Order of operations & grouping symbols - Two operations
Theory
When a calculation has two operations, do any multiplication or division before any addition or subtraction. When two operations share the same rank, work from left to right.
An operation is one step such as \(+\), \(-\), \(\times\) or \(\div\).
The order of operations ranks them: multiplication and division are done before addition and subtraction.
In \(50 - 4 \times 6\), the multiplication ranks first, so work out \(4 \times 6 = 24\), then \(50 - 24 = 26\).
Which operation goes first
| Rank | Operations |
|---|---|
| First | \(\times\) and \(\div\) |
| Then | \(+\) and \(-\) |
How to work it out
- Find any multiplication or division and do it first.
- Replace it with its answer.
- Finish the addition or subtraction, left to right.
Multiply first, then add.
| \(4 \times 6 + 3\) | \(=\) | \(27\) |
The multiplication ranks first.
| \(50 - 4 \times 6\) | \(=\) | \(26\) |
Divide first, then add.
| \(36 \div 6 + 2\) | \(=\) | \(8\) |
One multiplication, then an addition.
| \(4 \times 6 + 3\) | \(=\) | \(27\) |
Common pitfalls
Frequently asked questions
Why do we multiply before adding?
Multiplication is a shortcut for repeated addition, so it counts as a higher-rank step. Doing it first keeps every calculation giving the same answer.
What if there is only addition and subtraction?
They share the same rank, so work from left to right. In \(20 - 5 + 3\), do \(20 - 5 = 15\), then \(15 + 3 = 18\).
Does the order change the answer?
Yes. \(5 + 3 \times 4 = 17\) using the correct order, but \(32\) if you wrongly add first. The rule keeps everyone getting the same result.
How do I show which step is first?
Work out the multiplication or division and rewrite the line with its answer, then finish the addition or subtraction.