Divide \( \frac{5}{8} \div \frac{1}{9} \). Write the answer as a mixed number in lowest terms.

To divide \( \frac{5}{8} \) by \( \frac{1}{9} \), we can multiply \( \frac{5}{8} \) by the reciprocal of \( \frac{1}{9} \). The reciprocal of \( \frac{1}{9} \) is \( 9 \), so we have: \[ \frac{5}{8} \div \frac{1}{9} = \frac{5}{8} \times 9 \] Next, we can express \( 9 \) as a fraction: \[ \frac{5}{8} \times \frac{9}{1} = \frac{5 \times 9}{8 \times 1} = \frac{45}{8} \] Now, let's convert \( \frac{45}{8} \) into a mixed number. We perform the division \( 45 \div 8 \): - \( 8 \) goes into \( 45 \) five times (since \( 8 \times 5 = 40 \)). - The remainder is \( 45 - 40 = 5 \). Thus, we can express \( \frac{45}{8} \) as a mixed number: \[ \frac{45}{8} = 5 \frac{5}{8} \] So, the answer is: \[ 5 \frac{5}{8} \]