Inverse Operations

Contributor: Elephango Editors. Lesson ID: 10620

Learn a quick and easy way to double-check your math problems WITHOUT using technology! Watch videos, and complete an interactive to practice inverse operations!


Operations and Algebraic Thinking, Rules and Properties

learning style
Auditory, Visual
personality style
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

  • How do you check your work when solving math problems?
  • Do you draw pictures?

Maybe you like to use a calculator to be super sure.

  • Did you know that there is another way to check your work, and it just might save you time?

No, it's not magic. It's inverse operations!

Inverse means opposite, so an inverse operation is an opposite operation.

For example, the opposite operation of addition is subtraction; and the opposite operation of multiplication is division.

Inverse operations are important in math for two reasons!

Inverse Operations to Check Your Work

You can check your work by performing the inverse operation!

For example, look at the expression 25 - 12.

You solve this expression and write your answer like this:

25 - 12 = 13

You can use inverse operations to check this answer.

The above operation is subtraction, the inverse operation is addition. We will check our work by using addition.

13 + 12 = 25

The answer is correct! Both equations are true!

You can also check your work this way with multiplication and division.

Look at the expression 63 ÷ 7.

You solve the expression and write your answer like this:

63 ÷ 7 = 9

Let's use inverse operations to check our work. In this case the inverse operation is multiplication.

9 x 7 = 63

Again, the answers are correct! Both equations are true!

Inverse Operations to Help Solve Problems

Inverse operations are also important to help us understand and solve problems.

For example, look at the expression 40 ÷ 5.

In order to solve this expression, you could divide 40 into 5 equal groups. Or you could use inverse operations!

The inverse operation of division is multiplication. Rethink 40 ÷ 5 in terms of multiplication.

"5 times what equals 40"

This could also be written like this:

5 x ? = 40

Now, you can figure out the missing factor pretty easily. Is it 5 x 1, 5 x 2, 5 x 3, so on and so on?

5 x 8 = 40 which also means 40 ÷ 5 = 8

This also works for subtraction and addition!

Look at the expression 13 - 8.

You could count back from 13 eight times or use inverse operations!

"8 plus what equals 13"

This can also be written like this:

8 + ? = 13

Now, you can find the missing addend.

8 + 5 = 13 which also means 13 - 8 = 5

Let's watch an inverse operations video from Krista King Math before moving on:

  • Ready for some practice?

Visit the Got It? section to try using inverse operations on your own!

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