1. **State the problem:** Calculate the value of the expression $$\left(\frac{7}{8} + \frac{2}{9}\right) \times \left(3 \times \frac{1}{5}\right)$$. 2. **Use the formula:** To solve, first add the fractions inside the parentheses, then multiply the results. 3. **Add the fractions:** $$\frac{7}{8} + \frac{2}{9} = \frac{7 \times 9}{8 \times 9} + \frac{2 \times 8}{9 \times 8} = \frac{63}{72} + \frac{16}{72} = \frac{79}{72}$$ 4. **Multiply inside the second parentheses:** $$3 \times \frac{1}{5} = \frac{3}{1} \times \frac{1}{5} = \frac{3}{5}$$ 5. **Multiply the two results:** $$\frac{79}{72} \times \frac{3}{5} = \frac{79 \times 3}{72 \times 5} = \frac{237}{360}$$ 6. **Simplify the fraction:** Find the greatest common divisor (GCD) of 237 and 360. - 237 factors: 3 × 79 - 360 factors: 2^3 × 3^2 × 5 Common factor is 3. Divide numerator and denominator by 3: $$\frac{\cancel{3} \times 79}{\cancel{3} \times 120} = \frac{79}{120}$$ 7. **Final answer:** $$\boxed{\frac{79}{120}}$$