Not all numbers are easy to calculate in your head, even for simple addition or subtraction. Generally, it is relatively easy to perform calculations with numbers that have few digits and end in a 5, or numbers with many 0 digits. But when the number is large with multiple digits and does not end in a round number, compatible numbers help with quick calculations. For example, 1,013 - 356 is not easy to calculate quickly in your head.
Compatible number estimation is a simple form of rounding. When challenging numbers are encountered, simply round those numbers to near whole numbers that are easy to work with. For example, 1,013 can be rounded down to 1,000, and 356 can be rounded down to 350.
The compatible numbers should make the operation easy to do in your head without a calculator. The result will be an estimated answer that is close to the actual answer. For example, 1,000 - 350 = 650, which is an estimated answer.
Often, the estimated answer can be used to solve a multiple-choice question. Depending on how you round the numbers in your problem, you can guess what the answer may be. For example, since both 1,013 and 356 have to be rounded down to obtain the answer 650, you can guess that the true answer will be close to but a little higher than 650. If two of the multiple choices are 648 and 657, you can guess that the answer is 657 because it is slightly higher than 650.
To find the actual value of the answer, simply account for how much you originally changed the numbers. For example, you subtracted 13 from 1,013 and 6 from 356. Subtract 6 from 13 and add the difference to your estimated answer: 13 - 6 = 7 and 650 + 7 = 657.
Another type of compatible numbers used in addition and subtraction are numbers that come together to form a nice, round number. These round numbers usually end in 5 or 0. For example, because 16 and 34 come together to form 50, they are considered compatible pairs. Knowing how numbers come together helps you subtract more difficult numbers. For example, if you know that 7 and 8 come together to form 15, you can figure out that any number ending in 7 that is subtracted by a number with a final digit of 5 will result in a number with a final digit of 8. For example, 35 - 17 = 18.