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Fraction Sequences

Fraction Sequences involve patterns where terms are fractions. Patterns can be in numerators (arithmetic progression), denominators (arithmetic progression), both, or the fractional value itself. These problems test your ability to find patterns in rational numbers.

10Worksheets
200+Practice Questions
IntermediateDifficulty
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 Sequences

Fraction Sequences involve patterns where terms are fractions. Patterns can be in numerators (arithmetic progression), denominators (arithmetic progression), both, or the fractional value itself. These problems test your ability to find patterns in rational numbers.

Prerequisites

Fraction operations Numerator and denominator concepts Arithmetic progression Simplifying fractions
Why This Matters: Fraction Sequences problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test pattern recognition with rational numbers.

How to Solve Fraction Sequences Problems

1

Step 1: Separate numerators and denominators into two sequences

2

Step 2: Find the pattern in the numerators (AP, GP, etc.)

3

Step 3: Find the pattern in the denominators

4

Step 4: For next term: apply pattern to numerator and denominator

5

Step 5: Simplify the fraction if needed

6

Step 6: Verify the pattern holds for all given terms

7

Step 7: Present the next term in simplified form

Pro Strategy: Always separate fractions into numerator and denominator sequences. Each may follow its own pattern (often arithmetic progression). Simplify fractions before analyzing if needed.

Example Problem

Example: Find the next term: 1/2, 2/3, 3/4, 4/5, ___ Solution: Step 1: Numerators: 1,2,3,4 (AP with d=1) Step 2: Denominators: 2,3,4,5 (AP with d=1) Step 3: Next numerator = 5, next denominator = 6 Step 4: Next term = 5/6 Answer: 5/6

Pro Tips & Tricks

  • Pattern may be in numerator only (denominator constant)
  • Pattern may be in denominator only (numerator constant)
  • Both numerator and denominator may be in AP
  • Fractional value may form AP or GP
  • Check if fractions simplify to reveal pattern
  • Reciprocals may form a simpler pattern

Shortcut Methods to Solve Faster

If numerators increase by constant, pattern is AP in numerator
If denominators increase by constant, pattern is AP in denominator
Write terms as a single fraction before analyzing
Check if aₙ = (n + a)/(n + b) form

Common Mistakes to Avoid

Not simplifying fractions before analysis
Analyzing fractional value instead of numerator/denominator separately
Missing that both parts follow patterns
Forgetting to simplify final answer

Exam Importance

Fraction Sequences 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
CAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Fraction Sequences?

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

20 practice questions
Detailed solutions
Step-by-step explanations
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