Compatible numbers are useful in estimating the sum, difference, product or quotient of a problem. A compatible number will tend to be one that is very close to the number in the problem, but one which is more convenient and easy to use.
An example of when you might want to use compatible numbers might be when you are required to estimate the answer to the question 29 ÷ 6.5
In this example, the compatible numbers you could use instead of 29 and 6.5 could be 28 and 7. This is because 28 ÷ 7 = 4.
As a result of doing this estimation using compatible numbers, you now know roughly what the answer to the problem 29 ÷ 6.5 is likely to be. If we work out the exact answer to the question, we find out that the actual quotient is 4.46. We can be fairly confident that this is the correct answer as a result of the estimation using compatible numbers that we have already done.