That depends on the number.
If it's a whole number, like 311 divided by 12, we're going to have 11 as a remainder (once we do long division), and therefore the remainder will be 11/12.
But if the number is irrational, like 311.27374...and so on, then when you do long division, the remainder will be 11.27374.../12.
12 goes into 300 twenty-five times, giving us a remainder of zero. If the dividend were 312 instead of 300, the answer would be 26 instead of 25, still giving us a remainder of zero. So the largest possible denominator in this problem, 300/12, would occur if the dividend was 311.9999...and so on.
To review long division, you can go over the steps located here: www.mathsisfun.com/long_division.html
