The order of operations
Operational priorities
What is 2 + 3 x 4 equal to?
Some say 20, others 14. Only one of the two is correct — and it’s not a matter of opinion: there is a rule, and everyone follows it, from calculators to computers.
The rule
We calculate in this order:
- What’s inside brackets
- Powers
- Multiplication and division
- Addition and subtraction
So 2 + 3 x 4 = 2 + 12 = 14. Multiplication takes precedence over addition.
The pitfall: from left to right
Within the same level of operations, we calculate from left to right. This is where most mistakes occur.
12 : 3 x 2 = 4 x 2 = 8 (and not 12 : 6 = 2)
10 - 4 - 3 = 6 - 3 = 3 (and not 10 - 1 = 9)
Division and subtraction are not ‘symmetrical’: the order matters.
Brackets take precedence over everything
2 + 3 x 4 = 14
(2 + 3) x 4 = 20
Brackets aren’t just for decoration: they change the result. When you’re in doubt, it’s always fine to add more.
Remember: if a calculation seems ambiguous to you, it isn’t — it just means you haven’t applied the rule yet. Write down the steps one by one.