Compensation in math

Compensation in math is the process of reformulating an addition, subtraction, multiplication, or division problem to one that can be computed more easily mentally.

Examples of additive compensation

Add 97 + 64

It may not be easy to add 97 and 64 mentally. However, one small adjustment

such as rewriting the problem as 97 + 3 + 61 can help us to get an answer quickly

97 + 3 + 61 = 100 + 61 = 161

Add 25, 27 , and 18

It is not easy to do any of these additions mentally.

25 + 27            25 + 18         27 + 18                             

However, if we take 2 from 27 and add that to 18, the problem becomes

25 + 25 + 20 and this is very easy to do mentally since 25 + 25 = 50 and 50 + 20 = 70

Examples of equal additions method

 The equal additions method is a compensation used when doing subtractions.

Subtract 39 from 57.

57 - 39 can be thought of as  58 - 40

58 - 40 = 18

To make the subtraction 58 - 40, we added 1 to 57 and 39 so that we still have the same subtraction problem.  

Subtract 27 from 33.

33 - 27 can be thought of as 40 - 34 by adding 7 to 33 and 27

40 - 34 = 6 

Examples of multiplicative compensation

Multiply 42 by 5

42 x 5 can be found using multiplicative compensation  as follows

42 x 5 = 21 x 10 = 210

Notice that 42 was divided by 2 and 5 was multipled by 2

Multiply 22 by 25

22 x 25 = 11 x 50 = 550

22 was divided by 2 and 25 by multiplied by 2. 5 times 11 is easy to do. It is 55 Then, all we need to do is to put the 0 next to 55 to get 550

Examples of division compensation

With division compensation, you can divide or multiply both divisor and dividend by the same number.

Divide 84 by 14

84  / 14 is the same as 42 / 7 and if you know your multiplication table, you know that 42 / 7 = 6

Divide 225 by 5

It may be easier to double both numbers

225 / 5 = 450 / 10 = 45