Compensation in Mathematics Explained Clearly

In Mathematics, compensation is a strategy in mental math in which you can change one addend to a multiple of 10 and then adjust the other addend to maintain the balance. For example, in 33 + 12 = ?, if you add 10 in 33, it will become 33 + 10 = 43. Now, you have to add 2 more to maintain balance as 10 is 2 less than 12. Accordingly, 43 + 2 = 45. Hence, on adding 33 and 12, we get the result 45. Compensation in Math is an important strategy to make the equations easier. Also, it enables students to think flexibly about numbers.

Compensation Addition Strategy

Let us understand compensation addition strategy with an example below:

Example:

Add 48 + 36 using the compensation strategy

Solution:

Here, we will first change 48 to a multiple of 10 by adding 2

48 + 2 = 50

Now, we will compensate by taking 2 aways from 36. Accordingly we get:

36 - 2 = 34

Now, we have

50 + 34 = 84

Therefore, 48 + 36 = 84

Remember, it is more efficient to add two digit numbers to the nearest 10.

Compensation Subtraction Strategy

Compensating subtraction means taking away or adding a number to minuend to change to a multiple of 10 and then subtracting or adding the same number from subtrahend to get the difference. Compensation subtraction strategy works using the following equation

Minuend - Subtrahend = Difference

Let us understand compensation subtraction strategy with an example below:

Example 1:

Subtract 74 - 36 using compensation strategy

Solution:

Here, we will first change the minuend 74 to a multiple of 10 by taking away 4.

74 - 4 = 70

Now, we will compensate by subtracting 4 from the subtrahend. Accordingly we get:

36 - 4 = 32

Now, the new expression we have

70 - 32 = 38

Therefore, 74 - 36 = 38

Example 2:

Subtract 57 - 39

Solution:

Here, we will first change the minuend 57 to a multiple of 10 by adding 3 to it.

57 + 3 = 60

Now, we will compensate by adding 3 to the subtrahend. Accordingly we get:

39 + 3 = 42

Now, the new expression we have

60 - 42 = 18

Therefore, 57 - 39 = 18

Compensation Multiplication Strategy

Compensating multiplication strategy means converting the multiplier to a multiple of 10 and multiplying it by a given multiplicand. Further, subtract or add as many lots of the number as you need to maintain the balance. Compensation multiplication strategy works using the following equation.

Multiplicand Multiplier = Product

Example 1:

Multiply 27 → 13 using compensation multiplication strategy.

Solution:

Here, we will first change the multiplier 13 to a multiple of 10 by taking away 3. This gives:

13 → 10

Now, we will multiply the given multiplicand with a new multiplier. Accordingly, the new expression is:

27 → 10 = 270

Now, we will add (27 → 3 = 81) to the product (Note: It is because we have taken 3 from the multiplier to make the equation easier). Accordingly, the equation will be

270 + (27 3 = 81)

= 270 + 81

= 351

Therefore, 27 → 13 = 351

Example 2:

Multiply 14 → 8 using compensation multiplication strategy.

Solution:

Here, we will first change the multiplier 8 to a multiple of 10 by adding 2. This gives:

8 →10

Now, we will multiply the given multiplicand with a new multiplier. Accordingly, the new expression is:

14 →10 = 140

Now, we will subtract (14 → 2 = 28) from the product (Note: It is because we have added 2 to the multiplier to make the equation easier). Accordingly, the equation will be

140 + (14 2 = 28)

= 140 - 28

= 112

Therefore, 14 → 8 = 112