Subtraction Using Compensation
Basics on the topic Subtraction Using Compensation
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 thirtyfive minus twenty. Thirtyfive minus twenty equals fifteen, which means that thirtythree 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
Transcript Subtraction Using Compensation
To make their board game come to life, Mr. Squeaks invented a machine to teleport himself and Imani into Land O'Sweets! They land on the island in Lilly's Lolly Lake and notice a sign! : "Like lollie's, life can be sweet, solve this problem for a very nice treat!" While Mr. Squeaks and Imani try to win the game, let's help them learn about "subtraction using compensation". One way to solve subtraction equations is called compensation. Compensation is something given in return for something, in math we use this with numbers. It can be a helpful strategy to add or subtract because it makes the numbers friendlier, or, easier to subtract. When subtracting using compensation... Start by adding or subtracting to make one of the numbers friendlier. Whatever you do on one side you must do to the other side as well. Mr. Squeaks and Imani need to solve twentyfour minus fifteen to get a sweet treat from Lilly! When using compensation, first choose which number to make friendlier. Here, we can take fifteen and add five (...) to make it twenty. Since we added five to fifteen, we MUST add five to twentyfour. What is twentyfour plus five? (...) twentynine! Next, create a new equation using the new numbers. Our new equation is twentynine minus twenty. Finally, solve the new equation using a tool or strategy that works for you. Here, we can count back by tens! What is twentynine minus twenty? (...) Nine! That means twentyfour minus fifteen ALSO equals nine. : "Look Imani, a boat! Our sweet treat is a ride to the next challenge!" Mr. Squeaks and Imani have made it to Minty's Mansion! But, in order to unlock the gate and go through they must solve another problem! Let's use subtraction with compensation to help them. They need to solve thirtythree minus eighteen. Remember, start by choosing which number to make friendlier. Here we can add two (...) to thirtythree to make it thirtyfive. Since we added two (...) to thirtythree, we MUST add two to eighteen to make it twenty. Next, create a new equation using the new numbers. Our new equation is thirtyfive minus twenty. Finally, solve by counting back by tens! What is thirtyfive minus twenty? (...) fifteen! That means thirtythree minus eighteen ALSO equals fifteen. : "We did it! We got the gate opened!" : "What is that sign over there though? Secret passage... is it... a shortcut?" : "If a secret tunnel is what you need, solve this problem to find some speed." How can Mr. Squeaks and Imani use compensation to solve fortyeight minus twentytwo? (...) Start by adding or subtracting to make one of the numbers friendlier. Here we can add two (...) to fortyeight to make it fifty. Since we added two (...) to fortyeight we MUST add two to twentytwo to make it twentyfour! Next, create a new equation with the new numbers. Our new equation is fifty minus twentysix. Finally, solve by counting back by fives! What is fifty minus twentyfour? (...) twentysix! Before we see if Mr. Squeaks and Imani won the game, let's review! When using compensation in subtraction... First choose which number to make friendlier. Whatever you do to one number MUST be done to the other. Next, create a new equation using the new numbers. Finally, solve the new equation using a tool or strategy that works for you. Now, let's see if they won! : "We did it, Imani! Let's go home!" : "That was fun but I'm glad to be home!" Mr. Squeaks]: "It sure was SWEET!"
Subtraction Using Compensation exercise

Make the numbers friendlier.
HintsNumbers 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.Solution16 + 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.
 What you do to one number you must do to the other, so also add 4 to 2 to make 6.
 20  6 = 14.

Sort the steps for subtracting with compensation.
HintsFirst, 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.
HintsIf 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.
SolutionWhen 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.
HintsAdd 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.
HintsFor 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!
Solution35  13 = ?
 35 + 5 = 40
 13 + 5 = 18
 40  18 = 22

Complete the blanks to solve the equations.
HintsFriendlier 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
Subtract By Adding
Using Place Value to Subtract Two Digit Numbers (No Regrouping)
Subtraction Using Compensation
Missing Numbers in Subtraction—Let's Practice!
Subtract Using Addition — Let's Practice!
Make a Number Line to Subtract — Let's Practice!
Subtraction Using Compensation — Let's Practice!