Skill: Add mixed numbers

To add mixed numbers:

1. Add the whole-number parts.
2. Add the fractional parts. If the denominators are different, rewrite the fractions with a common denominator.
3. If the fraction sum is greater than or equal to $1$, regroup it as a whole number and a fraction.
4. 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,

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