Skip to main content
Academy11+

📊 Comparing & Ordering Fractions

Learn to compare fractions and put them in order from smallest to largest. Master different methods for comparing fractions effectively.

Beginner Level
35-45 minutes
Fraction Comparison

What is Comparing Fractions?

Comparing fractions helps us understand which is larger or smaller! 📊

Comparing fractions means determining which fraction represents a larger or smaller part of a whole. This skill is essential for ordering fractions and solving real-world problems involving fractions.

Same Denominator
Easy comparison

When denominators are the same, compare numerators. Larger numerator = larger fraction.

Cross-Multiplication
Universal method

Multiply numerator of first fraction by denominator of second, and vice versa. Compare the results.

Decimal Conversion
Convert and compare

Convert fractions to decimals by dividing numerator by denominator. Compare the decimal values.

Key Concepts

Same Denominator

When denominators are equal, compare numerators. The fraction with the larger numerator is larger.

Cross-Multiplication

Multiply numerator of first fraction by denominator of second, and vice versa. Compare the products.

Decimal Conversion

Convert fractions to decimals by dividing numerator by denominator. Compare the decimal values directly.

Detailed Examples

Example 1: Same Denominator

Compare 3/5 and 4/5

Denominators: Both 5
Numerators: 3 vs 4
Since 4 > 3
Therefore: 4/5 > 3/5
Rule: Larger numerator = larger fraction

Same Denominator Method

• Check if denominators are equal
• Compare numerators directly
• Larger numerator = larger fraction
• Smaller numerator = smaller fraction
• Equal numerators = equal fractions

Example 2: Cross-Multiplication

Compare 2/3 and 3/4

Cross-multiply: 2 × 4 = 8
And: 3 × 3 = 9
Since 9 > 8
Therefore: 3/4 > 2/3
Rule: Larger product = larger fraction

Cross-Multiplication Method

• Multiply numerator of first by denominator of second
• Multiply numerator of second by denominator of first
• Compare the two products
• Larger product = larger fraction
• Works for any two fractions

Example 3: Decimal Conversion

Compare 5/8 and 3/5

Convert 5/8: 5 ÷ 8 = 0.625
Convert 3/5: 3 ÷ 5 = 0.6
Since 0.625 > 0.6
Therefore: 5/8 > 3/5
Rule: Larger decimal = larger fraction

Decimal Conversion Method

• Divide numerator by denominator
• Convert both fractions to decimals
• Compare decimal values
• Larger decimal = larger fraction
• Use calculator for accuracy

Interactive Activities

📊

Activity 1: Fraction Comparator

Compare fractions using different methods.

📈

Activity 2: Fraction Ordering

Order fractions from smallest to largest.

🔢

Activity 3: Decimal Converter

Convert fractions to decimals and compare.

🎯

Activity 4: Comparison Quiz

Test your fraction comparison skills.

Practice Questions

Practise this with a free account

4 practice questions on this topic, from easy to 11+ level. Reading the guide is free for everyone; practice is for members, and signing up is free.

Sign up free to practiseSign in

Tips and Tricks

Same Denominator Method

  • • Check if denominators are equal
  • • Compare numerators directly
  • • Larger numerator = larger fraction
  • • Use this method when possible
  • • Always check your answer

Cross-Multiplication Method

  • • Works for any two fractions
  • • Multiply numerator of first by denominator of second
  • • Multiply numerator of second by denominator of first
  • • Compare the two products
  • • Larger product = larger fraction

Decimal Conversion Method

  • • Divide numerator by denominator
  • • Convert both fractions to decimals
  • • Compare decimal values
  • • Use calculator for accuracy
  • • Larger decimal = larger fraction

Memory Tricks

  • • "Same bottom, compare top"
  • • "Cross-multiply to compare"
  • • "Convert to decimals"
  • • "Same bottom: larger top = larger fraction"
  • • "Always check your answer"