At the malt shop a large chocolate shake takes 8/9 of a pint of milk. if the medium shake takes 1/7 the amount of a large, how much does the medium shake take?

8/9 + 1/7= 56/63 + 9/63= 56+9= 65/63 = 1  2/63     
it equals 1 and 2 over 63

First, we need to make the denominators equal. An easy way to do this is to multiply the 2 denominators together. 7x9= 63. So now the denominators are 1/63 and 8/63, but now we need to fix the numerators. since we multiplied 7 by 9 we should also multiply 1 by 9. This makes the medium shake 9/63 the amount of a large. For the large shake we multiplied 9 by 7 so we should multiply 8 by 7. This makes the large shake. 56/63

Now we have 56/63-8/63 easier seen as 56-8 with a denominator of 63.

After subtracting we can see that a medium shake uses 48/63 pints of milk.
But we aren't done yet. Now we need to simplify. I am assuming you can do that.

The answer is 16/21 pints of milk to create a medium shake.