Subtracting Fractions with Like 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 Like 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 that share the same denominator by subtracting the numerators and keeping the denominator.

You have \frac{5}{8} of a cake and eat \frac{2}{8}. Same size slices, so subtract the count: \frac{3}{8} remains.

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: With matching denominators, subtract the numerators while keeping the piece size (denominator) the same.

Common stuck point: Students subtract the denominators too, writing \frac{5}{8} - \frac{2}{8} = \frac{3}{0}.

Sense of Study hint: Cover the denominators with your finger -- subtract only the top numbers, then uncover and keep the bottom number unchanged.

Worked Examples

Example 1

easy
Subtract \frac{7}{10} - \frac{3}{10}.

Solution

  1. 1
    Denominators are equal (10), so subtract only the numerators: 7 - 3 = 4.
  2. 2
    Result: \frac{4}{10}.
  3. 3
    Simplify: \gcd(4, 10) = 2, so \frac{4}{10} = \frac{2}{5}.

Answer

\frac{2}{5}
Subtracting like-denominator fractions mirrors adding them: operate only on the numerators and keep the denominator fixed. Always check whether the result simplifies.

Example 2

medium
A board is \frac{9}{12} of a metre long. A piece of \frac{5}{12} of a metre is cut off. What length remains?

Practice Problems

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

Example 1

easy
Compute \frac{11}{15} - \frac{4}{15}.

Example 2

hard
You need \frac{13}{8} cups of milk for a recipe, but only have \frac{5}{8} of a cup. How much more milk do you need? Express your answer as a mixed number.
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Background Knowledge

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

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