Order of operations
You learn the order to work in when there is more than one operation in a calculation.
How to work it out
- First work out what is in the brackets.
- Then the squares, like 4² = 4 × 4.
- Then times and divide, from left to right.
- Finally plus and minus, from left to right.
13 × 4 = 1222 + 12 = 14
A worked example
8 + 4 × 3
- Look at which operations there are: addition and multiplication.
- Do the multiplication first: 4 × 3 = 12.
- Then do the addition: 8 + 12 = 20.
- So 8 + 4 × 3 = 20.
More examples
(8 + 4) × 3
- Do the brackets first: 8 + 4 = 12.
- Then multiply: 12 × 3 = 36.
3 × 5² − 20
- Do the power first: 5² is 5 × 5 = 25.
- Then multiply: 3 × 25 = 75.
- Last of all, subtract: 75 − 20 = 55.
20 − 6 ÷ 2
- Do the division first: 6 ÷ 2 = 3.
- Then subtract: 20 − 3 = 17.
Try it yourself
(2 + 3)² − 5
(20 − 6) × 2 =
Watch out
You just work from left to right: for 8 + 4 × 3 you say 36.
First check whether there is a multiplication or a division. Those come before addition and subtraction.
You think 5² is the same as 5 × 2.
A square is the number times itself: 5² is 5 × 5.
Tips
- Multiplication and division are equally strong: do them from left to right.
- Addition and subtraction are equally strong too: do those from left to right as well.
Why it works
Without an agreement, 8 + 4 × 3 could have two answers: 36 or 20. That is why everyone uses the same order: first brackets, then powers, then multiplication and division, then addition and subtraction. That way everyone gets the same answer.