Comparing Fractions Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Comparing Fractions.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Determining which of two fractions is greater, less, or equal using common denominators, benchmarks, or cross-multiplication.

To compare \frac{3}{4} and \frac{5}{6}, rewrite them with the same denominator so the numerators can be compared directly.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Fractions can only be directly compared when they refer to same-sized pieces (common denominator) or are related to a known benchmark like \frac{1}{2}.

Common stuck point: Students assume the fraction with the larger denominator is always larger.

Sense of Study hint: Compare each fraction to 1/2 first: if one is above 1/2 and the other below, you already know the answer.

Worked Examples

Example 1

easy
Compare \frac{4}{7} and \frac{3}{7} using the <, >, or = symbol.

Solution

  1. 1
    The denominators are the same (7), so the pieces are the same size.
  2. 2
    Compare the numerators: 4 > 3.
  3. 3
    Therefore \frac{4}{7} > \frac{3}{7}.

Answer

\frac{4}{7} > \frac{3}{7}
When two fractions have identical denominators, they represent the same size pieces. The fraction with the larger numerator is greater because it contains more of those equal-sized pieces.

Example 2

medium
Compare \frac{5}{9} and \frac{7}{12} using a common denominator.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Compare \frac{2}{3} and \frac{3}{4} using cross-multiplication.

Example 2

hard
Without finding a common denominator, use benchmark reasoning to compare \frac{11}{20} and \frac{8}{15}.
← Back to Comparing Fractions Formula Explained Practice Mode

Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsequivalent fractions