1. **State the problem:** Find the quotient of $$\frac{7}{8} \div \frac{5}{4}$$ and simplify the answer completely. 2. **Recall the rule for dividing fractions:** To divide by a fraction, multiply by its reciprocal. 3. **Apply the rule:** $$\frac{7}{8} \div \frac{5}{4} = \frac{7}{8} \times \frac{4}{5}$$ 4. **Multiply the numerators and denominators:** $$\frac{7 \times 4}{8 \times 5} = \frac{28}{40}$$ 5. **Simplify the fraction:** Find the greatest common divisor (GCD) of 28 and 40, which is 4. 6. **Divide numerator and denominator by 4:** $$\frac{\cancel{28}^{7}}{\cancel{40}^{10}} = \frac{7}{10}$$ 7. **Final answer:** $$\frac{7}{10}$$