Skill: Add mixed numbers with like denominators

Explanation and Free Practice Resources

This understanding concerns adding positive mixed numbers whose fractional parts have the same denominator by combining whole-number parts and fractional numerators while preserving the common unit fraction. When the fractional sum is one or more wholes, the excess is regrouped into the whole-number part, with results interpreted as either mixed numbers or improper fractions; unlike denominators, negative values, and more advanced generalizations are not included.

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Detailed Explanation: Add mixed numbers with like denominators

To add mixed numbers with like denominators:

Add the whole-number parts.
Add the numerators, keeping the common denominator.
If the fraction is one whole or more, regroup it as a whole number.

Example:

2\frac{3}{5}+1\frac{4}{5}

Step 1: Add the whole numbers.

2+1=3

Step 2: Add the fractional parts.

The denominators are both $5$ , so keep the denominator and add the numerators:

\frac{3}{5}+\frac{4}{5}=\frac{7}{5}

Step 3: Regroup the improper fraction.

Since $5$ fifths make $1$ whole,

\frac{7}{5}=\frac{5}{5}+\frac{2}{5}=1\frac{2}{5}

Now add that extra whole to the $3$ whole numbers:

3+1\frac{2}{5}=4\frac{2}{5}

Therefore,

\boxed{2\frac{3}{5}+1\frac{4}{5}=4\frac{2}{5}}

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

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