Order of operations & grouping symbols - With brackets
Theory
Grouping symbols (brackets) are always worked out first, before any multiplication, division, addition or subtraction outside them. Brackets can change the answer of a calculation.
Grouping symbols, written \(( \ )\), gather part of a calculation so it is done as one step.
Whatever is inside the brackets is worked out first.
So \((6 + 4) \times 5 = 10 \times 5 = 50\), while without brackets \(6 + 4 \times 5 = 26\).
Brackets can change the answer
| Calculation | Result |
|---|---|
| \((6 + 4) \times 5\) | \(50\) |
| \(6 + 4 \times 5\) | \(26\) |
How to work it out
- Do the operation inside the grouping symbols first.
- Replace the bracket with its single value.
- Finish the rest in the normal order.
Add inside the brackets first.
| \((6 + 4) \times 5\) | \(=\) | \(50\) |
The bracket gives \(9\).
| \(90 \div (4 + 5)\) | \(=\) | \(10\) |
Subtract inside first.
| \((9 - 4) \times 5\) | \(=\) | \(25\) |
Count the children first, then share.
| \(90 \div (4 + 5)\) | \(=\) | \(10\) |
Common pitfalls
Frequently asked questions
What are grouping symbols?
They are brackets \(( \ )\) that gather part of a calculation so it is worked out as a single step, before anything outside them.
Do brackets really change the answer?
Yes. \((6 + 4) \times 5 = 50\), but \(6 + 4 \times 5 = 26\). The brackets decide the order.
What if there are brackets and a product?
Do the bracket first, then the multiplication or division, then the addition or subtraction.
When should I add brackets myself?
Add them when you need an addition or subtraction to happen before a multiplication or division, such as \(30 - (12 + 10)\).