7/8 as a decimal is 0.875. We get this by dividing 8 into 7000 and moving the decimal point three places to the left. The movement of the decimal point makes up for adding three zeroes to the 7 so that we could divide by 8.
Dividing by 6/9 is the same as dividing by 2/3, which is the same as multiplying by 3/2. If we do this first to the fraction we get 7/8*3/2=21/16; if we multiply 0.875 by 3/2 we get 1.3125, which is of course the same as the fraction 21/16 or 1 5/16.