The same expression can give two completely different answers depending on which operation you do first. BODMAS and DMAS exist so everyone — everywhere — gets the same answer, every time.
Try solving 2 + 3 × 4 in your head right now. If you got 20, you added first. If you got 14, you multiplied first. Only one of those is correct — and the rule that decides which is exactly what this guide covers.
DMAS is the simpler, earlier version of the rule, usually taught first: Division, Multiplication, Addition, Subtraction. It's used for expressions that don't involve brackets or powers.
BODMAS is the fuller rule, adding two more layers: Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction. Once brackets and powers start appearing in expressions, BODMAS is the rule to reach for.
| Letter | Stands For | Example |
|---|---|---|
| B | Brackets | ( ), [ ], { } |
| O | Orders (powers, square roots) | 3², √16 |
| D | Division | 12 ÷ 4 |
| M | Multiplication | 5 × 6 |
| A | Addition | 7 + 2 |
| S | Subtraction | 9 − 3 |
The United States teaches the same rule under a different name: PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Different letters, same underlying rule, same answers.
Without an agreed order, the same expression could honestly mean different things to different people — which is a disaster for anything that relies on math being consistent, from bank statements to spreadsheet formulas to construction blueprints.
2 + 3 × 4: solving left to right (2+3=5, then 5×4=20) gives 20. Solving with correct order (3×4=12 first, then 2+12) gives 14. Only 14 is correct — multiplication happens before addition, regardless of reading order.
For expressions with no brackets or powers, DMAS says: do all division and multiplication first (reading left to right), then do all addition and subtraction (reading left to right).
10 − 2 × 3 + 4: multiply first, 2×3=6. Then work left to right: 10−6=4, then 4+4=8. Final answer: 8.
Once brackets and powers are involved, BODMAS extends the same idea: clear all brackets first (innermost first if nested), then resolve all powers and roots, then division/multiplication, then addition/subtraction.
2 × (3+4)² ÷ 7: brackets first, 3+4=7. Then the power: 7²=49. Then multiply and divide left to right: 2×49=98, then 98÷7=14.
This is the single most misunderstood part of BODMAS. The letters M and D (or D and M) are not a strict sequence — multiplication doesn't automatically happen before division just because "M" comes first in the acronym. Division and multiplication have exactly equal priority, and whichever one appears first when reading left to right gets done first.
This treats multiplication as if it always outranks division — but they're equals.
The fix: read left to right: 20 ÷ 4 comes first (=5), then 5 × 2 = 10. Division and multiplication are resolved in the order they appear, not with one always going before the other.
The exact same idea applies to A and S. Addition doesn't automatically happen before subtraction — they share equal priority, resolved strictly left to right.
This treats addition as if it always outranks subtraction — but again, they're equals.
The fix: read left to right: 18 − 4 comes first (=14), then 14 + 6 = 20. Grouping "4 + 6" together first changes the answer entirely, and it's not allowed unless brackets say so.
When brackets sit inside other brackets, always resolve the innermost set first, then work outward.
[(4+2) × 3 − 5] ÷ 4: innermost brackets first, 4+2=6. Then 6×3=18. Then 18−5=13. Finally 13÷4=3.25.
6 + 12 ÷ 3 × 2 − 1: division/multiplication left to right first: 12÷3=4, then 4×2=8. Now: 6+8−1. Left to right: 6+8=14, then 14−1=13.
2³ + 4 × (5−2): brackets first, 5−2=3. Then the power: 2³=8. Then multiply: 4×3=12. Finally add: 8+12=20.
100 ÷ 5 ÷ 2: division only, left to right. 100÷5=20, then 20÷2=10 — not 100÷(5÷2), which would incorrectly give 40.
This is the most common mistake of all — treating every expression as if only reading order matters.
The fix: BODMAS overrides plain reading order. Brackets and powers always resolve first, then multiplication/division as a pair (left to right), then addition/subtraction as a pair (left to right). Reading order only decides ties within the same priority level, never across levels.
Tap any expression below to see it solved one step at a time, with the BODMAS rule applied at each stage.
Tap an expression above to see the full step-by-step solution.
Spreadsheet programs like Excel and Google Sheets follow BODMAS automatically. Typing =2+3*4 into any cell returns 14, not 20 — the software applies the exact same order-of-operations rule covered here, silently, every single time a formula runs.
Order-of-operations conventions weren't fully standardized until the 1600s–1900s, as algebraic notation itself developed. Before that, mathematicians often wrote out calculations in words or used their own personal grouping conventions, which sometimes caused genuine disagreements over what a written expression meant.
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BODMAS isn't just a school exercise — it's the silent agreement that makes written math reliable everywhere it's used.
| Field | Where Order of Operations Shows Up |
|---|---|
| Spreadsheets & Programming | Every formula and line of code follows strict operator precedence, identical in spirit to BODMAS |
| Finance | Interest, tax, and discount calculations often chain several operations that must resolve in the correct order |
| Engineering & Science | Formulas with multiple terms (like physics equations) rely entirely on consistent order of operations |
| Everyday Math | Splitting a bill, calculating a sale price, or working out a recipe scaled up or down |
Beyond these direct uses, BODMAS is a training ground for a broader skill: breaking a complicated problem into a fixed, reliable sequence of smaller steps — the same instinct that later underpins algebra, equations, and multi-step word problems.
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