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Subtract fractions with unlike denominators

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.

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:

34−23\frac{3}{4}-\frac{2}{3}

1. Find a common denominator.
The least common denominator of 44 and 33 is 1212.

2. Rewrite each fraction with denominator 1212.

34=3×34×3=912\frac{3}{4}=\frac{3\times3}{4\times3}=\frac{9}{12} 23=2×43×4=812\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12}

3. Subtract the numerators and keep the common denominator.

912−812=9−812=112\frac{9}{12}-\frac{8}{12}=\frac{9-8}{12}=\frac{1}{12}

So,

34−23=112\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

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

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