Ordering Fractions Examples in Math

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

Arranging three or more fractions from least to greatest (or greatest to least).

Convert all fractions to a common denominator and then read off the order from the numerators.

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: Finding a common denominator turns fraction ordering into simple whole-number ordering of numerators.

Common stuck point: Choosing an efficient common denominator when ordering many fractions.

Sense of Study hint: Convert each fraction to a decimal by dividing top by bottom, then sort the decimals -- it's often faster than finding a common denominator.

Worked Examples

Example 1

easy
Order \frac{1}{2}, \frac{1}{3}, and \frac{1}{4} from least to greatest.

Solution

  1. 1
    All fractions have numerator 1 (unit fractions). Larger denominator \Rightarrow smaller piece.
  2. 2
    Order of denominators from largest to smallest: 4 > 3 > 2.
  3. 3
    So the fractions from least to greatest: \frac{1}{4} < \frac{1}{3} < \frac{1}{2}.

Answer

\frac{1}{4} < \frac{1}{3} < \frac{1}{2}
For unit fractions (numerator = 1), the fraction with the largest denominator is the smallest because you are dividing a whole into more pieces. This is a useful shortcut that applies only when numerators are equal.

Example 2

medium
Order \frac{5}{6}, \frac{3}{4}, \frac{7}{12}, and \frac{2}{3} from least to greatest.

Practice Problems

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

Example 1

easy
Order \frac{2}{5}, \frac{3}{10}, and \frac{1}{2} from greatest to least.

Example 2

hard
Arrange \frac{4}{9}, \frac{5}{12}, \frac{7}{18}, and \frac{11}{36} from least to greatest.
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Background Knowledge

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

fraction comparison