Skill: Subtract fractions with unlike denominators

Explanation and Free Practice Resources

Subtracting fractions with unlike denominators requires rewriting them as equivalent fractions with a common denominator, because only quantities expressed in the same-sized units can be compared and subtracted. The numerator difference is taken over that denominator, then the result is simplified or expressed as an improper fraction or mixed number; this applies to positive and signed rational fractions at this level, but not to symbolic algebraic fractions or more advanced generalizations.

On this page:

Learn “Subtract fractions with unlike denominators” with a detailed explanation of the concept
Master “Subtract fractions with unlike denominators” with unlimited, free practice problems
Download (or modify) a free worksheet on Subtract fractions with unlike denominators you can use at home or in class with practice problems that scaffold and explore “Subtract fractions with unlike denominators” from different perspectives.
Start working on adaptive units like “Fraction Addition and Subtraction - Advanced” or “Fraction Addition and Subtraction - Intro” that introduce, teach, or practice “Subtract fractions with unlike denominators” to maximize your learning.

Detailed Explanation: Subtract fractions with unlike denominators

To subtract fractions with unlike denominators, first rewrite them with a common denominator. The denominator tells the size of the pieces, so the pieces must be the same size before subtracting.

Example:

\frac{3}{4}-\frac{2}{3}

1. Find a common denominator.
The least common denominator of $4$ and $3$ is $12$ .

2. Rewrite each fraction with denominator $12$ .

\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12}

\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}

3. Subtract the numerators and keep the common denominator.

\frac{9}{12}-\frac{8}{12}=\frac{9-8}{12}=\frac{1}{12}

So,

\boxed{\frac{3}{4}-\frac{2}{3}=\frac{1}{12}}

Remember: Find a common denominator, make equivalent fractions, subtract the numerators, and simplify if possible.

Learn by doing: Subtract fractions with unlike denominators

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Your results

Practice with unlimited practice problems

Fraction Subtraction - Basic (Simplifying Answers) - One Changed Denominator

Earned ?

Download/Modify Free Grade 7 'Subtract fractions with unlike denominators' Worksheet

Print this free 'Subtract fractions with unlike denominators' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.

Units Teaching This Skill

These adaptive units introduce, teach, or reinforce this skill (Subtract fractions with unlike denominators) through scaffolded problems that grow in difficulty as concepts are understood.