3 3/4 + 2 2/3

To convert $3\frac{3}{4}$ to an improper fraction, multiply the whole number (3) by the denominator (4) and add the numerator (3). Keep the same denominator.

$$3\frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$$

To convert $2\frac{2}{3}$ to an improper fraction, multiply the whole number (2) by the denominator (3) and add the numerator (2). Keep the same denominator.

$$2\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$$

The expression becomes:

$$\frac{15}{4} + \frac{8}{3}$$

The least common multiple (LCM) of 4 and 3 is 12.
Convert each fraction to an equivalent fraction with a denominator of 12.
For $\frac{15}{4}$, multiply the numerator and denominator by 3:

$$\frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}$$

For $\frac{8}{3}$, multiply the numerator and denominator by 4:

$$\frac{8}{3} = \frac{8 \times 4}{3 \times 4} = \frac{32}{12}$$

The expression becomes:

$$\frac{45}{12} + \frac{32}{12}$$

Now that the fractions have a common denominator, add their numerators.

$$\frac{45}{12} + \frac{32}{12} = \frac{45 + 32}{12} = \frac{77}{12}$$

Divide the numerator (77) by the denominator (12).

$$77 \div 12 = 6 \text{ with a remainder of } 5$$

So, $\frac{77}{12}$ can be written as $6\frac{5}{12}$.