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Basic BODMAS Rule

Introduction

The BODMAS rule helps us solve arithmetic expressions in the correct order. It stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. This pattern is important because many exam questions test if you apply the correct sequence instead of solving left to right blindly.

Pattern: Basic BODMAS Rule

Pattern

Always solve expressions in the fixed order: Brackets → Orders → Division/Multiplication → Addition → Subtraction.

Step-by-Step Example

Question

Evaluate: 15 + 6 ÷ 3 × 2

Options:

  • A) 12
  • B) 15
  • C) 19
  • D) 21

Solution

  1. Step 1: Identify if any brackets exist

    Check for brackets. None present.

  2. Step 2: Check for orders (powers/roots)

    No powers or roots present.

  3. Step 3: Apply division first

    6 ÷ 3 = 2 → Expression becomes 15 + 2 × 2.

  4. Step 4: Apply multiplication next

    2 × 2 = 4 → Expression becomes 15 + 4.

  5. Step 5: Finish with addition

    15 + 4 = 19.

  6. Final Answer:

    19 → Option C.

  7. Quick Check:

    Division (6 ÷ 3 = 2), Multiplication (2 × 2 = 4), Addition (15 + 4 = 19) ✅

Quick Variations

1. With brackets: (15 + 6) ÷ 3 × 2

2. With subtraction: 25 - 12 ÷ 3 × 2

3. With powers: 10 + 2² × 3

Trick to Always Use

  • Step 1 → Solve brackets first.
  • Step 2 → Handle powers/roots before multiplication/division.
  • Step 3 → Do division & multiplication left to right, then addition/subtraction.

Summary

Summary

  • Always follow the order Brackets → Orders → Division/Multiplication → Addition → Subtraction.
  • Never perform addition/subtraction before completing all multiplication/division.
  • Scan the expression twice to ensure BODMAS sequence is correctly applied.
  • Left-to-right rule applies only within Division/Multiplication or Addition/Subtraction groups.

Example to remember:
15 + 6 ÷ 3 × 2 = 19 (because Division → Multiplication → Addition)

Practice

(1/5)
1. Simplify: 18 ÷ 3 + 4 × 2
easy
A. 14
B. 16
C. 18
D. 20

Solution

  1. Step 1: Perform division first

    18 ÷ 3 = 6. Expression becomes 6 + 4 × 2.

  2. Step 2: Apply multiplication

    4 × 2 = 8. Expression becomes 6 + 8.

  3. Step 3: Finish with addition

    6 + 8 = 14.

  4. Final Answer:

    14 → Option A.

  5. Quick Check:

    (18 ÷ 3 = 6, 4 × 2 = 8, 6 + 8 = 14) ✅
Hint: Perform ÷ and × before +.
Common Mistakes: Adding 18 + 3 or doing operations left-to-right without BODMAS.
2. Simplify: 30 - 12 ÷ 4 × 2
easy
A. 18
B. 24
C. 26
D. 28

Solution

  1. Step 1: Apply division first

    12 ÷ 4 = 3. Expression becomes 30 - 3 × 2.

  2. Step 2: Apply multiplication

    3 × 2 = 6. Expression becomes 30 - 6.

  3. Step 3: Perform subtraction

    30 - 6 = 24.

  4. Final Answer:

    24 → Option B.

  5. Quick Check:

    (12 ÷ 4 = 3, 3 × 2 = 6, 30 - 6 = 24) ✅
Hint: Do ÷ then ×, then handle -.
Common Mistakes: Doing 30 - 12 first or mixing order of ÷ and ×.
3. Simplify: (10 + 6) ÷ 4 × 3
easy
A. 9
B. 10
C. 12
D. 15

Solution

  1. Step 1: Solve the bracket first

    (10 + 6) = 16.

  2. Step 2: Apply division

    16 ÷ 4 = 4. Expression becomes 4 × 3.

  3. Step 3: Apply multiplication

    4 × 3 = 12.

  4. Final Answer:

    12 → Option C.

  5. Quick Check:

    (10 + 6 = 16, 16 ÷ 4 = 4, 4 × 3 = 12) ✅
Hint: Always simplify inside brackets first, then ÷/× left to right.
Common Mistakes: Multiplying 6 × 3 before dividing the bracket result by 4.
4. Simplify: 100 ÷ (5 × 2) + 8
medium
A. 10
B. 12
C. 16
D. 18

Solution

  1. Step 1: Solve inside the bracket

    (5 × 2) = 10.

  2. Step 2: Apply division

    100 ÷ 10 = 10. Expression becomes 10 + 8.

  3. Step 3: Perform addition

    10 + 8 = 18.

  4. Final Answer:

    18 → Option D.

  5. Quick Check:

    (5 × 2 = 10, 100 ÷ 10 = 10, 10 + 8 = 18) ✅
Hint: Brackets first, then ÷, then +.
Common Mistakes: Adding 5 + 2 inside bracket or dividing before resolving the bracket.
5. Simplify: 50 - { 4 × (9 ÷ 3) }
medium
A. 38
B. 34
C. 36
D. 32

Solution

  1. Step 1: Solve the innermost bracket

    (9 ÷ 3) = 3.

  2. Step 2: Apply multiplication

    4 × 3 = 12. Expression becomes 50 - 12.

  3. Step 3: Perform subtraction

    50 - 12 = 38.

  4. Final Answer:

    38 → Option A.

  5. Quick Check:

    (9 ÷ 3 = 3, 4 × 3 = 12, 50 - 12 = 38) ✅
Hint: Work from the deepest bracket outward, then ×, then -.
Common Mistakes: Subtracting 50 - 4 first or ignoring bracket order.

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