The order of priority
In a calculation mixing several operations, you never just calculate from left to right. This exact order must be followed, in this order:
- Whatever is in brackets, first of all.
- Multiplication and division, left to right.
- Addition and subtraction, left to right.
Always start with brackets
Brackets let you force a different order: whatever is written inside must be calculated first, whatever the operation.
(2 + 3) × 4 = 5 × 4 = 20
Without brackets, 2 + 3 × 4 would give a different result (see below)
A full example
Let's calculate 2 + 3 × 4, following the order of priority.
- No brackets here.
- Spot the multiplication: 3 × 4 = 12.
- Finish with the addition: 2 + 12 = 14.
2 + 3 × 4 = 14 (not 20)
What to do with equal priority
When two operations of equal priority follow each other (two multiplications, or a multiplication and a division), you simply work them out left to right, in the order they appear.
20 ÷ 4 × 2 = 5 × 2 = 10
Division and multiplication have equal priority → work left to right
Properties of operations
Certain properties let you reorganise a calculation to make it simpler, without changing the result.
- Commutative property of addition: changing the order of the terms changes nothing. 4 + 7 = 7 + 4. (True for multiplication too: 3 × 6 = 6 × 3.)
- Associative property of addition: you can group the terms differently. (2 + 3) + 5 = 2 + (3 + 5). (True for multiplication too.)
- Distributive property of multiplication: multiplying a sum is the same as multiplying each term separately, then adding. 4 × (10 + 2) = 4 × 10 + 4 × 2 = 40 + 8 = 48.
Mistakes to avoid
- Calculating left to right without following the order of priority.
- Forgetting to deal with brackets first, before everything else.
- Thinking a subtraction is allowed to "jump ahead" of a multiplication that comes before it in the writing.
Worked exercises
5 + 2 × 6
(8 − 3) × 4
18 − 4 × 3 + 2
Now it's your turn!
On EasyMaths, your child practises the order of operations with exercises that never repeat and instant marking.
Start the exercises →Frequently asked questions
What is the order of operations?
1) Whatever is in brackets, first. 2) Multiplication and division, in the order they appear, left to right. 3) Addition and subtraction, in the order they appear, left to right.
Why doesn't 2 + 3 × 4 equal 20?
Because multiplication takes priority over addition: you calculate 3 × 4 = 12 first, then 2 + 12 = 14. If you actually wanted (2 + 3) × 4 = 20, you would need to write brackets.
What is the distributive property of multiplication?
It's a property that lets you "distribute" a multiplication over an addition or subtraction: 4 × (10 + 2) = 4 × 10 + 4 × 2. It's a very useful mental maths tool — for example 4 × 12 = 4 × 10 + 4 × 2 = 40 + 8 = 48.