Formulas and rules

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

Arithmetic 11

Addition combines amounts. Line up digits by place value and carry when a column passes 9.

Subtraction finds the difference. Borrow from the next column when needed.

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...

n = 2^a x 3^b x 5^c x ...

Every whole number over 1 is a product of primes.

The HCF is the largest shared factor. The LCM is the smallest shared multiple.

Decimals show parts of a whole using tenths, hundredths and thousandths. Line up the decimal points to add.

a : b ; total / (a + b) = one part

A ratio compares amounts. To share in a ratio, find one part then multiply.

Printable cheat sheet