Add mixed numbers

Adding mixed numbers means combining whole-number units and fractional parts, converting fractions to equivalent forms with a common denominator when needed, and regrouping fractional parts that make one or more additional wholes. The result is expressed as a mixed number or improper fraction in simplest form, with attention to the misconception that unlike denominators can be added directly; this scope concerns positive mixed numbers with ordinary proper fractional parts, not negative, complex, or algebraically generalized cases.

Detailed Explanation: Add mixed numbers

To add mixed numbers:

Add the whole-number parts.
Add the fractional parts. If the denominators are different, rewrite the fractions with a common denominator.
If the fraction sum is greater than or equal to $1$ , regroup it as a whole number and a fraction.
Combine the whole numbers and simplify if needed.

Example

Add:

2\frac{3}{4}+1\frac{5}{6}

Step 1: Add the whole-number parts.

2+1=3

Step 2: Find a common denominator for the fractions.

The least common denominator of $4$ and $6$ is $12$ :

\frac{3}{4}=\frac{9}{12} \qquad\text{and}\qquad \frac{5}{6}=\frac{10}{12}

Now add the fractions:

\frac{9}{12}+\frac{10}{12}=\frac{19}{12}

Do not add unlike denominators directly. The denominator tells the size of the pieces, so the fractions must first have the same denominator.

Step 3: Regroup the improper fraction.

Since $\frac{19}{12}$ is greater than $1$ :

\frac{19}{12}=1\frac{7}{12}

Step 4: Add the extra whole to the whole-number sum.

3+1\frac{7}{12}=4\frac{7}{12}

Therefore,

\boxed{2\frac{3}{4}+1\frac{5}{6}=4\frac{7}{12}}

Learn by doing: Add mixed numbers

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

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