Subtracting Fractions with Unlike Denominators Examples in Math

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

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

Concept Recap

Subtracting fractions with different denominators by first rewriting them with a common denominator, then subtracting numerators.

To find \frac{3}{4} - \frac{1}{3}, convert to twelfths: \frac{9}{12} - \frac{4}{12} = \frac{5}{12}. Same idea as addition, just subtract.

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: Rewrite with a common denominator so both fractions refer to same-sized pieces, then subtract the counts.

Common stuck point: Subtracting numerators in the wrong order after converting, leading to negative results unexpectedly.

Sense of Study hint: After converting, write the first fraction's new numerator on top and subtract the second from it -- keep the original order from the problem.

Worked Examples

Example 1

easy
Subtract \frac{3}{4} - \frac{1}{6}.

Solution

  1. 1
    Find the LCD of 4 and 6: \text{LCD} = 12.
  2. 2
    Convert: \frac{3}{4} = \frac{9}{12} and \frac{1}{6} = \frac{2}{12}.
  3. 3
    Subtract: \frac{9}{12} - \frac{2}{12} = \frac{7}{12}.

Answer

\frac{7}{12}
Just as with addition of unlike fractions, you must first find equivalent fractions with a common denominator. Once the pieces are the same size, subtracting numerators gives the result.

Example 2

medium
A runner completed \frac{7}{8} of a race, then stopped. If the race is 1 km long, what fraction of the race is left? If another runner has already finished \frac{2}{5} of the remaining distance, how much of the total race has that runner covered?

Practice Problems

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

Example 1

easy
Compute \frac{5}{6} - \frac{1}{4}.

Example 2

hard
Compute \frac{11}{12} - \frac{3}{8} - \frac{1}{6}.
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Background Knowledge

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

subtracting fractions like denominatorsequivalent fractionsleast common multiple