2/3×(7/5-3/4)

To solve the expression \( \frac{2}{3} \times \left( \frac{7}{5} - \frac{3}{4} \right) \), we first need to compute the difference inside the parentheses: 1. Find a common denominator for \( \frac{7}{5} \) and \( \frac{3}{4} \). The least common multiple of 5 and 4 is 20. 2. Rewrite each fraction with the common denominator: - For \( \frac{7}{5} \): \[ \frac{7}{5} = \frac{7 \times 4}{5 \times 4} = \frac{28}{20} \] - For \( \frac{3}{4} \): \[ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \] 3. Now subtract these two fractions: \[ \frac{28}{20} - \frac{15}{20} = \frac{28 - 15}{20} = \frac{13}{20} \] 4. Next, multiply this result by \( \frac{2}{3} \): \[ \frac{2}{3} \times \frac{13}{20} = \frac{2 \times 13}{3 \times 20} = \frac{26}{60} \] 5. Now simplify \( \frac{26}{60} \): - Both 26 and 60 can be divided by 2: \[ \frac{26 \div 2}{60 \div 2} = \frac{13}{30} \] Thus, the final result is: \[ \frac{13}{30} \]