 Inverse Operations

In this worksheet, students will practise using inverse operations. Key stage:  KS 4

Curriculum topic:

Curriculum subtopic:

Difficulty level:   QUESTION 1 of 10

Inverse operations are really important in maths, for example when you have to solve equations (which is a huge topic), you can't do it without these inverse operations.

Inverse operations require us to do the opposite.

The opposite of + is -

The opposite of - is +

The opposite of x is ÷

The opposite of ÷ is x

Examples:

What is the opposite of +7?

Ans: -7

What is the opposite of dividing by 2?

And: Multiplying by 2

I add 7 and then multiply by 2. If my answer is 18, what was my original number?

This one is a bit more challenging. We have two operations, + 7 and x 2. The inverse operations for these would be - 7 and ÷ 2

But which one do we use first?

If we are doing the opposites, we are going backwards. In the question, we added 7 first then multiplied by 2. When we are doing the inverse, we swap this order as well.

Do to solve this we divide by 2 first, then subtract 7.

18 ÷ 2 = 9

9 - 7 = 2

Now it's your turn to have a go!

The inverse of + 4 is...

The inverse operation of ÷ 6 is...

Match the operations with their inverses.

Column B

+ 2
- 2
- 6
+ 6
x 5
x 3
÷ 3
÷ 5

I divide a number by 7 then subtract 4, what are the inverse operations?

Column B

+ 2
- 2
- 6
+ 6
x 5
x 3
÷ 3
÷ 5

I add 7 to a number and get 15. What is the number?

I multiply a number by 6 to get 18. What was my number?

Match the operations with their inverses.

Column B

x 2 + 3
x 2 ÷ 5
+ 3 ÷ 5
-3 ÷ 2
x 5 ÷ 2
x 3 + 7
-7 ÷ 3
x 5 - 3

I subtract 7 from a number and then half it. Which of these is the inverse operation?

x 2 + 7

+ 7 x 2

I double a number and add 6 to get 18. What was my original number?

I half a number and add 4 to get 9. What was my original number?

• Question 1

The inverse of + 4 is...

-4
- 4
EDDIE SAYS
The opposite of + is -, so the opposite of + 4 is...
• Question 2

The inverse operation of ÷ 6 is...

EDDIE SAYS
The opposite of divide is multiply, so the opposite of divide by 6 is... Is this becoming less daunting?
• Question 3

Match the operations with their inverses.

Column B

+ 2
- 2
- 6
+ 6
x 5
÷ 5
÷ 3
x 3
EDDIE SAYS
You just need to remember those inverse operations, + is the opposite of - etc. Once you know the inverse operation, is the number important in this question?
• Question 4

I divide a number by 7 then subtract 4, what are the inverse operations?

EDDIE SAYS
The inverse operation for subtract 4 is add 4. The inverse operation for ÷ 7 is x 7. But did you swap the order? The subtract 4 should have come first.
• Question 5

I add 7 to a number and get 15. What is the number?

8
EDDIE SAYS
The opposite of adding 7 is subtracting 7. If I take 7 away from 15, I get...
• Question 6

I multiply a number by 6 to get 18. What was my number?

3
EDDIE SAYS
The opposite of multiplying by 6 is dividing by 6. If I divide 18 by 6, I get... You're getting better at this with each question!
• Question 7

Match the operations with their inverses.

Column B

x 2 + 3
-3 ÷ 2
+ 3 ÷ 5
x 5 - 3
x 5 ÷ 2
x 2 ÷ 5
-7 ÷ 3
x 3 + 7
EDDIE SAYS
Its all about remembering those inverse operations, + is the opposite of - etc. The key error you could make here is forgetting that we have to swap the order as well!
• Question 8

I subtract 7 from a number and then half it. Which of these is the inverse operation?

x 2 + 7
EDDIE SAYS
The key rule to remember is that when finding the inverse, you must remember to swap the order of operations as well. Great work if you spotted that!
• Question 9

I double a number and add 6 to get 18. What was my original number?

6
EDDIE SAYS
Remember, find the inverses of the operations and then reverse the order. So, (18 - 6) ÷ 2 = ?
• Question 10

I half a number and add 4 to get 9. What was my original number?

10
EDDIE SAYS
Remember, find the inverses of the operations and then reverse the order. So we do, (9-4) x 2 = 10! Well done, that’s another activity completed!
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