Comparison Examples in Math

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

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 how two quantities relate in terms of size or value, using the symbols <, >, or =.

Which is bigger? Which is smaller? Are they the same? Comparison answers these questions with precision.

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: Comparison establishes relationships between quantities that drive all inequalities.

Common stuck point: Comparing negative numbers or fractions with different denominators.

Sense of Study hint: Convert both numbers to the same form first — common denominators for fractions, or decimals for mixed types — then compare directly.

Worked Examples

Example 1

easy
Compare \dfrac{5}{8} and \dfrac{3}{5}. Which is greater?

Solution

  1. 1
    Find a common denominator: \text{lcm}(8,5) = 40.
  2. 2
    Convert: \dfrac{5}{8} = \dfrac{25}{40} and \dfrac{3}{5} = \dfrac{24}{40}.
  3. 3
    Since 25 > 24, we have \dfrac{25}{40} > \dfrac{24}{40}, so \dfrac{5}{8} > \dfrac{3}{5}.

Answer

\dfrac{5}{8} > \dfrac{3}{5}
To compare fractions with different denominators, rewrite them with a common denominator, then compare numerators directly. The fraction with the larger numerator is the greater fraction.

Example 2

medium
Place -\dfrac{7}{3}, -2.4, -\dfrac{5}{2}, and -2 in order from least to greatest.

Practice Problems

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

Example 1

easy
Insert <, >, or = between each pair: (a) 0.75 and \dfrac{3}{4}, (b) \dfrac{2}{3} and \dfrac{3}{4}.

Example 2

medium
Without a calculator, determine which is larger: \sqrt{50} or 7.1.
← Back to Comparison Formula Explained Practice Mode

Background Knowledge

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

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