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