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Add mixed numbers with like denominators

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.

Detailed Explanation: Add mixed numbers with like denominators

To add mixed numbers with like denominators:

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

Example:

235+1452\frac{3}{5}+1\frac{4}{5}

Step 1: Add the whole numbers.

2+1=32+1=3

Step 2: Add the fractional parts.

The denominators are both 55, so keep the denominator and add the numerators:

35+45=75\frac{3}{5}+\frac{4}{5}=\frac{7}{5}

Step 3: Regroup the improper fraction.

Since 55 fifths make 11 whole,

75=55+25=125\frac{7}{5}=\frac{5}{5}+\frac{2}{5}=1\frac{2}{5}

Now add that extra whole to the 33 whole numbers:

3+125=4253+1\frac{2}{5}=4\frac{2}{5}

Therefore,

235+145=425\boxed{2\frac{3}{5}+1\frac{4}{5}=4\frac{2}{5}}

Learn by doing: Add mixed numbers with like denominators

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

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