Order of operations
BODMAS / BIDMAS quick reference
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The rule
- 1. Brackets first — ( ) and [ ].
- 2. Orders / Indices — powers and roots, like 2³ and √9.
- 3. Division & Multiplication — same priority, work left to right.
- 4. Addition & Subtraction — same priority, work left to right.
Important: division does not always beat multiplication, and addition does not always beat subtraction. Equal-rank operations go from left to right.
The written method
Change one part on each line
Copy the whole expression again after every move. This keeps the untouched numbers in their proper places and makes mistakes easier to spot.
Work out: 3 + 2 × (5 − 1)
- 1Brackets3 + 2 × (5 − 1) = 3 + 2 × 4
- 2Multiply3 + 2 × 4 = 3 + 8
- 3Add3 + 8 = 11
- 4Answer3 + 2 × (5 − 1) = 11
Equal-rank rule
Division and multiplication: read left to right
24 ÷ 6 × 2
= 4 × 2 ← do 24 ÷ 6 first
= 8
Do not multiply 6 × 2 first. The ÷ and × have the same rank, so the operation you meet first from the left goes first. Use the same rule for + and −.
Common mistakes
Working left to right too soon
In 4 + 3 × 5, do 3 × 5 first. The answer is 19, not 35.
Treating D and M as separate ranks
Division and multiplication are partners. Read them left to right.
Dropping part of the question
Rewrite the full expression on every line, including every sign and bracket.
Forgetting a power after brackets
In 2 × (4 − 1)², do the bracket, then 3², then multiply.
Quick check
Try these one line at a time
18 − 8 ÷ 2+
18 − 4 = 14
5 + 3 × (4 − 2)²+
5 + 3 × 2² = 5 + 3 × 4 = 5 + 12 = 17
20 − 6 + 2+
14 + 2 = 16