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Basic BODMAS Rule

Introduction

BODMAS rule हमें arithmetic expressions को सही क्रम में solve करने में मदद करता है। इसका अर्थ है Brackets, Orders, Division, Multiplication, Addition, और Subtraction. यह pattern इसलिए महत्वपूर्ण है क्योंकि कई exam questions यह जांचते हैं कि आप सही sequence लागू करते हैं या बिना सोचे left to right solve कर देते हैं।

Pattern: Basic BODMAS Rule

Pattern

हमेशा expressions को इसी fixed order में solve करें: 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: देखें क्या brackets हैं

    Brackets को check करें। यहाँ कोई bracket नहीं है।

  2. Step 2: Orders (powers/roots) check करें

    यहाँ कोई powers या roots नहीं हैं।

  3. Step 3: पहले division करें

    6 ÷ 3 = 2 → Expression बन जाता है 15 + 2 × 2.

  4. Step 4: अब multiplication करें

    2 × 2 = 4 → Expression बन जाता है 15 + 4.

  5. Step 5: अंत में 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. Brackets के साथ: (15 + 6) ÷ 3 × 2

2. Subtraction के साथ: 25 - 12 ÷ 3 × 2

3. Powers के साथ: 10 + 2² × 3

Trick to Always Use

  • Step 1 → सबसे पहले brackets solve करें।
  • Step 2 → Multiplication/Division से पहले powers/roots handle करें।
  • Step 3 → Division & Multiplication को left to right करें, फिर addition/subtraction करें।

Summary

Summary

  • हमेशा इस order को follow करें: Brackets → Orders → Division/Multiplication → Addition → Subtraction.
  • Multiplication/Division पूरे होने से पहले Addition/Subtraction कभी ना करें।
  • Expression को दो बार scan करें ताकि BODMAS सही लागू हो।
  • Left-to-right rule सिर्फ Division/Multiplication या Addition/Subtraction groups के अंदर लागू होता है।

याद रखने वाला example:
15 + 6 ÷ 3 × 2 = 19 (क्योंकि पहले Division → फिर Multiplication → फिर 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.

Mock Test

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