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Level 8Grade 8skill: bodmas· 9 min read

BODMAS: the Order of Operations

In short: BODMAS ranks operations: Brackets, Orders, Division/Multiplication, then Addition/Subtraction — you obey the rank, not the page order, so 2 + 3 × 4 = 14, not 20. Division and multiplication share a rank (left to right), as do addition and subtraction. In word problems, rewrite 'of', 'discount', and 'sales tax' as multiplications and always check which base the percentage acts on.

BODMAS is a priority ladder, not a reading order

Look at 2 + 3 × 4. Read it like a sentence, left to right, and you get 5 × 4 = 20. That answer is wrong. The real value is 14, because multiplication outranks addition and gets done first: 3 × 4 = 12, then 2 + 12 = 14. This single idea — that operations have a fixed rank and you obey the rank, not the page order — is the whole subject.

BODMAS names the ranks from highest to lowest: Brackets, Orders (powers and roots), Division and Multiplication, Addition and Subtraction. The trap most Grade-8 students fall into is treating D above M and A above S. They don't. Division and multiplication share one rank; addition and subtraction share another. Inside a shared rank — and only then — you work left to right.

  1. Clear the brackets first, working the innermost pair outward.
  2. Evaluate orders (powers and roots) next.
  3. Do all × and ÷ together, left to right, as they appear.
  4. Do all + and − together, left to right, as they appear.
  5. In word problems, translate 'of', 'increased by', 'discount', and 'sales tax' into ×/÷ before you rank anything.

Why the ranking exists (and where percentages hide) Why it works

B — Brackets
Whatever sits inside ( ) is one bundled quantity; resolve it fully before it interacts with anything outside.

(5 − 1)² = 4² = 16, not 5 − 1² = 4

O — Orders
Powers and roots bind tighter than any ×, ÷, +, −.

2 × 3² = 2 × 9 = 18, never (2 × 3)² = 36

DM — same rank
× and ÷ are equal; go strictly left to right.

24 ÷ 6 × 2 = 4 × 2 = 8, not 24 ÷ 12 = 2

AS — same rank
+ and − are equal and lowest; go strictly left to right.

10 − 4 + 3 = 6 + 3 = 9, not 10 − 7 = 3

Here is the insight worth keeping: every percentage is a multiplication wearing a costume. '12% of 250' is 250 × 0.12 = 30. 'Increased by 12%' is × 1.12. 'After 20% off' is × 0.80. Once you rewrite the words as ×, the BODMAS ladder tells you exactly what to do first — and on which number. And the ranking itself isn't an arbitrary rule teachers invented: multiplication is repeated addition, so it packages a bigger chunk of value and has to be settled before the loose +/− terms.

Worked examples

Evaluate 7 + 2 × (5 − 1)² ÷ 8. = 11
  1. Brackets: (5 − 1) = 4.
  2. Orders: 4² = 16.
  3. × and ÷ left to right: 2 × 16 = 32, then 32 ÷ 8 = 4.
  4. + and −: 7 + 4 = 11.
Evaluate 6 − 4 × 3 + 2. = −4 (reading left to right would wrongly give 8)
  1. Multiplication ranks above +/−: 4 × 3 = 12.
  2. Rewrite: 6 − 12 + 2.
  3. Left to right: 6 − 12 = −6, then −6 + 2 = −4.
A jacket costs a shop $2,000. They mark it up 25%, then advertise '10% off the marked price'. What is the selling price, and the actual profit percent? = Selling price $2250; profit 12.5%
  1. Marked price = 2000 × 1.25 = 2500.
  2. Discount is on the marked price, not the cost: 2500 × 0.90 = 2250.
  3. Selling price = $2250.
  4. Profit = 2250 − 2000 = 250, taken on the cost: 250 ÷ 2000 = 12.5%.
A phone has a base price of $8,000. A $1,000 coupon applies before tax, and 18% sales tax is charged. What does the customer pay? = $8260 (taxing $8000 first, then subtracting the coupon, wrongly gives $8440)
  1. Coupon first (it applies before tax): 8000 − 1000 = 7000.
  2. sales tax is charged on the discounted base: 7000 × 1.18 = 8260.
  3. Amount paid = $8260.
A share price rises 20% one week and falls 20% the next. Starting at $500, what is the net change? = Down $20, a 4% loss (not 0%)
  1. After the rise: 500 × 1.20 = 600.
  2. The fall of 20% is on the new price, not the original: 600 × 0.80 = 480.
  3. Net change = 480 − 500 = −20, i.e. −4%.

Common mistakes

Reading left to right instead of by rank

✗ 2 + 3 × 4 = 20

You added 2 + 3 first because it came first on the line. But × outranks +, so 3 × 4 = 12 must happen before the addition.

Fix: Scan the whole expression for × and ÷ and settle those first: 2 + 12 = 14.

order_of_ops_lr

Applying the wrong operation

✗ 8 + 12 ÷ 4 = 56

You multiplied 12 × 4 = 48 instead of dividing, then added 8. The symbol is ÷, not ×.

Fix: Do the division as written: 12 ÷ 4 = 3, then 8 + 3 = 11.

wrong_operation

Stopping one step early

✗ Selling price of the jacket = $2500

$2500 is only the marked price — a correct intermediate value. You reported it before applying the 10% discount.

Fix: Finish the chain: 2500 × 0.90 = 2250. Ask 'is there another operation left?' before writing the answer.

partial_computation

Losing a negative sign

✗ 6 − 4 × 3 + 2 = 4

The arithmetic is right the whole way to −4: 4 × 3 = 12, then 6 − 12 = −6, then −6 + 2 = −4. The slip is at the end — you reported the size of the answer and dropped the minus, turning −4 into 4.

Fix: Copy the sign along with the digits. Carry the minus explicitly: 6 − 12 = −6, then −6 + 2 = −4, and write −4, not 4.

sign_error

Taking the percentage of the wrong base

✗ Phone total = $8440

You charged 18% sales tax on the full $8,000 and then subtracted the coupon. The coupon applies before tax, so sales tax should sit on $7,000.

Fix: Fix the base first: 8000 − 1000 = 7000, then 7000 × 1.18 = 8260.

base_confusion

Using the percent number as the answer

✗ 12% of 250 = 12

You copied the number 12 straight from the '%' sign instead of computing a share of 250.

Fix: A percent is a multiplication: 250 × 0.12 = 30.

percent_as_whole

Practice

Work these adaptive BODMAS problems. Expect multi-step expressions with powers and brackets, plus discount, sales tax, and percentage-change questions where the tempting answer is the wrong one. Write down every intermediate value and check the base before you compute a percentage.

Related skills

First, make sure of

Frequently asked questions

Does BODMAS mean division always comes before multiplication?

No. Division and multiplication sit at the same rank, and you work them left to right as they appear. In 24 ÷ 6 × 2 you do 24 ÷ 6 = 4 first because it is on the left, then 4 × 2 = 8. Doing the multiplication first would wrongly give 2.

Why is 2 + 3 × 4 equal to 14 and not 20?

Multiplication outranks addition, so 3 × 4 = 12 is settled before the addition: 2 + 12 = 14. The 20 comes from reading left to right and adding 2 + 3 first, which ignores precedence.

Is BODMAS the same as PEMDAS or BIDMAS?

Yes, they are the same rules with different names. Brackets/Parentheses, Orders/Indices/Exponents, then Division and Multiplication together, then Addition and Subtraction together. The letters differ by country; the ranking is identical.

When a discount and sales tax both apply, which do I calculate first?

Follow the wording of the problem, because it decides the base. If a coupon applies before tax, subtract it first and charge sales tax on the smaller amount; on $8,000 with a $1,000 pre-tax coupon and 18% sales tax you pay 7000 × 1.18 = $8260, not $8440.

How do percentages fit into the BODMAS ladder?

Rewrite the percentage as a multiplication before ranking anything: '12% of 250' is 250 × 0.12 = 30, and 'increased by 12%' is × 1.12. Once it is a multiplication, BODMAS tells you exactly when to apply it and the words tell you which number to apply it to.