Questions: Perform the indicated operation and simplify. (Enter your answer as a simplified mixed number.) 5/8 ÷ 25/64 × 5/6

Solution Steps

To solve the given expression, we need to follow these steps:

1. Perform the division of the first two fractions.
2. Multiply the result by the third fraction.
3. Simplify the resulting fraction and convert it to a mixed number if necessary.

We start with the expression: \[ \frac{5}{8} \div \frac{25}{64} \] To divide fractions, we multiply by the reciprocal: \[ \frac{5}{8} \times \frac{64}{25} = \frac{5 \times 64}{8 \times 25} = \frac{320}{200} = \frac{8}{5} \]

Next, we multiply the result from Step 1 by the third fraction: \[ \frac{8}{5} \times \frac{5}{6} = \frac{8 \times 5}{5 \times 6} = \frac{40}{30} = \frac{4}{3} \]

The fraction \(\frac{4}{3}\) can be expressed as a mixed number: \[ \frac{4}{3} = 1 \frac{1}{3} \]

Final Answer