Skill: Add fractions with like denominators

Explanation and Free Practice Resources

The learner understands that fractions with the same denominator name equal-sized parts of the same whole, so their sum is found by combining the numerators while retaining the common denominator; a number line or area model shows this as joining quantities measured in the same fractional unit. The reasoning includes simplifying or expressing results as mixed numbers when appropriate, including sums greater than one, but does not extend to adding fractions with unlike denominators.

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Detailed Explanation: Add fractions with like denominators

When fractions have the same denominator, they name equal-sized parts of the same whole. Add the numerators and keep the common denominator.

Example:

\frac{3}{8}+\frac{7}{8}

Each fraction is measured in eighths, so combine the eighths:

\frac{3+7}{8}=\frac{10}{8}

There are $10$ eighths. Since $8$ eighths make one whole, regroup:

\frac{10}{8}=\frac{8}{8}+\frac{2}{8}=1\frac{2}{8}

Simplify $\frac{2}{8}$ to $\frac{1}{4}$ :

\frac{3}{8}+\frac{7}{8}=1\frac{1}{4}

The denominator stayed $8$ because the size of each part did not change; we only combined the number of eighths.

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

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