(6) \( \frac{5}{8} \div \frac{5}{7}+1 \frac{1}{16} \)

To solve the expression \( \frac{5}{8} \div \frac{5}{7} + 1 \frac{1}{16} \), start by handling the division first. To divide fractions, multiply by the reciprocal: \[ \frac{5}{8} \div \frac{5}{7} = \frac{5}{8} \times \frac{7}{5} = \frac{7}{8} \] Next, convert \( 1 \frac{1}{16} \) to an improper fraction. \[ 1 \frac{1}{16} = 1 + \frac{1}{16} = \frac{16}{16} + \frac{1}{16} = \frac{17}{16} \] Now, add \( \frac{7}{8} \) and \( \frac{17}{16} \). To do this, find a common denominator. The least common multiple of 8 and 16 is 16. Convert \( \frac{7}{8} \) to sixteenths: \[ \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \] Now, add the two fractions: \[ \frac{14}{16} + \frac{17}{16} = \frac{14 + 17}{16} = \frac{31}{16} \] Finally, you can convert \( \frac{31}{16} \) back to a mixed number: \[ \frac{31}{16} = 1 \frac{15}{16} \] So, the final answer is: **\( 1 \frac{15}{16} \)**