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Mathematical Operations

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Mathematical Operations

📋 Quick-reference guides with key formulas and must-know concepts. Perfect for daily practice, last-minute revision, and on-the-go learning.

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Mathematical Operations – Cheat Sheet

Mathematical Operations is an important topic in Logical Reasoning and Quantitative Aptitude, frequently tested in SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.

This cheat sheet helps candidates solve mathematical operation problems involving BODMAS/PEMDAS rules, symbolic operations, coded operations, operation substitution, operation interchange, equation solving, inequality problems, and missing operator questions. It covers shortcut techniques for quick and accurate problem-solving.

About This Cheat Sheet

Complete guide to Mathematical Operations for competitive exams:

BODMAS/PEMDAS

  • Brackets First
  • Orders/Exponents
  • Division & Multiplication
  • Addition & Subtraction

Symbolic Operations

  • +, -, ×, ÷
  • =, ≠, <, >
  • ≤, ≥
  • Operator Meanings

Coded Operations

  • Symbols Representing Operations
  • Finding Symbol Meanings
  • Decoding Codes
  • Applying Rules

Operation Substitution

  • Replacing One Operation
  • Swapping Two Operations
  • Effect on Result
  • Equation Modification

Equation Solving

  • Finding Unknown Values
  • Simple Equations
  • Combined Operations
  • Verification

Inequality Problems

  • <, >, ≤, ≥
  • Finding Relationships
  • Comparing Expressions
  • Logical Deduction

Missing Operator

  • Finding Correct Operator
  • Equation Completion
  • Expression Verification
  • Operator Puzzles

Shortcut Techniques

  • Quick Verification
  • Elimination Method
  • BODMAS Tricks
  • Exam-Oriented Tips

Topics Covered

This cheat sheet covers all important Mathematical Operations topics for quick revision:

Topic Description Key Rule / Example
BODMAS/PEMDAS Order of operations: Brackets, Orders, Division, Multiplication, Addition, Subtraction (2+3)×4 = 20
Symbolic Operations Using +, -, ×, ÷, =, ≠, <, >, ≤, ≥ a + b = c means a plus b equals c
Coded Operations Symbols representing operations @ means +, # means -, & means ×
Operation Substitution Replacing one operation with another a + b → a - b
Operation Interchange Swapping two operations a + b × c → a × b + c
Equation Solving Finding unknown values x + 5 = 10 → x = 5
Inequality Problems Using <, >, ≤, ≥ 2x + 3 > 7 → x > 2
Missing Operator Finding the correct operator 6 ? 3 = 18 → ×
Digit Operations Forming numbers, digit values 2 + 3 = 5

Key Rules & Reference Tables

BODMAS Rule

StepOperationExample
1Brackets (B)(2+3) = 5
2Orders/Exponents (O)2² = 4
3Division (D)6÷3 = 2
4Multiplication (M)2×3 = 6
5Addition (A)2+3 = 5
6Subtraction (S)5-2 = 3

Coded Operations

CodeMeaningExample
@+ (Addition)A @ B = A + B
#- (Subtraction)A # B = A - B
&× (Multiplication)A & B = A × B
$÷ (Division)A $ B = A ÷ B
%= (Equal to)A % B = A = B

Operation Substitution

OriginalSubstitutedEffect
+-a + b → a - b
-×a - b → a × b
×÷a × b → a ÷ b
÷+a ÷ b → a + b

Inequality Symbols

SymbolMeaningExample
<Less thana < b
>Greater thana > b
≤Less than or equal toa ≤ b
≥Greater than or equal toa ≥ b
=Equal toa = b
≠Not equal toa ≠ b

Why This Cheat Sheet is Important

Master BODMAS Rules

Apply the correct order of operations to solve complex expressions accurately.

Decode Coded Operations

Learn to interpret symbols representing operations and apply them correctly.

Solve Equations Fast

Find unknown values and verify equations using logical reasoning.

High Exam Weightage

Mathematical Operations questions appear frequently in all competitive exams.

Competitive Exams Covered

  • SSC CGL
  • SSC CHSL
  • SSC MTS
  • Bank PO & Clerk
  • IBPS Exams
  • Railway Recruitment Exams
  • UPSC CSAT
  • Defence Exams
  • Insurance Exams
  • CAT
  • State Government Exams

Quick Exam-Oriented Examples

Question 1:

Solve: 2 + 3 × 4 = ?

Step 1: Apply BODMAS: Multiplication before Addition.

Step 2: 3 × 4 = 12

Step 3: 2 + 12 = 14

Answer: 14

Question 2:

Solve: (2 + 3) × 4 = ?

Step 1: Apply BODMAS: Brackets first.

Step 2: (2 + 3) = 5

Step 3: 5 × 4 = 20

Answer: 20

Question 3:

If @ means +, # means -, & means ×, and $ means ÷, then find: 4 @ 6 # 2 & 3 = ?

Step 1: Replace symbols: 4 + 6 - 2 × 3

Step 2: Apply BODMAS: 2 × 3 = 6

Step 3: 4 + 6 - 6 = 4

Answer: 4

Question 4:

If '+' means '×' and '×' means '+', then find: 4 + 3 × 2 = ?

Step 1: Replace symbols: + → ×, × → +

Step 2: 4 + 3 × 2 becomes 4 × 3 + 2

Step 3: Apply BODMAS: 4 × 3 = 12, then 12 + 2 = 14

Answer: 14

Question 5:

If '+' and '-' are interchanged and '×' and '÷' are interchanged, then find: 4 + 6 - 2 × 3 ÷ 6 = ?

Step 1: Interchange: + ↔ -, × ↔ ÷

Step 2: 4 - 6 + 2 ÷ 3 × 6

Step 3: Apply BODMAS: 2 ÷ 3 × 6 = (2/3) × 6 = 4

Step 4: 4 - 6 + 4 = 2

Answer: 2

Question 6:

Find the value of x: x + 5 = 12

Step 1: x + 5 = 12

Step 2: Subtract 5 from both sides: x = 12 - 5

Step 3: x = 7

Answer: 7

Question 7:

Find the value of x: 3x + 4 = 19

Step 1: 3x + 4 = 19

Step 2: Subtract 4: 3x = 15

Step 3: Divide by 3: x = 5

Answer: 5

Question 8:

Which of the following is true for x = 3?

A) 2x + 1 > 7    B) 2x + 1 < 7    C) 2x + 1 = 7

Step 1: Substitute x = 3 in 2x + 1: 2(3) + 1 = 7

Step 2: Check options: 2x + 1 = 7 is true.

Answer: C) 2x + 1 = 7

Question 9:

Which operator should replace '?' to make the equation true?

6 ? 3 = 18

Step 1: Check options: 6 + 3 = 9, 6 - 3 = 3, 6 × 3 = 18, 6 ÷ 3 = 2

Step 2: 6 × 3 = 18 ✓

Answer: × (Multiplication)

Question 10:

Find the value of x: (x + 3) × 2 = 16

Step 1: (x + 3) × 2 = 16

Step 2: Divide by 2: x + 3 = 8

Step 3: Subtract 3: x = 5

Answer: 5

Question 11:

Solve: 8 ÷ 4 × 2 + 6 - 3 = ?

Step 1: Apply BODMAS: Division and Multiplication before Addition and Subtraction.

Step 2: 8 ÷ 4 = 2

Step 3: 2 × 2 = 4

Step 4: 4 + 6 - 3 = 7

Answer: 7

Final Takeaway

Mathematical Operations questions test your ability to apply BODMAS rules, decode coded operations, perform operation substitution and interchange, solve equations, and find missing operators. The key is to follow the correct order of operations and apply logical reasoning to decode symbols and patterns.

Regular practice of BODMAS problems, coded operations, equation solving, inequality problems, and missing operator questions will significantly improve your speed and accuracy. This cheat sheet serves as a complete revision resource for mastering Mathematical Operations questions in competitive examinations.

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Explore BODMAS rules, symbolic operations, coded operations, operation substitution, operation interchange, equation solving, inequality problems, missing operator puzzles, and shortcut techniques in one place for quick and effective revision.

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