BODMAS Rule: Order of Operations, Rules and Examples

BODMAS Rule gives the correct sequence for simplifying arithmetic expressions. Solve Brackets first, followed by Orders such as powers and roots, then Division and Multiplication from left to right, and finally Addition and Subtraction from left to right. This page explains the rules, shortcuts and solved BODMAS questions.

On this page

What is the BODMAS Rule?

BODMAS is an order of operations used to simplify mathematical expressions correctly. It stands for Brackets, Orders, Division, Multiplication, Addition and Subtraction.

First simplify grouping symbols such as brackets, then evaluate powers or roots. Division and multiplication have the same priority, so calculate them from left to right. Addition and subtraction also have the same priority and must be calculated from left to right. For example, 8 + 12 ÷ 3 × 2 = 8 + 4 × 2 = 16.

BODMAS Rule Formula & Tricks

Important Formulas

BODMAS sequence
B → O → D/M → A/S

B means Brackets, O means Orders, D/M means Division or Multiplication from left to right, and A/S means Addition or Subtraction from left to right.

Order of operations
Brackets → Powers/Roots → Division/Multiplication → Addition/Subtraction

This sequence determines which operation to perform first when an expression contains different operations.

Nested brackets
( { [ expression ] } )

When brackets are nested, simplify the innermost bracket first, then move outward.

Quick Tricks

Do not always divide before multiplying

Division and multiplication have equal priority. Read the expression from left to right and perform whichever of the two appears first.

Example: 18 ÷ 3 × 2 = 6 × 2 = 12, not 18 ÷ 6 = 3.
Do not always add before subtracting

Addition and subtraction also have equal priority. Calculate from left to right after completing higher-priority operations.

Example: 20 − 8 + 3 = 12 + 3 = 15, not 20 − 11 = 9.
Use one operation at a time

Rewrite the expression after each step. This prevents an operation from being skipped or performed before its priority.

Example: 24 − 6 × 2 + 8 = 24 − 12 + 8 = 12 + 8 = 20.

BODMAS Rule Concepts

Brackets and Nested Grouping Symbols

Expressions inside brackets are simplified before operations outside the brackets.

For nested brackets, solve the innermost grouping first and then simplify the outer grouping. Parentheses (), square brackets [] and braces {} all act as grouping symbols. A vinculum, or horizontal bar, also indicates that the complete expression below it should be treated as grouped.

Example: 3 × [8 − (5 − 2)] = 3 × [8 − 3] = 3 × 5 = 15.

Orders: Powers and Roots

Orders include powers, roots and other indices, and they are evaluated after brackets but before division or multiplication.

A power gives repeated multiplication, while a root reverses a power. For example, 3² = 9 and √16 = 4. If an expression contains several orders at the same level, evaluate them according to the stated expression and simplify systematically.

Example: 5 + 2³ × 3 = 5 + 8 × 3 = 29.

Division and Multiplication from Left to Right

Division and multiplication have equal precedence, so the first operation encountered from the left is performed first.

BODMAS does not mean that all division must be completed before multiplication. The same left-to-right rule applies when multiplication appears before division. Fractions and division bars should be simplified carefully as grouped expressions.

Example: 48 ÷ 6 × 4 = 8 × 4 = 32, while 48 × 4 ÷ 6 = 192 ÷ 6 = 32.

Addition and Subtraction from Left to Right

Addition and subtraction have equal precedence and are evaluated from left to right after higher-priority operations are complete.

Do not rearrange addition and subtraction without changing the expression into an equivalent form. Complete every multiplication or division first, then process the remaining addition and subtraction from left to right.

Example: 30 − 12 + 5 − 3 = 18 + 5 − 3 = 23 − 3 = 20.

BODMAS Rule Video Lessons

Watch short topic-wise lessons for quick revision.

13 Lessons
Lesson 1 of 13 Quick Revision

BODMAS with Overline Expressions

Learn how to apply BODMAS rules to simplify expressions containing overlines, following the correct order of operations step by step.

Continue with more lessons and practice in PrepShots.Watch More in App - Start ₹1 Trial →
More BODMAS Rule Lessons Scroll to explore →

Practice BODMAS Rule Questions

Practise published questions related to this topic.

1An officer simplifies 1/(√3 + √2) . The simplified form is:→ 2Simplify: √75 + √48 - √27→ 3An officer checks the cost ratio: √18 ÷ √2 .Simplify.→ 4Simplify: √2 + 1/√2 + 1/(2+√2) - 1/(2-√2)→ 5Find the value of x in the following expression. (0.36)³ × (0.216)³ ÷ (0.1296)³ = (60 ÷ 100)^(x+1)→ 6Simplify: ((2⁴ × 3⁴ × 5⁴))/((2² × 3² × 5²))→ 7Find the value of m which satisfies (14/5)¹¹ × (5/14)¹⁷ × (14/5)¹⁴ = (5/14)^(3m+7)→ 8Simplify: ( (16⁻¹ × 8²)/(4⁻³ × 2⁵) )^(1/3)→ 9Simplify the following. 5¹⁵ ÷ 25^(13/2) ÷ 125^(2/3) + 5¹⁷ ÷ 125^(16/3) + 5³→ 10Simplify: (10 × a⁵ × b⁶)/(2 × a² × b³)→

BODMAS Rule Quick Quiz

Attempt 5 questions and check your score instantly.

Quick Revision Notes

BODMAS Rule Revision Points

Use these rules while simplifying an arithmetic expression.

  • BODMAS means Brackets, Orders, Division, Multiplication, Addition and Subtraction.
  • Solve the innermost brackets before the outer brackets.
  • Orders include powers, roots and indices.
  • Division and multiplication have equal priority; evaluate them from left to right.
  • Addition and subtraction have equal priority; evaluate them from left to right.
  • Rewrite the expression after each major step to avoid skipping an operation.
  • For 8 + 12 ÷ 3 × 2, calculate division and multiplication from left to right: 8 + 4 × 2 = 16.

BODMAS Rule FAQs

What is the correct order in the BODMAS Rule?

The order is Brackets, Orders, Division or Multiplication from left to right, and Addition or Subtraction from left to right.

Should multiplication be done before division in BODMAS?

No. Division and multiplication have the same priority. Perform whichever appears first when reading from left to right. For example, 24 ÷ 4 × 3 = 6 × 3 = 18.

Should addition be done before subtraction in BODMAS?

No. Addition and subtraction have equal priority. Solve them from left to right. Thus, 15 − 6 + 4 = 9 + 4 = 13.

How is 10 + 6 ÷ 2 × 3 simplified?

First perform division and multiplication from left to right: 6 ÷ 2 = 3, then 3 × 3 = 9. Therefore, 10 + 9 = 19.

How are nested brackets solved?

Start with the innermost bracket and move outward. For example, 2 × [7 − (4 − 1)] = 2 × [7 − 3] = 2 × 4 = 8.

How is a power handled in a BODMAS expression?

Evaluate the power after brackets and before multiplication or division. For example, 4 + 3² × 2 = 4 + 9 × 2 = 22.

Continue learning BODMAS Rule on PrepShots

Continue on PrepShots