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Add fractions with unlike denominators

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.

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

23+14\frac{2}{3}+\frac{1}{4}

  1. Find a common denominator.
    Multiples of 33 include (3,6,9,12)(3,6,9,12).
    Multiples of 44 include (4,8,12)(4,8,12).
    The least common denominator is (12)(12).

  2. Rewrite each fraction with denominator (12)(12).

23=2×43×4=812\frac{2}{3}=\frac{2\times4}{3\times4}=\frac{8}{12} 14=1×34×3=312\frac{1}{4}=\frac{1\times3}{4\times3}=\frac{3}{12}

  1. Add the numerators and keep the denominator.

812+312=1112\frac{8}{12}+\frac{3}{12}=\frac{11}{12}

So,

23+14=1112\boxed{\frac{2}{3}+\frac{1}{4}=\frac{11}{12}}

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

Learn by doing: Add fractions with unlike denominators

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    Fraction Addition - Basic (Simplifying Answers) - Two Changed Denominators

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