In math, compatible numbers are numbers that can be used easily in a mental calculation to estimate a certain result, such as a product or quotient. Compatible numbers are especially useful for division.
Often, people need to compute math in their heads, and using compatible numbers is a convenient method to produce desired results. Compatible numbers can be easily manipulated mentally. For example, the numbers five and twenty-five are compatible, since dividing five into twenty-five is a problem that can easily be solved in one's head (the answer being five). Another example of compatible numbers is four thousand and ten. Multiplying or dividing four thousand by ten is another easy mental calculation – all that needs to be done is add (for multiplication) or drop (for division) a zero from four thousand.
Even numbers that are not necessarily divisible can still be compatible numbers. For example, nine and seventy-one can be considered compatible numbers. Although seventy-one is not divisible by nine, seventy-two is divisible by nine; therefore, a mental calculation of seventy-one divided by nine is approximately equal to eight (the result of dividing seventy-two by nine). The use of compatible numbers allows people to make quicker mental calculations, thus saving time and the need for a calculator.