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## Basics on the topicCompensation in Addition

Addition can quickly become confusing. Especially if the addends in the ones place add to a number higher than ten. But there is a strategy that you can follow to make complicated addition operations easier: It’s called compensation.

## Compensation Strategy – Definition

What is compensation? And, how do you use compensation in addition? Let’s look at the definition for the compensation strategy:

Compensation is something given in return for something. In math, we use compensation with numbers. This can be a helpful strategy because it makes the numbers friendlier, or easier to add. However, when using addition compensation with manipulatives, always make sure that whatever you add or subtract to one side, you do the opposite to the other.

Step # What to do
1 Choose which addend to make friendlier,
or easier to add. You can do this by
looking for a zero or five in the ones place.
2 Make sure whatever you do to one addend,
you do the opposite to the other.
3 Create a new equation using the
4 Solve the equation!

## Compensation Math Addition – Example

In this example we are adding nuts and bolts to find out how many materials we have. How can we use the compensation strategy to add his thirty-two nuts and eight bolts?

nuts bolts
32 8

compensation 32 (+3) 8 (-3)
new equation 35 5

We can use compensation to make the new equation, thirty-five plus five which equals forty. Mr. Squeaks has forty materials to work with!

• Step one: choose which addend to make friendlier, or easier to add. You can do this by looking for a zero or five in the ones place.

• Step two: make sure whatever you do to one addend, you do the opposite to the other.

• Step three: create a new equation using the friendlier, or easier addends.

• Step four: solve the new equation!

Looking for extra practice with compensation in addition? After this video check out the interactive exercises and compensation addition worksheet.

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Compensation in Addition .
• ### Identify the equation using the new addends.

Hints

Remember, Imani is subtracting 2 from the number 22. He is adding 2 to the number 5.

Think about the new equation. It will be (22 - 2) plus (5 + 2).

Solution

Now that Imani has used compensation, their new equation is 20 + 7.

They subtracted 2 from 22 to get 20, and added 2 to 5 to get 7.

Now they can add the numbers more easily to make 27!

• ### Show the steps.

Hints

Remember, compensation in math means something is given in return for something else.

If one number is added to a digit, the same number must be subtracted from the second digit.

Look at this example. When adding 25 + 6, we can make 25 more friendly. We can turn 25 into 30 by adding +5, which means we have to subtract -5 from the other addend, 6. The new equation is 30 + 1.

Solution

Mr. Squeaks used compensation to make 36 into a friendly number, 40. He added +4 to 36 (36 + 4 = 40), so he had to subtract -4 from 4 (4 - 4 = 0). The new equation is 40 + 0, which we can solve.

40 + 0 = 40.

• ### Which shows compensation?

Hints

Remember, when using compensation, whatever is added to one addend needs to be subtracted from the other.

Solution

Since Imani is using compensation, they want to make friendly numbers. They see 32, and subtract -2 to create 30. Since -2 was subtracted from one addend, it needs to be added to the other addend, 8. 8 plus +2 creates 10.

The new equation is : 30 + 10, which Imani can use to solve more easily. 30 + 10 = 40

• ### What are the steps taken when using compensation?

Hints

The first step for using compensation is to choose which number to make friendlier.

Once you make one number friendly, you will need to decide which number to subtract from one and add to the other.

Remember, when we say which number is friendlier, we mean which number is easiest to add to.

For example, in 15 + 7, you would choose to add 5 to 15 to make it a friendly 20. From there, you would need to subtract 5 from 7 to even the equation.

Solution

These are the steps used in compensation.

For example, look at 25 + 8.

Step 1: Choose which number to make friendlier. Since 25 ends in a 5, I can add 5 to make it a friendly 30.

Step 2: Add the amount chosen to one number, and subtract the amount chosen from the other. In this example, we add 5 to 25 to make 30 (25 + 5 = 30), and subtract 5 from 8 to make 3 (8 - 5 = 3).

Step 3: Create a new equation using the new addends. The new equation is: 30 + 3

Step 4: Solve the new equation: 30 + 3 = 33

• ### Identify the correct answer.

Hints

Remember, when finding a friendly number, we look at the ones place.

Solution

Numbers that have a zero or five in the ones place are friendly numbers, since many numbers can be easily added to 0 and 5.

• ### Solve the equations.

Hints

When using compensation, remember to make one number a friendly number first.

Compensation means something is given in return for something else. For example:

24 + 7 = ?

We can make 24 more friendly by adding +6 to make 30. Now, because we added 6 to one number, we must subtract 6 from the other. 7 - 6 makes 1.

The new equation is: 30 + 1.

30 + 1 = 31.

Solution

You may have solved these problems the same or differently, there are multiple ways to use compensation.

45 + 7 = 52.

We can make 7 a friendly number by adding +3 to make 10. Now, because we added 3 to one number, we must subtract 3 from the other number, 45. 45 -3 makes 42.

The new equation is: 42 + 10.

We add this new equation more easily to solve the problem: 42 + 10 = 52.

12 + 8 = 20.

We can make the 12 into a friendly 10 by subtracting 2 (12 - 2 = 10). Since we subtracted 2 from one number, we must add 2 to the other (8 + 2 = 10).

The new equation is: 10 + 10.

We use this new equation to solve: 10 + 10 = 20.

7 + 6 = 13

We can make 7 more friendly by adding +3 to make 10. Now, because we added 3 to one number, we must subtract 3 from the other number, 6. 6 - 3 makes 3.

The new equation is 10 + 3.

10 + 3 = 13