Order of operations is the agreed convention for evaluating expressions containing more than one operation. It ensures that a calculation has one consistent meaning by prioritizing grouping symbols, powers, multiplication and division, and then addition and subtraction, with ties handled from left to right. Understanding BIDMAS or BODMAS is essential for arithmetic, algebra, calculator use, and interpreting fractions, roots, and negative numbers correctly.
Working rule: Group first, powers next, then and left to right, and finally and left to right.
| Comparison | Correct idea | Why it matters |
|---|---|---|
| vs | Same priority, left to right | Prevents false rules like "always multiply first" |
| vs | Same priority, left to right | Preserves the actual structure of the expression |
| Brackets vs no brackets | Brackets override default order | Makes intended grouping explicit |
Key distinction: and are generally different expressions because the brackets change what the power applies to.
Exam habit: Before pressing equals, ask "What is grouped, what is powered, and which equal-priority operations must be read left to right?"