Concept 1 · free preview
BODMAS — order of operations
Understand
In a long expression, the order of work is fixed. Change the order and the answer changes, so this is the base of the whole chapter.
Rule
1. Brackets: first ( ), then { }, then [ ] — always inside out
2. Of: ‘of’ means multiply, but it is done before ÷
3. ÷ and ×: equal priority — left to right
4. + and −: equal priority — left to right
Example
36 ÷ 4 × 3 − 2 + 6 × 2 = 9 × 3 − 2 + 12 (left to right: 36 ÷ 4 first) = 27 − 2 + 12 = 37
Example
50 − [10 + {15 − (9 − 3)}] (9 − 3) = 6 → {15 − 6} = 9 → [10 + 9] = 19 → 50 − 19 = 31
Example
96 ÷ 4 of 6 = 96 ÷ 24 = 4. (Treating ‘of’ as a plain × and going left to right gives 144 — wrong.)
Common mistake
Doing × before ÷ out of habit is wrong. In 40 − 8 ÷ 2 × 4, first 8 ÷ 2 = 4, then 4 × 4 = 16 — not 8 ÷ 8.
Check yourself
40 − 8 ÷ 2 × 4 = ?