When you're doing division, for example, you make an estimate of the answer by replacing the numbers you're given by compatible numbers which are easier to divide. The result of dividing using compatible numbers gives you some idea of the answer of the result you'll get when you apply division to the numbers you were given. Let's say you're given 4009 divided by 19. Substitute 4000 for 4009 and 20 for 19, because they are close to the numbers you need to divide. 4000/20 is easier to divide, because you can reduce this to 400/2 by losing a zero in the numerator and denominator (easy division by 10). And then divide 2 into 400 giving 200. So the answer to 4009/19 is going to be close to 200. Actually, it's 211. Compatible numbers are just friendlier numbers than the ones you are given to work with, and they should give you confidence when you get the actual answer, because your estimate should be fairly close.