⭐ Sabse Important Points · एक नज़र में
- BODMAS Rule: Perform operations in the order: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
- Left-to-Right for Same Priority: Division and multiplication are of equal priority; solve from left to right. Similarly for addition and subtraction.
- Brackets Types: Solve in order: ( ) parentheses, { } braces, [ ] square brackets. Innermost bracket first.
- Bracket Order: Always solve innermost bracket first: ( ) then { } then [ ].
- Left-to-Right Rule: For operations of same priority (e.g., division and multiplication), work from left to right.
- Fraction Bar: Treat the numerator and denominator as if they are in brackets; simplify them separately before division.
Introduction · परिचय
BODMAS is a rule that defines the correct order of operations in a mathematical expression. It ensures that everyone evaluates the same expression and gets the same result. For RRB Group D, questions on simplification using BODMAS are common and test your accuracy and speed.
Understanding BODMAS
BODMAS stands for Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction. Operations are performed from left to right within the same priority level. Brackets are solved first, then orders, then division and multiplication (left to right), and finally addition and subtraction (left to right).
- Start with expression
- Solve Brackets (innermost first)
- Solve Orders (powers/roots)
- Perform Division/Multiplication (left to right)
- Perform Addition/Subtraction (left to right)
- Get final answer
📐 Formula / Rule Box · सूत्र याद रखो
BODMAS Rule
Perform operations in the order: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
Left-to-Right Rule
For operations of same priority (e.g., division and multiplication), work from left to right.
⭐ Key Points · याद रखने वाली बातें
- Brackets Types: Solve in order: ( ) parentheses, { } braces, [ ] square brackets. Innermost bracket first.
✍️ Solved Example 1 · हल किया हुआ उदाहरण
❓ Question: Simplify: 12 ÷ 3 × 2 + 5 - 1
✅ Solution: 12
💡 Explanation: First division and multiplication from left to right: 12 ÷ 3 = 4, then 4 × 2 = 8. Then addition and subtraction from left to right: 8 + 5 = 13, then 13 - 1 = 12.
Common Pitfalls and Special Cases
Many mistakes occur when the left-to-right rule is ignored or when brackets are not solved in the correct order. Also, remember that a fraction bar acts as a grouping symbol, and the 'of' operation is treated as multiplication but has higher priority than division in some contexts (though BODMAS typically treats 'of' as part of brackets or as multiplication). Always double-check the order of brackets.
⭐ Key Points · याद रखने वाली बातें
- Left-to-Right for Same Priority: Division and multiplication are of equal priority; solve from left to right. Similarly for addition and subtraction.
- Bracket Order: Always solve innermost bracket first: ( ) then { } then [ ].
- Fraction Bar: Treat the numerator and denominator as if they are in brackets; simplify them separately before division.
✍️ Solved Example 1 · हल किया हुआ उदाहरण
❓ Question: Simplify: 8 ÷ 2(2 + 2)
✅ Solution: 16
💡 Explanation: First solve bracket: 2 + 2 = 4. Expression becomes 8 ÷ 2 × 4. Division and multiplication from left to right: 8 ÷ 2 = 4, then 4 × 4 = 16. (Note: Some interpret implied multiplication as higher priority, but BODMAS strictly follows left-to-right for division and multiplication.)
Practice Questions · खुद हल करके देखो
पहले खुद try karo, phir “Answer dekho” dabakar check karo. 👇
Q1Simplify: 15 - 3 × 4 + 8 ÷ 2
👀 Answer dekho
✅ Answer: 7
💡 Explanation: First multiplication and division from left to right: 3 × 4 = 12, 8 ÷ 2 = 4. Expression becomes 15 - 12 + 4. Then addition and subtraction from left to right: 15 - 12 = 3, 3 + 4 = 7.
Q2Simplify: 5 + 2 × (10 - 4) ÷ 3
👀 Answer dekho
✅ Answer: 9
💡 Explanation: First bracket: 10 - 4 = 6. Expression: 5 + 2 × 6 ÷ 3. Multiplication and division left to right: 2 × 6 = 12, 12 ÷ 3 = 4. Then addition: 5 + 4 = 9.
Q3Simplify: 36 ÷ 6 × 2 + 4 - 1
👀 Answer dekho
✅ Answer: 15
💡 Explanation: Division and multiplication left to right: 36 ÷ 6 = 6, 6 × 2 = 12. Then addition and subtraction left to right: 12 + 4 = 16, 16 - 1 = 15.
⚠️ Common Mistakes · ये गलतियाँ बिल्कुल मत करना
- Ignoring left-to-right rule for division and multiplication: Always perform them from left to right, not multiplication before division.
- Solving brackets in wrong order: Always solve innermost bracket first, then move outward.
- Treating 'of' as division: 'of' means multiplication, but follow the order of operations; it is often solved before division if considered as part of brackets.
⚡ Quick Revision · Exam से पहले 2 मिनट में दोहराओ
- BODMAS Sequence: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
- Bracket Priority: ( ) first, then { }, then [ ].
- Left-to-Right Rule: For same priority operations, work from left to right.