To subtract these fractions, you need to find a common denominator. In this case, the common denominator is 7.

4 and 4/7 can be written as 4 + 4/7 which is equivalent to 28/7 + 4/7 = 32/7.

Therefore, 4 4/7 is equal to 32/7.

Likewise, 7 9/7 can be written as 7 + 9/7 which is equivalent to 49/7 + 9/7 = 58/7.

Therefore, 7 9/7 is equal to 58/7.

Now subtracting 32/7 from 58/7, we get:

58/7 - 32/7 = 26/7

Therefore, 4 4/7 - 7 9/7 = 26/7.