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## The Compensation Strategy in Maths

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

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

## Subtraction Compensation (Adjusting Numbers) – Method

Compensation is something given in return for something, in maths we use this when adjusting numbers. It can be a helpful strategy because it makes numbers friendlier, or easier to subtract. When adjusting numbers in 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 (Adjusting Numbers) – Example

How can you adjust numbers or 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 or by adjusting numbers?

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

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

## Compensation Subtraction Strategy (Adjusting Numbers) – Summary

Well done! You now know how to use compensation in subtraction or by using addition to adjust numbers to subtract. Let’s recap the main steps when adjusting numbers 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 adjusting numbers compensation strategy subtraction activities and subtraction compensation strategy worksheets.

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

## Subtraction - Adjusting Numbers exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Subtraction - Adjusting Numbers.
• ### How have the numbers been adjusted?

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? Add the same number to 2.

Solution

16 + 4 = 20. Numbers that end in 0, like 20, can be easier 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.
The new equation is 20 - 6.
• 20 - 6 = 14.
• 16 - 2 = 14 as well.

• ### How can we make 24 - 15 easier to solve?

Hints

First, add or subtract from one number to make it easier to work with.

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 easier to work with.
• 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, 29 - 20 = 9 as does 24 - 15 = 9.
• ### Solve 18 - 6 by adjusting the numbers.

Hints

We are making 18 easier to work with. What do we get if we add 2 to 18?

What you do to one number you must do to the other, so what do we get if we add 2 to 6?

The new equation, 20 - 8, has been created. What is the answer?

Solution
• 18 + 2 = 20
• 6 + 2 = 8
• 20 - 8 = 12
• 18 - 6 = 12
• ### How have the equations been adjusted?

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.

In this example, 5 has been added to both 24 and 15 to create the new equation.

Solution

12 - 7 = and 10 - 5 =

• Subtract 2 from 12 to make 10.
• Subtract 2 from 7 to make 5.
• 10 - 5 = 5, 12 - 7 = 5
18 - 16 = and 20 - 18 =
• Add 2 to 18 to make 20.
• Add 2 to 16 to make 18.
• 20 - 18 = 2, 18 - 16 = 2
23 - 16 = and 20 - 13 =
• Subtract 3 from 23 to make 20.
• Subtract 3 from 16 to make 13.
• 20 - 13 = 7, 23 - 16 = 7
27 - 18 = and 30 - 21 =
• Add 3 to 27 to make 30.
• Add 3 to 18 to make 21.
• 30 - 21 = 9, 27 - 18 = 9

• ### How can we make 35 - 13 easier to solve?

Hints

To make 35 easier to work with, we can add something to make 40.

What number would go in this gap 35 + __ = 40.

Remember, whatever is added to one side must also be added to the other side.

For example, if we were solving 48 - 22, we would add 2 to 48 to make 50 so we would also have to add 2 to 22.

Solution

35 - 13 = ?

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

• ### Solve the equations by adjusting the numbers.

Hints

How have the numbers been adjusted to make them easier to work with? What has been subtracted or added?

Use the new numbers to create a new equation and solve.

For example:

12 - 8 = ?
12 - 2 = 10
8 - 2 = 6
10 - 6 = 4
12 - 8 = 4

Solution

1
36 - 25 = ?
25 - 5 = 20
36 - 5 = 31
31 - 20 = 11
36 - 25 = 11

2
48 - 34 = ?
48 + 2 = 50
34 + 2 = 36
50 - 36 = 14
48 - 34 = 14