Skill: Add mixed numbers with like denominators

Explanation and Free Practice Resources

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.

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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:

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

Example:

2\frac{3}{8}+1\frac{6}{8}

Step 1: Add the whole numbers.

2+1=3

Step 2: Add the fractional parts.
The denominators stay $8$ because the pieces are the same size.

\frac{3}{8}+\frac{6}{8}=\frac{9}{8}

Now we have:

3\frac{9}{8}

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

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

Add that extra whole to $3$ :

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

Therefore,

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

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

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