Foundation and Higher · order of operations

BIDMAS.
One operation
at a time.

the order matters
more than the sum

the order every calculator follows —

BIDMAS

Brackets · Indices

Divide, Multiply · Add, Subtract

step 1 of 4

Work down the list

1. No brackets, so start with the index.

2. Then multiply. Add last.

✓ 19, not 7 × 4 = 28 or 14² = 196

3 + 4 × 2²

= 3 + 4 × 4 indices

= 3 + 16 multiply

= 19 add

step 2 of 4

Brackets change it

1. Same numbers, but brackets go first.

2. Then the index, then multiply.

✓ Brackets always win

(3 + 4) × 2²

= 7 × 2² brackets

= 7 × 4 indices

= 28

step 3 of 4

A fraction line

1. The line acts like brackets.

2. Finish top and bottom. Then divide.

✓ On a calculator: (8 + 4) ÷ (2 × 3)

8 + 42 × 3

= 126top, then bottom

= 2

step 4 of 4

Same level: left to right

1. Add and subtract are the same level.

2. So are × and ÷. Go left to right.

✓ It does not mean add before subtract

20 − 6 + 3

= 14 + 3 left to right

= 17 not 20 − 9 = 11

order of operations —

Brackets

first, always

Indices

powers and roots next

× ÷ then + −

left to right within each pair

Write one new line
for every operation.

The
Maths Habit

Download The Maths Habit app
to test your knowledge