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Fraction Operations

Fraction Operations problems require simplifying arithmetic expressions that contain fractions. You must apply BODMAS rules correctly, handling fraction addition, subtraction, multiplication, and division. These problems test your ability to work with fractions and follow order of operations.

10Worksheets
200+Practice Questions
MediumDifficulty
2-3 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Fraction Operations

Fraction Operations problems require simplifying arithmetic expressions that contain fractions. You must apply BODMAS rules correctly, handling fraction addition, subtraction, multiplication, and division. These problems test your ability to work with fractions and follow order of operations.

Prerequisites

Fraction addition and subtraction (finding common denominators) Fraction multiplication and division BODMAS rules Fraction simplification
Why This Matters: Fraction Operations problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test fraction arithmetic and BODMAS application.

How to Solve Fraction Operations Problems

1

Step 1: Identify all operations and brackets in the expression

2

Step 2: Evaluate brackets first (innermost to outermost)

3

Step 3: Within brackets, perform multiplication and division before addition and subtraction

4

Step 4: For fraction multiplication, multiply numerators and denominators

5

Step 5: For fraction division, multiply by reciprocal

6

Step 6: For fraction addition/subtraction, find common denominator

7

Step 7: Simplify the final fraction if possible

8

Step 8: Present the simplified answer

Pro Strategy: Always evaluate brackets first. For addition/subtraction of fractions, find the least common denominator (LCD). For multiplication, multiply numerators and denominators directly. For division, multiply by the reciprocal.

Example Problem

Example: Simplify (1/2 + 1/3) × 3/5 Solution: Step 1: Evaluate bracket: 1/2 + 1/3 = (3+2)/6 = 5/6 Step 2: Then: 5/6 × 3/5 = (5×3)/(6×5) = 15/30 = 1/2 Answer: 1/2

Pro Tips & Tricks

  • LCD for a/b and c/d is LCM(b,d)
  • a/b × c/d = (a×c)/(b×d)
  • a/b ÷ c/d = a/b × d/c = (a×d)/(b×c)
  • Simplify fractions at the end, not after every step
  • Cross-cancel when possible to simplify multiplication
  • Convert mixed numbers to improper fractions first

Shortcut Methods to Solve Faster

Find common denominator before adding/subtracting
Cross-cancel before multiplying fractions
Reciprocal of a/b is b/a
a/b + c/d = (ad + bc)/(bd)
a/b - c/d = (ad - bc)/(bd)

Common Mistakes to Avoid

Adding fractions without common denominator
Forgetting to multiply by reciprocal when dividing
Not simplifying final fraction
Evaluating operations in wrong order (ignoring BODMAS)

Exam Importance

Fraction Operations is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
INSURANCE
1-2 questions

Ready to Master Fraction Operations?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
Start Practicing Now