# Subtraction Using Compensation

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Subtraction Using Compensation
CCSS.MATH.CONTENT.2.OA.A.1

## The Compensation Strategy in Math

We're going to delve into a fascinating mathematical strategy known as the compensation strategy for subtraction. We will review the principles of this strategy in an interactive and engaging manner.

The compensation strategy helps you to move numbers around to make subtraction tasks easier to solve.

## Subtraction Compensation – Method

Compensation is something given in return for something, in math we use this with numbers. It can be a helpful strategy because it makes numbers friendlier, or easier to subtract. When using compensation with subtraction you can decide which number to make friendlier, or easier to subtract, just remember to always;

When using this strategy for subtraction:

Step # What to do
1 choose which numbers to make friendlier, or subtract
2 create a new equation using the new numbers
3 solve the new equation using a tool that works for you
4 the solution to the new equation is also the solution to the original equation!

## Compensation Subtraction Strategy – Example

How can you use compensation with subtraction equations? Take a look at the compensation strategy subtraction activity below. Is there a way to solve this equation using compensation?

Remember to use compensation to make these numbers friendlier, or easier to add.

There are many different ways that you can use compensation with subtraction equations. In this problem, we used compensation to create the new equations thirty-five minus twenty. Thirty-five minus twenty equals fifteen, which means that thirty-three minus eighteen also equals fifteen!

## Compensation Subtraction Strategy – Summary

Well done! You now know how to use compensation in subtraction or by using addition to subtract. Let’s recap the main steps when using compensation strategy in subtraction:

• First: choose which numbers to make friendlier, or subtract

• Then: create a new equation using the new numbers

• Next: solve the new equation using a tool that works for you

• Finally: the solution to the new equation is also the solution to the original equation!

Looking for extra practice? After this video check out our compensation strategy subtraction activities and subtraction compensation strategy worksheets.

## Frequently Asked Questions on Compensation Math

What is the primary advantage of the compensation strategy?
What happens if I make an error while adjusting numbers?

## Subtraction Using Compensation exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Subtraction Using Compensation.
• ### Make the numbers friendlier.

Hints

Numbers that end in 0, like 20, can be easier in subtraction equations.
What do you add to 16 to make 20?

What you do to one number you must also do to the other.
What number did you add to 16 to make it friendlier? Add the same number to 2.

Solution

16 + 4 = 20. Numbers that end in 0, like 20, can be friendlier in subtraction equations.

• 16 is closer to 20 than 10, so add 4 to 16 to make 20.
2 + 4 = 6.
• What you do to one number you must do to the other, so also add 4 to 2 to make 6.
The new equation is 20 - 6.
• 20 - 6 = 14.

• ### Sort the steps for subtracting with compensation.

Hints

First, add or subtract from one number to make it friendlier.

Next, do the same to the other number in the equation.

Third, create a new equation with the new numbers and solve.

The solution for the new equation will be the same as the equation with the original numbers.

Solution
• First, add 5 to 15 to make it friendlier.
• Next, do the same to 24.
• Create a new equation with the new numbers, 29 - 20
• Solve the new equation. The answer is the same for the first equation, 24- 15 = 9.
• ### Determine which equations use compensation, and which do not.

Hints

If something is added to one number in the equation, the same must be added to the other number.

If something is subtracted to one number in the equation, the same must be subtracted from the other number.

This is an example of compensation.

Solution

When using compensation in subtration, what is done to one number must be done exactly the same to the other number in the equation. Addition and subtraction, or different numbers, may not be mixed.

• ### Choose the correct numbers to complete the equations.

Hints

Add or subtract to make one number friendlier. Friendlier numbers usually end in 0 or 5.

What you do to one number, you must do to the other.

Create a new equation using the new numbers, and solve.

The answer for the new equation is the same answer for the original equation.

Solution
• 18 + 2 = 20
• 6 + 2 = 8
• 20 - 8 = 12
• 18 - 6 = 12
• ### Choose the correct numbers to make the equation friendlier.

Hints

For example, if 2 is added to 48 on the left, using compensation, what should be added to the 22 on the right?

For example, when you use compensation, never forget to add the same number to both numbers in the original equation.

Once you have added to both numbers in the equation and made it friendlier, don't forget to solve your new equation!

Solution

35 - 13 = ?

• 35 + 5 = 40
• 13 + 5 = 18
• 40 - 18 = 22

• ### Complete the blanks to solve the equations.

Hints

Friendlier numbers usually end in 0 or 5, such as 5, 10, 15, or 20.

In compensation, whatever is done to one number in the equation, must be done exactly the same to the other.

Solution
• 36 - 25 = ?
• 25 - 5 = 20
• 36 - 5 = 31
• 31 - 20 = 11
• 36 - 25 = 11