To estimate numbers using compatible numbers, first round the numbers to even numbers close to them that allow them to be added, subtracted, multiplied or divided mentally. For example, Basic Mathematics presents the problem 232 ÷ 11. Round 232 to 240 and 11 to 12 to provide a user-friendly estimate. 240 ÷ 12 can be easily figured by dividing 24 by 12 to produce 2, then adding a 0 to the end to make the answer 20.
Compatible number estimation problems can be rephrased by asking what number is needed to pair with a given number in order to produce an identified product. Study Zone gives the example of 46 ÷ 6. Rephrase that problem to ask what number, when multiplied by 6, comes closest to 46. By examining the multiplication tables, it is clear that 6 x 8 is 48. Therefore, 46 ÷ 6 is about 8.
Another strategy to using compatible number estimation is to identify the soonest place into which a number can be divided. Study Zone provides the example of 312 ÷ 5. Break 312 down to the hundreds, tens, and ones places. 3, or the hundreds place, cannot be divided by 5, but 31, or the tens place, can. Use the multiplication table to identify the number that, when multiplied by 5, comes closest to 30; the answer is 6. Since only an estimated answer is required, add a 0 to the end, producing the answer of 60.