Ctrl+k

Add mixed numbers with like denominators

A mixed number represents a whole-number quantity together with a fractional part, so adding mixed numbers with a common denominator involves combining whole units and like fractional units, then regrouping an improper fractional sum as an additional whole when needed. Equivalent-fraction and number-line representations support the understanding that the denominator names the unit partition and remains unchanged; unlike denominators, more general fraction algorithms, and negative mixed numbers are outside this scope.

Detailed Explanation: Add mixed numbers with like denominators

A mixed number has a whole-number part and a fractional part. When the denominators are alike:

  1. Add the whole numbers.
  2. Add the numerators, keeping the common denominator.
  3. If the fraction is improper, regroup it as a whole number and a fraction.

Example:

238+1682\frac{3}{8}+1\frac{6}{8}

Step 1: Add the whole numbers.

2+1=32+1=3

Step 2: Add the fractional parts.
The denominators stay 88 because the pieces are the same size.

38+68=98\frac{3}{8}+\frac{6}{8}=\frac{9}{8}

Now we have:

3983\frac{9}{8}

Step 3: Regroup 98\frac{9}{8}.
Since 88=1\frac{8}{8}=1, take out one whole:

98=118\frac{9}{8}=1\frac{1}{8}

Add that extra whole to 33:

3+118=4183+1\frac{1}{8}=4\frac{1}{8}

Therefore,

238+168=418\boxed{2\frac{3}{8}+1\frac{6}{8}=4\frac{1}{8}}

Learn by doing: Add mixed numbers with like denominators

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

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

      ?