Compensation in subtraction

Quick answer

Compensation in subtraction means making one number easier to work with by adjusting both numbers in the calculation. This helps you subtract more easily, especially with bigger numbers.

Learning outcome

By the end of this page, you will be able to adjust numbers in subtraction problems to make them easier to solve, using the compensation method.

• You can change one or both numbers to make subtraction simpler.
• You understand that adding or subtracting the same amount from both numbers keeps the difference the same.
• You can solve subtraction problems using compensation without needing a calculator.
• You can check if your answer is correct by using the compensation method.

Why this matters

Subtraction can sometimes be tricky, especially when dealing with large numbers or numbers that are not easy to work with. Compensation helps you make these problems simpler by adjusting the numbers to create friendlier values. This method is used in everyday life, such as when you're shopping and need to quickly calculate how much change you should get. It's also helpful when you're doing mental maths and want to make calculations faster and easier.

How it works

Compensation in subtraction works by adding or subtracting the same amount to both numbers in a subtraction problem. This keeps the difference the same, but makes the calculation easier.

1. Choose a subtraction problem, like 73 - 28.
2. Decide how to make one of the numbers friendlier, such as making 28 into 30 by adding 2.
3. Add the same amount to the other number, so 73 becomes 75.
4. Subtract the new numbers, so 75 - 30 = 45.
5. Check your answer by doing the original problem or using the compensation method again.

Examples you can see

Let’s look at a few examples to understand how compensation works:

Example 1: Making the second number friendlier

Problem: 64 - 27

Step 1: Make 27 easier to subtract by adding 3 to it, so 27 becomes 30.

Step 2: Add 3 to 64 too, so 64 becomes 67.

Step 3: Now subtract: 67 - 30 = 37.

Step 4: Check: 64 - 27 = 37. Correct!

Example 2: Making the first number friendlier

Problem: 91 - 48

Step 1: Add 2 to 48 to make it 50.

Step 2: Add 2 to 91 to make it 93.

Step 3: Now subtract: 93 - 50 = 43.

Step 4: Check: 91 - 48 = 43. Correct!

Example 3: Using compensation with larger numbers

Problem: 123 - 58

Step 1: Add 2 to 58 to make it 60.

Step 2: Add 2 to 123 to make it 125.

Step 3: Subtract: 125 - 60 = 65.

Step 4: Check: 123 - 58 = 65. Correct!

Try it as a mini adventure

Adventure: The Treasure Hunt

You are on a treasure hunt! You have a map that shows you need to find a treasure that is hidden 87 steps away from the starting point. However, you also have a clue that says the treasure is 32 steps further than the point where you already walked. How far have you walked so far?

Problem: 87 - 32

Let’s use compensation to solve this:

1. Make 32 easier by adding 2 to it, so it becomes 34.
2. Add 2 to 87 too, so it becomes 89.
3. Subtract: 89 - 34 = 55.
4. So, you have walked 55 steps.

You can check your answer by doing the original problem: 87 - 32 = 55. Correct!

Common mistakes

• Mistake: Forgetting to add or subtract the same amount from both numbers.
• Why it happens: Children may focus only on changing one number and forget that both numbers must change equally.
• Fix: Always double-check that you add or subtract the same amount from both numbers.

• Mistake: Making the wrong number friendlier.
• Why it happens: Sometimes children pick a number that doesn’t make the subtraction easier.
• Fix: Choose the number that will make the calculation simplest, usually the one with a zero or five in the units place.

• Mistake: Not checking the answer after using compensation.
• Why it happens: Children might rush through the problem and skip checking.
• Fix: Always go back and do the original problem to confirm your answer.

Parent and carer guide

Helping your child with compensation in subtraction is about encouraging them to think flexibly about numbers. Here are a few tips:

• Use real-life examples: When shopping, ask your child to calculate how much change you should get using compensation.
• Encourage practice: Give your child a few subtraction problems and ask them to use compensation to solve them.
• Check for understanding: Ask your child to explain their steps. This helps ensure they understand the concept, not just memorise the process.
• Be patient: It may take a few tries for your child to get the hang of compensation. Celebrate small wins and keep practicing.
• Don’t push too hard: If your child is struggling, take a break and try again later. Learning should be fun and not stressful.

Practice questions

1. Use compensation to solve: 62 - 39
2. Use compensation to solve: 75 - 47
3. Use compensation to solve: 83 - 56
4. Use compensation to solve: 94 - 28
5. Use compensation to solve: 112 - 67

Answers:

1. 62 - 39 = 23 (Add 1 to 39 to make 40, add 1 to 62 to make 63. 63 - 40 = 23)
2. 75 - 47 = 28 (Add 3 to 47 to make 50, add 3 to 75 to make 78. 78 - 50 = 28)
3. 83 - 56 = 27 (Add 4 to 56 to make 60, add 4 to 83 to make 87. 87 - 60 = 27)
4. 94 - 28 = 66 (Add 2 to 28 to make 30, add 2 to 94 to make 96. 96 - 30 = 66)
5. 112 - 67 = 45 (Add 3 to 67 to make 70, add 3 to 112 to make 115. 115 - 70 = 45)

FAQ

What is compensation in subtraction?

Compensation in subtraction is a method where you adjust both numbers in a subtraction problem to make it easier to solve. You add or subtract the same amount from both numbers, which keeps the difference the same but makes the calculation simpler.

Why does compensation work?

Compensation works because when you add or subtract the same number to both parts of a subtraction problem, the difference between them stays the same. This makes it easier to calculate mentally.

Can I use compensation with any subtraction problem?

Yes, you can use compensation with any subtraction problem. It is especially helpful when one or both numbers are difficult to subtract directly.

How can I help my child practice compensation?

You can help by giving your child subtraction problems and asking them to solve them using compensation. You can also use real-life situations, like calculating change or distances, to make the concept more relatable.

Is compensation the same as rounding?

No, compensation is different from rounding. Rounding changes one number to make it simpler, while compensation changes both numbers equally to keep the difference the same.