2 3/4+1 1/3

To add the mixed numbers \(2 \frac{3}{4}\) and \(1 \frac{1}{3}\), we first convert them to improper fractions.

1. Convert \(2 \frac{3}{4}\): \[ 2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \]

2. Convert \(1 \frac{1}{3}\): \[ 1 \frac{1}{3} = \frac{(1 \times 3) + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \]

Now, we can add the two improper fractions: \[ \frac{11}{4} + \frac{4}{3} \]

To add these fractions, we need a common denominator. The least common multiple of 4 and 3 is 12.

3. Convert \(\frac{11}{4}\) to a fraction with a denominator of 12: \[ \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12} \]

4. Convert \(\frac{4}{3}\) to a fraction with a denominator of 12: \[ \frac{4}{3} = \frac{4 \times 4}{3 \times 4} = \frac{16}{12} \]

Now, we can add the two fractions: \[ \frac{33}{12} + \frac{16}{12} = \frac{33 + 16}{12} = \frac{49}{12} \]

Finally, convert \(\frac{49}{12}\) back to a mixed number: \[ 49 \div 12 = 4 \quad \text{(whole number)}, \quad \text{remainder } 1 \] Thus, \(\frac{49}{12} = 4 \frac{1}{12}\).

Therefore, the result of \(2 \frac{3}{4} + 1 \frac{1}{3}\) is: \[ 4 \frac{1}{12} \]