AI-generated photorealistic illustration created for BrainiLab. A staged arithmetic still life, not a calculation to solve.
A shared rule for reading a calculation
The order of operations is: brackets, powers, multiplication and division, then addition and subtraction. Multiplication and division share a priority: work through them from left to right. Addition and subtraction also share a priority.
These conventions let people read the same written calculation in the same way. OpenStax sets out the equal-priority pairs, a detail that letter reminders such as BIDMAS can hide.
Brackets change the job
In 3 + 2 × 4, calculate 2 × 4 first. That leaves 3 + 8, so the answer is 11. There are two groups of four, with three more added.
Now put brackets around the addition: (3 + 2) × 4. The brackets tell you to find 3 + 2 first. Then 5 × 4 gives 20. This time there are five groups of four.
Powers come after brackets. A small raised 2 means “square this number”: 3² = 3 × 3 = 9, so 3² + 2 = 11. Revisit square numbers if that notation is new.
Left to right within a priority pair
Consider 12 ÷ 3 × 2. Division and multiplication have equal priority. Working left to right gives 12 ÷ 3 = 4, then 4 × 2 = 8. Doing 3 × 2 first would incorrectly change the grouping.
The same idea applies to 10 − 3 + 2. First 10 − 3 = 7, then 7 + 2 = 9. Addition does not jump ahead of subtraction.
Left to right is a rule within an equal-priority pair. It does not mean ignoring a multiplication because an addition appears earlier on the page. Start by spotting brackets and priorities, then take one step at a time.
