Skill: Add fractions with unlike denominators

Explanation and Free Practice Resources

Adding fractions with unlike denominators means expressing each fraction in an equivalent form with a common denominator so the addends represent equal-sized parts, then adding the numerators while preserving that unit and simplifying the result. This includes proper fractions and mixed numbers with whole-number denominators, including conversion between mixed and improper forms when useful; adding denominators directly and working with algebraic rational expressions are beyond this scope.

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Detailed Explanation: Add fractions with unlike denominators

To add fractions with unlike denominators, first rewrite them with the same denominator. Then add the numerators and keep the common denominator.

Example: Find

\frac{2}{3}+\frac{1}{4}

Find a common denominator.
Multiples of $3$ include $(3,6,9,12)$ .
Multiples of $4$ include $(4,8,12)$ .
The least common denominator is $(12)$ .
Rewrite each fraction with denominator $(12)$ .

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

\frac{1}{4}=\frac{1\times3}{4\times3}=\frac{3}{12}

Add the numerators and keep the denominator.

\frac{8}{12}+\frac{3}{12}=\frac{11}{12}

So,

\boxed{\frac{2}{3}+\frac{1}{4}=\frac{11}{12}}

Remember: Do not add the denominators. Once the denominators match, add only the numerators.

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Fraction Addition - Basic (No Simplifying Answers) - One Changed Denominator

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