Inverse operations

Quick answer

Inverse operations are maths operations that undo each other. Addition and subtraction are inverse operations, and multiplication and division are inverse operations.

Learning outcome

By the end of this page, you will understand how inverse operations work and be able to use them to check your maths.

• You can use subtraction to check addition.
• You can use division to check multiplication.
• You can spot when two operations are inverse.
• You can use inverse operations to solve simple problems.

Why this matters

Understanding inverse operations helps you check your answers and solve problems more easily. You already use them every day without realising it!

In school, inverse operations help you solve equations and check if your answers are right. In real life, they help you work out how much money you have left after spending, or how many items you started with after some were taken away.

As you get older, inverse operations become the foundation for algebra. You'll learn to use them to solve more complex problems and find missing numbers in equations.

How it works

Think of inverse operations like a seesaw. If you go up, you go down. If you add, you subtract. If you multiply, you divide.

Here's how to think about it:

1. When you do something to a number, the inverse operation does the opposite.
2. If you add 5 to a number, you can take away 5 to get back to the original number.
3. If you multiply a number by 3, you can divide by 3 to get back to the original number.

This is like having a magic key that unlocks your answer!

Examples you can see

Let's look at some simple examples:

Example 1: Addition and Subtraction

If you have 7 apples and get 3 more, you have 10 apples.

7 + 3 = 10

To check this, you can subtract:

10 - 3 = 7

You're back to where you started!

Example 2: Multiplication and Division

If you have 4 boxes with 6 toys in each box, you have 24 toys.

4 × 6 = 24

To check this, you can divide:

24 ÷ 6 = 4

You're back to the number of boxes!

Example 3: Working Backwards

You had some money. You spent £8 and now have £5 left.

To find how much you started with, you can add:

5 + 8 = 13

You started with £13.

Example 4: Checking Your Work

You calculated 12 × 5 = 60.

To check, divide:

60 ÷ 5 = 12

You're back to your original number!

Try it as a mini adventure

The Mystery Box Challenge

You're on a treasure hunt! You find a box with a note: "I started with some coins. I added 15 more coins. Now I have 32 coins. How many did I start with?"

Let's solve this together!

4th time: You need to work backwards using the inverse operation.

5th time: If you added 15, you must subtract 15 to find the original amount.

6th time: 32 - 15 = ?

7th time: You started with 17 coins!

8th time: Great job! You found the first clue!

9th time: Now you have 17 coins. You spend 7 coins on a map. How many do you have left?

10th time: Use subtraction to check: 17 - 7 = 10 coins left.

Common mistakes

• Mistake: Using the wrong inverse operation
• Why it happens: Confusing which operation is the opposite
• Fix: Remember that addition and subtraction are inverses, and multiplication and division are inverses

• Mistake: Forgetting to check your answer
• Why it happens: Rushing through problems
• Fix: Always use the inverse operation to verify your answer

• Mistake: Thinking inverse operations only work with numbers
• Why it happens: Not seeing the bigger picture
• Fix: Remember that inverse operations work with any maths problem

Parent and carer guide

Helping your child understand inverse operations is easy and fun!

5-minute tips:

1. Ask your child to explain how they checked their maths today
2. Use real-life examples like shopping or cooking
3. Play the "magic key" game: Do something, then ask them to undo it
4. Practice checking answers together
5. Don't worry if they make mistakes - they're part of learning!

When your child is learning inverse operations:

• Be patient and encouraging
• Use everyday situations to show how it works
• Don't rush - let them think through problems
• Remember that inverse operations are just "undoing" what you did

Practice questions

1. If 8 + 5 = 13, what is 13 - 5?
2. If 6 × 7 = 42, what is 42 ÷ 7?
3. If 15 - 9 = 6, what is 6 + 9?
4. If 9 × 4 = 36, what is 36 ÷ 4?
5. If 20 + 12 = 32, what is 32 - 12?
6. If 8 × 6 = 48, what is 48 ÷ 6?
7. If 18 - 7 = 11, what is 11 + 7?
8. If 5 × 9 = 45, what is 45 ÷ 9?
9. If 25 + 15 = 40, what is 40 - 15?
10. If 7 × 8 = 56, what is 56 ÷ 8?

Answers:

1. 8
2. 6
3. 15
4. 9
5. 20
6. 8
7. 18
8. 5
9. 25
10. 7

FAQ

What are inverse operations?

Inverse operations are maths operations that undo each other. Addition and subtraction are inverse operations, and multiplication and division are inverse operations.

Why do we need inverse operations?

Inverse operations help us check our answers and solve problems more easily. They're like magic keys that help us get back to where we started.

Can you give me more examples?

Yes! If you multiply by 3, you can divide by 3 to get back to your original number. If you subtract 5, you can add 5 to get back to your original number.

Do inverse operations only work with numbers?

No! Inverse operations work with any maths problem. They help you understand how to undo any operation.

How can I practice inverse operations at home?

Try checking your maths homework with inverse operations. You can also play games where you do something and then undo it, like adding coins and then taking some away.