01 — Explanation
What order do I carry out operations in?
Follow BIDMAS, from top to bottom:
| Order | Letter | Operation |
|---|---|---|
| 1st | B | Brackets |
| 2nd | I | Indices (powers/roots) |
| 3rd | D/M | Division and Multiplication — equal priority, work left to right |
| 4th | A/S | Addition and Subtraction — equal priority, work left to right |
Common Slip
BIDMAS does not mean addition always beats subtraction just because A comes before S in the word. They have equal priority — work through left to right: , not .
02 — Explanation
How do the four operations work with negative numbers?
The same signs apply to division. Subtracting a negative is the same as adding: .
Example: — the two minus signs combine into a plus.
03 — Explanation
How do I apply BIDMAS to a mixed expression with brackets and indices?
Example: work out .
- Inside the brackets, do the index first: .
- Finish the bracket: , leaving .
- Multiply before subtracting: .
- Subtract: .
04 — Explanation
How do I apply this to fractions and negatives together?
Example: evaluate .
- Multiplication comes first. Cancel common factors before multiplying:
- Convert the mixed number: .
- Find a common denominator () and add:
05 — Explanation
How do I apply the four operations to a practical situation like temperature change?
Treat a rise in temperature as addition and a fall as subtraction, keeping careful track of the sign of the starting value.
Example: the temperature at midnight is . By midday it has risen by , and by midnight the following day it has fallen by from its midday value. Find the temperature at midnight the following day.
- Rise from midnight to midday: .
- Fall from midday to the next midnight: .
- Final temperature: .
Exam Tip
in worded problems, underline the key words "rise", "fall", "increase" and "decrease" as you read — they tell you directly whether to add or subtract, without needing to guess from context.
06 — Common mistakes
Common mistakes to avoid
- Ignoring priority and working strictly left to right, e.g. treating as instead of .
- Assuming addition always beats subtraction because of the order of letters in BIDMAS — they're equal priority, so work left to right.
- Dropping a negative sign when subtracting a negative number, e.g. rushing into instead of .