Order of operations (BIDMAS)
We calculate in this order: brackets, powers, multiplication and division, and last addition and subtraction. Operations with the same priority are done from left to right. That is why 3 + 4 · 2 = 11, not 14.
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The order
We want to know which operation to do first.
| Order | What | Example |
|---|---|---|
| 1 | Brackets | (5 − 2) is worked out first |
| 2 | Powers | 3² = 9 is worked out before multiplying |
| 3 | Multiplication and division, from left to right | 12 ÷ 3 · 2 = 4 · 2 = 8 |
| 4 | Addition and subtraction, from left to right | 10 − 4 + 3 = 6 + 3 = 9 |
Multiplication is repeated addition. 4 · 2 is a single number that belongs together, so it is worked out first:
3 + 4 · 2 = 3 + 2 + 2 + 2 + 2 = 11
A power is repeated multiplication, so it is worked out even earlier.
Same priority: left to right
Multiplication and division have the same priority. We do them in the order they are written.
12 ÷ 3 · 2 = 4 · 2 = 8
It is the same with plus and minus: 10 − 4 + 3 = 6 + 3 = 9.
Brackets, powers and fraction bars
Brackets are worked out first.
(3 + 4) · 2 = 7 · 2 = 14
A power belongs to the number right before it. Here only the three is squared.
2 · 3² = 2 · 9 = 18
A fraction bar works like brackets around the numerator and brackets around the denominator: (4 + 6)/2 = 10 ÷ 2 = 5.
Example
Example 1: 20 − 12 ÷ 4 + 1
We want to do minus, divide and plus in the right order.
Division comes before addition and subtraction.
20 − 12 ÷ 4 + 1 = 20 − 3 + 1
Minus and plus have the same priority. We do them from the left.
20 − 3 = 17
Last, we add one.
17 + 1 = 18
A calculator that follows the rules also gives 18. If we work from the left without the rules, it goes wrong: 8 ÷ 4 + 1 = 3.
Example 2: 3 + 4 · (5 − 2)²
We want to work out the expression, one level at a time.
First the brackets: five minus two is three.
3 + 4 · (5 − 2)² = 3 + 4 · 3²
Then the power: 3 · 3 = 9.
3 + 4 · 3² = 3 + 4 · 9
Then the multiplication: 4 · 9 = 36.
3 + 4 · 9 = 3 + 36
Last, the addition.
3 + 36 = 39
A calculator that follows the rules also gives 39. If we do 3 + 4 first, it goes wrong: 7 · 9 = 63.
Pitfalls
Working from the left whatever the operation: 3 + 4 · 2 = 14.
Times before plus: 3 + 4 · 2 = 3 + 8 = 11.
Always doing times before divide: 12 ÷ 3 · 2 = 12 ÷ 6 = 2.
They have the same priority and are done from the left: 12 ÷ 3 = 4 and 4 · 2 = 8.
Multiplying before the power: 2 · 3² = 6² = 36.
The power belongs only to the three: 3² = 9 and 2 · 9 = 18.
Practise on your own
0 of 4 correct1Work out 6 + 3 · 5.
2Work out (6 + 3) · 5.
3Work out 18 − 12 ÷ 3 · 2.
4Work out 2 · (7 − 3)² − 5.
Common questions
Does multiplication always come before division?
No. Multiplication and division have the same priority and are done from left to right. The same goes for addition and subtraction.
Does a calculator follow the order of operations?
The calculator on a phone and ordinary school calculators do, but not all calculators. Try 3 + 4 · 2. If you get 11, the calculator follows the rules.
What about −3²?
The power is worked out before the minus sign: −3² = −(3 · 3) = −9. If we want to square −3, we write (−3)² = (−3) · (−3) = 9.
How do you calculate when there are brackets inside brackets?
Start with the innermost brackets and work outwards: 2 · (10 − (3 + 1)) = 2 · (10 − 4) = 2 · 6 = 12.
Read also
- Years 6–9Negative numbersHow do you calculate with negative numbers?
- Years 7–9 and upper secondaryPowers and the laws of exponentsHow do you calculate with powers?
- Years 6–9Solving equations step by stepHow do you solve an equation?
- Years 7–9 and upper secondarySimplifying expressionsHow do you simplify an expression?
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