Mental Subtraction by Compensation

Mental Subtraction by Compensation

Compensation is a mental strategy for subtraction. The idea is to replace the number you are subtracting with a nearby, easier number, then correct the answer for that change.

1) Make the subtrahend friendlier

Choose a number close to the original subtrahend that is easier to subtract mentally. Common choices are round numbers such as 10, 20, 50, or 100.

2) Subtract the friendly number

Work out the easier subtraction first.

3) Correct the result

If you made the subtrahend bigger, your subtraction became too large, so add back the amount you changed. If you made the subtrahend smaller, your subtraction became too small, so subtract the difference.

Example idea

For a subtraction like 63 - 19, you can think of 19 as 20, then correct:

• 63 - 20 = 43
• Since 20 is 1 more than 19, add 1 back: 43 + 1 = 44

Check your answer

Verify by estimating: the result should be a little less than the starting number, not larger. You can also add your answer and the subtrahend to see whether you get the original minuend.