BODMAS & Equation Solver
Type any expression with brackets, powers and fractions — the solver finishes one operation per step, highlights the part it is working on and names the BODMAS rule it used. Then solve linear equations the balance way, and practise with instant marking.
BODMAS sets the order of operations: Brackets, Orders (powers), Division and Multiplication (equal rank, left to right), then Addition and Subtraction (also left to right). So 12 + 3 × (8 − 5)² ÷ 9 = 12 + 3 × 9 ÷ 9 = 12 + 27 ÷ 9 = 15. Division never beats multiplication — whichever comes first wins.
Simplify
Step-by-step solution
One operation per step. The yellow part is what is being worked out; the green part is the new value.
Solve
Step-by-step solution
Whatever is done to one side is done to the other — that keeps the equation balanced.
Six letters that fix the order of operations
BODMAS tells you which operation to do next. Do them in the wrong order and the same sum gives a different answer — this tool shows you exactly where that happens.
Type the sum
Use the keypad for × ÷ ² and brackets, or type + - * / ^ from the keyboard.
Read one step at a time
Each step resolves a single operation and names the rule that chose it.
Check the trap
If working left to right would give a different answer, the tool shows that wrong answer too.
Practise
Switch to Practice for marked questions, or print a 10-question worksheet.
The BODMAS order
B → O → D M → A S
- Brackets — innermost first: ( ) then [ ] then { }
- Orders — powers and roots, e.g. 2³ or √9
- Division and Multiplication — equal rank, left to right
- Addition and Subtraction — equal rank, left to right
So 36 ÷ 6 × 2 is 6 × 2 = 12, not 36 ÷ 12 = 3. Division does not beat multiplication; whichever comes first wins.
Why −3² is not the same as (−3)²
A power is worked out before the minus sign is applied, because O comes before S.
−3² = −(3 × 3) = −9
(−3)² = (−3) × (−3) = +9
The bracket is what pulls the minus sign inside. This is the single most common sign mistake in Class 7–9 papers.
Hidden multiplication: 6 ÷ 2(1 + 2)
Writing a number right next to a bracket means multiply, so 2(1 + 2) is 2 × (1 + 2).
This tool follows the convention used in Indian school textbooks and in BODMAS: finish the bracket, then treat × and ÷ as equal and work left to right.
6 ÷ 2(1 + 2) = 6 ÷ 2 × 3 = 3 × 3 = 9
Some calculators give 1 by treating 2(1+2) as one bundle. Exam answers follow the 9 convention — and the safest habit is to add brackets yourself: 6 ÷ [2(1 + 2)].
Solving a linear equation
An equation is a balance. Add, subtract, multiply or divide — as long as you do it to both sides.
3(x − 2) = x + 4
- Open brackets: 3x − 6 = x + 4
- Subtract x: 2x − 6 = 4
- Add 6: 2x = 10
- Divide by 2: x = 5
Always put the answer back in: 3(5 − 2) = 9 and 5 + 4 = 9. ✓
Exact fractions, not rounded decimals
When a sum does not come out whole, the answer is kept as an exact fraction and the decimal is shown beside it.
3 + 4 × 2 ÷ (1 − 5)² = 72 = 3.5
A recurring decimal is marked with … , for example 73 = 2.333333…
“Of” in BODMAS
In Indian textbooks the O also stands for “of”, which simply means multiply: ½ of 8 = ½ × 8 = 4.
Because “of” is multiplication, this tool ranks it with × and ÷ and works left to right, so 1/2 of 8 = 4 as expected. If a question mixes “of” with division, put brackets round the fraction to be safe.
BODMAS & Equation Solver — your questions
What does BODMAS stand for?
Brackets, Orders, Division, Multiplication, Addition, Subtraction. Brackets come first, innermost ones before outer ones, then powers and roots. Division and multiplication share equal rank and are done left to right, and addition and subtraction share equal rank and are also done left to right. BIDMAS and PEMDAS are the same rule with different names.
Is 36 ÷ 6 × 2 equal to 12 or 3?
It is 12. Division and multiplication have equal rank, so you work from left to right: 36 ÷ 6 = 6, then 6 × 2 = 12. Treating the M in BODMAS as coming before the D would give 36 ÷ 12 = 3, which is the single most common BODMAS mistake in Class 6 and 7 papers.
Why is −3² not the same as (−3)²?
The power is worked out before the minus sign is applied, because Orders come before Subtraction. So −3² means −(3 × 3) = −9, while (−3)² means (−3) × (−3) = +9. The bracket is what pulls the minus sign inside the squaring, and missing it is the commonest sign error in Class 7 to 9.
What is the answer to 6 ÷ 2(1 + 2)?
Following BODMAS as Indian school textbooks teach it, the answer is 9. A number written next to a bracket means multiply, so finish the bracket first and then treat × and ÷ as equal, working left to right: 6 ÷ 2 × 3 = 3 × 3 = 9. The safest habit is to add your own brackets so the intention is clear.
How do I solve a linear equation step by step?
Treat the equation as a balance and do the same thing to both sides. For 3(x − 2) = x + 4: open the brackets to get 3x − 6 = x + 4, subtract x to get 2x − 6 = 4, add 6 to get 2x = 10, then divide by 2 to get x = 5. Always substitute back to check, since 3(5 − 2) = 9 and 5 + 4 = 9.
What does the O in BODMAS mean in Indian textbooks?
It stands for Orders, meaning powers and roots such as 2³ or √9, and many Indian textbooks also read it as “of”. “Of” simply means multiply, so ½ of 8 = ½ × 8 = 4. Because it is multiplication, it is ranked with × and ÷ and worked left to right; add brackets if a question mixes “of” with division.
Can I get a BODMAS worksheet with answers?
Yes. Open the Practice tab, choose BODMAS, equations or mixed at easy, medium or hard, then press Build a 10-question worksheet. It generates ten fresh questions with a teacher's answer key that you can print on A4 or copy into a notebook, and New set produces a different sheet each time.