Skill: Add fractions with like denominators

Explanation and Free Practice Resources

Like-denominator fractions represent quantities partitioned into the same-sized parts, so their sum combines the counts of those parts while preserving the common denominator; the result may be rewritten as an equivalent fraction in simplest form or as a mixed number when it exceeds one. Number lines and fraction bars show why denominators are not added, a common misconception, and connect the operation to composing a whole. This scope excludes addition with unlike denominators and the more general use of common denominators required for it.

Detailed Explanation: Add fractions with like denominators

When fractions have the same denominator, they are made of the same-sized parts. Add the numerators, which tell how many parts there are, and keep the denominator.

Example:

38+28\frac{3}{8}+\frac{2}{8}
  1. The denominator is 88 in both fractions, so each fraction is divided into eighths.
  2. Add the numerators:
3+2=53+2=5
  1. Keep the common denominator, 88:
38+28=58\frac{3}{8}+\frac{2}{8}=\frac{5}{8}

So, the answer is 58\frac{5}{8}.

Do not add the denominators. The pieces are still eighths, not sixteenths. You are combining the number of same-sized pieces, just as combining 33 eighth-size pieces with 22 eighth-size pieces gives 55 eighth-size pieces.

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


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