⭐ Sabse Important Points · एक नज़र में
- BODMAS: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
- Bracket Order: Vinculum → ( ) → { } → [ ] (innermost to outermost).
- Brackets: Solve innermost bracket first: ( ), { }, [ ] in that order.
- Vinculum: A bar over an expression acts as a bracket; solve it first.
- Left-to-Right Rule: For operations of same priority (e.g., division and multiplication), work from left to right.
- Nested Brackets: Always simplify the innermost bracket before moving outward.
Introduction · परिचय
BODMAS is a rule used to solve mathematical expressions with multiple operations in a fixed order. It ensures that everyone gets the same answer for the same expression. For SSC MTS, BODMAS is a fundamental topic that tests your ability to simplify numerical expressions accurately and quickly.
BODMAS Rule and Order of Operations
BODMAS stands for Brackets, Orders (powers and roots), Division, Multiplication, Addition, and Subtraction. It defines the sequence in which operations must be performed in an expression. Always start with the innermost bracket and proceed outward. Division and multiplication have equal priority and are performed left to right. Similarly, addition and subtraction have equal priority and are performed left to right.
- Start with innermost bracket
- Solve Orders (powers/roots)
- Perform Division/Multiplication left to right
- Perform Addition/Subtraction left to right
- Final Answer
📐 Formula / Rule Box · सूत्र याद रखो
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
- BODMAS: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
- Brackets: Solve innermost bracket first: ( ), { }, [ ] in that order.
✍️ Solved Example 1 · हल किया हुआ उदाहरण
❓ Question: Simplify: 12 ÷ 3 × 2 + 5 - 4
✅ Solution: 9
💡 Explanation: First, division and multiplication from left to right: 12 ÷ 3 = 4, then 4 × 2 = 8. Now expression is 8 + 5 - 4. Addition and subtraction left to right: 8 + 5 = 13, then 13 - 4 = 9.
Handling Brackets and Nested Operations
Brackets group parts of an expression to be solved first. When brackets are nested, solve the innermost bracket first, then move outward. The order of brackets is: Vinculum (bar) → Parentheses ( ) → Braces { } → Square Brackets [ ]. Sometimes a vinculum (a line over an expression) is used; treat it as the innermost bracket. After removing brackets, apply BODMAS to the remaining expression.
⭐ Key Points · याद रखने वाली बातें
- Bracket Order: Vinculum → ( ) → { } → [ ] (innermost to outermost).
- Vinculum: A bar over an expression acts as a bracket; solve it first.
- Nested Brackets: Always simplify the innermost bracket before moving outward.
✍️ Solved Example 1 · हल किया हुआ उदाहरण
❓ Question: Simplify: 5 + 2 × [3 + {4 - (2 + 1)}]
✅ Solution: 17
💡 Explanation: Innermost bracket: (2+1)=3. Then {4-3}=1. Then [3+1]=4. Now expression: 5 + 2 × 4. Multiplication first: 2×4=8. Then 5+8=13. Wait, check: 5+2×[3+{4-3}] = 5+2×[3+1] = 5+2×4 = 5+8=13. So answer is 13, not 17. Correction: The correct answer is 13.
Practice Questions · खुद हल करके देखो
पहले खुद try karo, phir “Answer dekho” dabakar check karo. 👇
Q1Simplify: 18 ÷ 3 × 2 + 4 - 1
👀 Answer dekho
✅ Answer: 15
💡 Explanation: Division and multiplication left to right: 18÷3=6, then 6×2=12. Now 12+4-1: addition and subtraction left to right: 12+4=16, 16-1=15.
Q2Simplify: 7 + 3 × (10 - 4) ÷ 2
👀 Answer dekho
✅ Answer: 16
💡 Explanation: Bracket first: (10-4)=6. Expression becomes 7 + 3 × 6 ÷ 2. Multiplication and division left to right: 3×6=18, then 18÷2=9. Finally 7+9=16.
Q3Simplify: 20 - [3 + {2 × (5 - 3)}]
👀 Answer dekho
✅ Answer: 13
💡 Explanation: Innermost bracket: (5-3)=2. Then {2×2}=4. Then [3+4]=7. Finally 20-7=13.
⚠️ Common Mistakes · ये गलतियाँ बिल्कुल मत करना
- Ignoring left-to-right rule for same priority: Always perform division and multiplication from left to right, not in any other order.
- Solving brackets in wrong order: Always start with the innermost bracket (vinculum first, then parentheses, braces, square brackets).
- Forgetting to apply BODMAS after removing brackets: After simplifying brackets, continue with orders, then division/multiplication, then addition/subtraction.
⚡ Quick Revision · Exam से पहले 2 मिनट में दोहराओ
- BODMAS Sequence: Brackets → Orders → Division/Multiplication (left to right) → Addition/Subtraction (left to right).
- Bracket Hierarchy: Vinculum → ( ) → { } → [ ] (innermost to outermost).
- Left-to-Right Rule: For operations of equal priority, always work from left to right.