8 1/7-4 4/7: 3 5/8

To solve the expression \( 8 \frac{1}{7} - 4 \frac{4}{7} : 3 \frac{5}{8} \), we first need to convert all mixed numbers to improper fractions.

1. Convert mixed numbers to improper fractions:

   • For \( 8 \frac{1}{7} \): \[ 8 \frac{1}{7} = \frac{8 \times 7 + 1}{7} = \frac{56 + 1}{7} = \frac{57}{7} \]

   • For \( 4 \frac{4}{7} \): \[ 4 \frac{4}{7} = \frac{4 \times 7 + 4}{7} = \frac{28 + 4}{7} = \frac{32}{7} \]

   • For \( 3 \frac{5}{8} \): \[ 3 \frac{5}{8} = \frac{3 \times 8 + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8} \]

2. Substituting back into the expression: \[ \frac{57}{7} - \frac{32}{7} : \frac{29}{8} \]

3. Perform the subtraction: Since both fractions are over the same denominator, we carry out the subtraction: \[ \frac{57}{7} - \frac{32}{7} = \frac{57 - 32}{7} = \frac{25}{7} \]

4. Now, we need to divide \( \frac{25}{7} \) by \( \frac{29}{8} \): Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{25}{7} \div \frac{29}{8} = \frac{25}{7} \times \frac{8}{29} \]

5. Now, we multiply the numerators and the denominators: \[ \frac{25 \times 8}{7 \times 29} = \frac{200}{203} \]

Thus, the final result of the expression \( 8 \frac{1}{7} - 4 \frac{4}{7} : 3 \frac{5}{8} \) is: \[ \frac{200}{203} \]