Formulas and rules

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

Arithmetic 5

a x b = rows x columns

Multiplication is repeated addition, shown as a rectangular grid.

dividend / divisor = quotient

Division shares a total into equal groups. It undoes multiplication.

By 2: even last digit. By 3: digit sum divisible by 3. By 5: last digit 0 or 5. By 9: digit sum divisible by 9. By 10: last digit 0.

A factor divides a number exactly. A multiple is found by multiplying a number by a whole number.

A prime has exactly two factors: 1 and itself. Primes start 2, 3, 5, 7, 11, 13...

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.

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

Printable cheat sheet