Formulas and rules

Every key math formula and rule, organised by topic and school level, with examples and study tips.

Fractions 9

numerator / denominator

A fraction is equal parts of a whole. The denominator is the number of parts, the numerator the number taken.

a/b = (a x k)/(b x k)

Multiplying or dividing top and bottom by the same number keeps the value.

Divide the numerator and denominator by their HCF.

With the same denominator, the larger numerator is bigger. With the same numerator, the smaller denominator is bigger.

a/b + c/d = (ad + bc) / bd

Find a common denominator, then add the numerators. Never add denominators.

a/b x c/d = ac / bd

Multiply numerators together and denominators together.

a/b / c/d = a/b x d/c

Keep, flip, multiply: keep the first fraction, flip the second and multiply.

a b/c = (a x c + b) / c

A mixed number has a whole part and a fraction. Convert to an improper fraction to calculate.

1/2 = 0.5 = 50%

Divide the numerator by the denominator for a decimal; multiply by 100 for a percentage.

Printable cheat sheet