplifying a fraction means making it as small as possible while keeping the same value. To simplify, divide both the numerator and denominator by their Highest Common Factor (HCF).

If the denominators are the same, add or subtract the numerators and keep the denominator. If the denominators are different, find a common denominator first, rewrite each fraction, then add or subtract.

Multiply the numerators together and the denominators together.

To divide fractions, flip the second fraction (find its reciprocal) and then multiply.

Divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator.

A recurring decimal has digits that repeat forever, shown with a dot above the repeating digit (e.g. $0.\dot{3}$ means 0.333...). To convert one into a fraction, set the decimal equal to $x$, multiply both sides to shift the repeating block, then subtract to eliminate it.