Simplify \( 2 \frac{3}{4} \div 3 \frac{1}{3}+1 \frac{2}{5} \)

To simplify \( 2 \frac{3}{4} \div 3 \frac{1}{3}+1 \frac{2}{5} \), let's first convert all mixed numbers to improper fractions. 1. Convert \( 2 \frac{3}{4} \): \[ 2 \frac{3}{4} = 2 \times 4 + 3 = 8 + 3 = \frac{11}{4} \] 2. Convert \( 3 \frac{1}{3} \): \[ 3 \frac{1}{3} = 3 \times 3 + 1 = 9 + 1 = \frac{10}{3} \] 3. Convert \( 1 \frac{2}{5} \): \[ 1 \frac{2}{5} = 1 \times 5 + 2 = 5 + 2 = \frac{7}{5} \] Now we can rewrite the expression: \[ \frac{11}{4} \div \frac{10}{3} + \frac{7}{5} \] Next, we perform the division by multiplying by the reciprocal: \[ \frac{11}{4} \div \frac{10}{3} = \frac{11}{4} \times \frac{3}{10} = \frac{11 \times 3}{4 \times 10} = \frac{33}{40} \] Now, add \( \frac{33}{40} \) and \( \frac{7}{5} \). First, convert \( \frac{7}{5} \) to have a common denominator of 40: \[ \frac{7}{5} = \frac{7 \times 8}{5 \times 8} = \frac{56}{40} \] Now add the two fractions: \[ \frac{33}{40} + \frac{56}{40} = \frac{33 + 56}{40} = \frac{89}{40} \] Since \( \frac{89}{40} \) is an improper fraction, we can convert it back to a mixed number: \[ \frac{89}{40} = 2 \frac{9}{40} \] So the simplified result of \( 2 \frac{3}{4} \div 3 \frac{1}{3}+1 \frac{2}{5} \) is: \[ \boxed{2 \frac{9}{40}} \]