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. By the end you will be able to solve long, mixed expressions step by step, spot the mistakes that catch most students, and see how the same rule runs inside spreadsheets, calculators and computer programs.
DMAS is the simpler, earlier version of the rule, usually taught first: Division, Multiplication, Addition, Subtraction. It is used for expressions that do not 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 appear, 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 |
Different countries teach the same rule under different names. You may meet BIDMAS (Indices), BEDMAS (Exponents) or PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). The letters change, but the rule and the answers are exactly the same.
In UK-style courses the O in BODMAS means orders (powers and roots), as used in this article. In many South Asian textbooks the O means “of”, as in “half of 20”. There, “of” is a multiplication that is worked out straight after the brackets, before division and multiplication. For simple expressions both give the same answer. They can differ in cases such as 8 ÷ 2 of 2, so follow the convention in your own syllabus, and add brackets in your own writing. The full explanation is in Brackets, Fractions & Decimals in BODMAS.
PEMDAS is often misread as “multiplication always before division” because M comes before D in the word. That is the same trap as in BODMAS, and the fix is the same: multiplication and division are equal partners, as explained in Section 6.
Without an agreed order, the same expression could honestly mean different things to different people. That would be a disaster for anything that relies on mathematics being consistent, from bank statements to spreadsheet formulas to construction drawings.
2 + 3 × 4. Solving left to right (2 + 3 = 5, then 5 × 4 = 20) gives 20. Solving with the correct order (3 × 4 = 12 first, then 2 + 12) gives 14. Only 14 is correct, because multiplication happens before addition regardless of reading order.
A good way to see why: 2 + 3 × 4 means “2, plus three groups of 4”. The 3 × 4 belongs together as one chunk. If you had 2 coins and then collected 3 bags with 4 coins in each, you would have 2 + 12 = 14 coins, not 20.
Think of BODMAS as a ladder. You always start at the top rung and work down. Some rungs hold two operations that share the same priority, and you handle those from left to right.
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. Now 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 and multiplication, then addition and subtraction.
2 × (3 + 4)² ÷ 7. Brackets first: 3 + 4 = 7. Then the power: 7² = 49. Then multiply and divide from left to right: 2 × 49 = 98, then 98 ÷ 7 = 14.
What counts as an “order”? Squares, cubes and any other power (see Exponents & Powers) and roots such as √16 (see Squares, Cubes & Roots). They are done after brackets and before division and multiplication. So 3 + 4² means 3 + 16 = 19, not 7² = 49.
This is the single most misunderstood part of BODMAS. The letters D and M (and A and S) are not a strict sequence. Multiplication does not automatically happen before division just because “M” comes before “D” in some versions of the acronym. Division and multiplication have exactly equal priority, and whichever one appears first when reading left to right is done first. The same is true of addition and subtraction.
Why left to right? Because subtraction is really adding a negative, and division is really multiplying by a reciprocal. So 18 − 4 + 6 is 18 + (−4) + 6, a chain of additions that can be done in order. In the same way, 20 ÷ 4 × 2 is 20 × ¼ × 2, a chain of multiplications. They sit on the same rung because each pair is the same operation in two forms.
This treats multiplication as if it always outranks division, but they are 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.
This treats addition as if it always outranks subtraction, but again they are equals.
The fix: read left to right: 18 − 4 comes first (= 14), then 14 + 6 = 20. Grouping “4 + 6” first changes the answer entirely, and it is not allowed unless brackets say so.
When brackets sit inside other brackets, always resolve the innermost set first, then work outwards. Round brackets ( ), square brackets [ ] and curly brackets { } all mean the same thing. Different shapes just make nesting easier to read.
[(4 + 2) × 3 − 5] ÷ 4. Innermost brackets first: 4 + 2 = 6. Inside the square brackets: 6 × 3 = 18, then 18 − 5 = 13. Finally 13 ÷ 4 = 3.25.
Some symbols act as hidden brackets. Learn to see them.
Negative numbers and powers. Brackets decide whether the minus sign is part of the base.
−3² means −(3²) = −9. But (−3)² = (−3) × (−3) = +9.
Also 5 − (−3) = 5 + 3 = 8, and 5 − 3 × (−2): multiply first, 3 × (−2) = −6, so 5 − (−6) = 5 + 6 = 11. (For more on signs, see Operations of Integers.)
The minus sign is not inside the power, so there is no “negative times negative” here.
The fix: the power only applies to the 4, so −4² = −(4 × 4) = −16. If you want the minus sign to be squared too, write (−4)², which is +16. When in doubt, add brackets to show what you mean.
6 + 12 ÷ 3 × 2 − 1. Division and multiplication from left to right: 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. It is not 100 ÷ (5 ÷ 2), which would incorrectly give 40.
(6 + 2) × (9 − 4) ÷ 2². Both brackets first: 8 and 5. Then the power: 2² = 4. Now 8 × 5 ÷ 4, left to right: 8 × 5 = 40, then 40 ÷ 4 = 10.
√16 + 3 × 2. The root is an order, so it comes first: √16 = 4. Then multiply: 3 × 2 = 6. Then add: 4 + 6 = 10. (Doing 4 + 3 = 7 first and then × 2 = 14 is the left-to-right mistake.)
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 and division as a pair (left to right), then addition and subtraction as a pair (left to right). Reading order only decides ties within the same 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.
A shopper buys 3 notebooks at Rs 120 each and 2 pens at Rs 85 each, and has a Rs 50 discount coupon. The total is 3 × 120 + 2 × 85 − 50. Multiply first: 360 and 170. Then left to right: 360 + 170 = 530, and 530 − 50 = Rs 480.
If the shopper had added first, 3 × (120 + 2) × (85 − 50), the answer would be completely different and meaningless.
To convert Celsius (C) to Fahrenheit, F = 9 ÷ 5 × C + 32. For C = 25: 9 ÷ 5 = 1.8, then 1.8 × 25 = 45, then 45 + 32 = 77 °F. For C = 35: 9 ÷ 5 × 35 = 63, and 63 + 32 = 95 °F.
A metal plate is 12 cm by 8 cm and has a square hole of side 3 cm. Area = 12 × 8 − 3². The power first: 3² = 9. Then multiply: 12 × 8 = 96. Then subtract: 96 − 9 = 87 cm².
Three test marks are 72, 85 and 91. Their average is (72 + 85 + 91) ÷ 3 = 248 ÷ 3 ≈ 82.7. Without the brackets, 72 + 85 + 91 ÷ 3 would divide only the last mark: 72 + 85 + 30.3 ≈ 187.3, which is nonsense for an average. (See Basic Data & Statistics.)
A = P × (1 + r)n, with P = 10,000, r = 0.08 and n = 3. Brackets first: 1 + 0.08 = 1.08. Then the power: 1.083 = 1.259712. Then multiply: 10,000 × 1.259712 = 12,597.12. (See Percentages.)
Spreadsheet programs such as Excel and Google Sheets follow the order of operations automatically. Typing =2+3*4 into any cell returns 14, not 20. Programming languages follow the same idea, called operator precedence: in most of them, 20 / 4 * 2 gives 10, because division and multiplication are resolved left to right. One caution: some tools treat a leading minus sign differently. Excel, for instance, returns 9 for =-3^2, not −9, so write =-(3^2) if you want −9. When you are not sure, add brackets.
Scientific calculators follow BODMAS. Many very basic calculators do not: they calculate each operation as you press it, so 2 + 3 × 4 can come out as 20. If you use one, enter the multiplication first, or use the memory keys. Always check an answer against a rough estimate: 2 + 3 × 4 should be about 2 + 12, so 20 should look suspicious.
You may have seen a viral puzzle such as 6 ÷ 2(1 + 2) argued over online. The trouble is not BODMAS. It is the way the expression is written. If you treat 2(1 + 2) as an ordinary multiplication, the left-to-right rule gives (6 ÷ 2) × 3 = 9. Some textbooks and calculators treat the implied multiplication (a number touching a bracket) as binding tighter, which gives 6 ÷ (2 × 3) = 1.
Careful writers avoid the problem. They add brackets, or use a fraction bar, so only one reading is possible. In your own work, never write an expression that depends on a convention, and always write 6 ÷ (2 × 3) or (6 ÷ 2) × 3 so nobody can misread it.
The conventions for order of operations developed gradually over several centuries, alongside algebraic notation itself. Before that, mathematicians often wrote out calculations in words or used their own personal grouping habits, which sometimes caused genuine disagreements about what a written expression meant.
Writing one operation per line, and copying down everything that has not changed, is the best habit you can build. It makes mistakes easy to find.
Tap the correct answer for each question. Your score is tracked as you go, and your best score is saved on this device.
1. Multiply first: 3 × 2 = 6. Then 12 − 6 = 6, and 6 + 4 = 10.
2. Brackets first: 12 − 3 = 9. Then 9 × 2 = 18, and 18 + 4 = 22. (The brackets change the answer from 10 to 22.)
3. Left to right: 48 ÷ 6 = 8, then 8 ÷ 2 = 4.
1. 6 ÷ 2 = 3, then 3 × 3 = 9. Then 8 + 9 = 17, and 17 − 4 = 13.
2. Brackets: 12 − 4 = 8. Power: 8² = 64. Then 64 ÷ 4 = 16 and 3 × 2 = 6. Finally 16 + 6 = 22.
3. (2 + 3) × 4 − 1 = 5 × 4 − 1 = 20 − 1 = 19.
4. 3 × 120 + 2 × 85 − 50 = 360 + 170 − 50 = Rs 480.
5. 9 ÷ 5 = 1.8, then 1.8 × 35 = 63, then 63 + 32 = 95.
Acronyms help only when the learner understands the logic behind them. Start with a story: 2 coins plus 3 bags of 4 coins. Show that the order of operations is an agreement, and that the agreement exists so everyone gets the same answer. Insist on one step per line, and on copying unchanged parts down, since this exposes most errors. Let students colour-code each operation level. Raise the “equal partners” idea early, because the belief that M always comes before D (and A before S) causes more lost marks than any other part of this topic. Introduce the ambiguous expressions as a lesson in clear writing, not as a trick.
BODMAS is not just a school exercise. It is the silent agreement that makes written mathematics reliable everywhere it is 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 Maths | 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. That is the same instinct that later underpins algebra, equations and multi-step word problems.
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