9 5/7 - 3 6/7

To subtract the mixed numbers \( 9 \frac{5}{7} \) and \( 3 \frac{6}{7} \), follow these steps:

1. Convert the mixed numbers to improper fractions.

   • For \( 9 \frac{5}{7} \): \[ 9 \frac{5}{7} = \frac{(9 \times 7) + 5}{7} = \frac{63 + 5}{7} = \frac{68}{7} \]
   • For \( 3 \frac{6}{7} \): \[ 3 \frac{6}{7} = \frac{(3 \times 7) + 6}{7} = \frac{21 + 6}{7} = \frac{27}{7} \]

2. Now subtract the improper fractions: \[ \frac{68}{7} - \frac{27}{7} = \frac{68 - 27}{7} = \frac{41}{7} \]

3. Convert \( \frac{41}{7} \) back to a mixed number:

   • Divide 41 by 7. The quotient is 5 and the remainder is 6.
   • So, \( \frac{41}{7} = 5 \frac{6}{7} \).

Thus, \( 9 \frac{5}{7} - 3 \frac{6}{7} = 5 \frac{6}{7} \).