Compatible numbers are numbers that are as close as possible to the original numbers used in an equation while still appropriate for mental computation. Compatible numbers are most often used to estimate the solution of multiplication and division problems.
In multiplication, compatible numbers are those that can be multiplied using a small factor, usually smaller than 10. In finding compatible numbers for multiplication, one number is increased and the other decreased. For example, to estimate the solution of 205 times 39, the student can use the compatible numbers of 200 and 40. Since both numbers end in 0, the student visualizes 20 times 4, which is 80. The student then adds in the zeros removed initially and ends up with an estimate of 8000, which is near the correct answer of 7995.
In division, compatible numbers are those that can be divided and have a whole number solution. Usually, a compatible divisor is less than 10. In finding compatible numbers for division, if one number is increased, the other must be increased as well; the same pattern applies to numbers that are decreased. For example, to estimate to solution of 232 divided by 11, the student can use the compatible numbers of 240 and 12. The student visualizes 24 divided by 12, which is 2, and adds in the zero originally found in the dividend to come up with an estimate of 20. This is close to the correct answer of 19.33.