# What Is an Inverse Operation?

## What Is an Inverse Operation?

An inverse operation is the opposite of an operation. It reverses an operation.

If the inverse operation reverses the operation, the operation reverses the inverse operation.

## Addition and Subtraction

The inverse operation of addition is subtraction.

Imagine we **add** 2 to 3...

3 **+ 2** → 5

...we can reverse the operation by **subtracting** 2:

3 ← 5 **− 2**

Subtraction has reversed the addition. *Subtraction is the inverse operation of addition...*

### ...and Vice Versa

If subtraction is the inverse operation of addition, the inverse operation of subtraction is addition.

Imagine we **subtract** 2 from 3...

3 **− 2** → 1

...we can reverse the operation by **adding** 2:

3 ← 1 **+ 2**

Addition has reversed the subtraction. *Addition is the inverse operation of subtraction.*

## Multiplication and Division

The inverse operation of multiplication is division.

Imagine we **multiply** 4 by 2...

4 **× 2** → 8

...we can reverse the operation by **dividing** by 2:

4 ← 8 **÷ 2**

Division has reversed the multiplication. *Division is the inverse operation of multiplication...*

### ...and Vice Versa

If division is the inverse operation of multiplication, the inverse operation of division is multiplication.

Imagine we **divide** 4 by 2...

4 **÷ 2** → 2

...we can reverse the operation by **multiplying** by 2:

4 ← 4 **× 2**

Multiplication has reversed the division. *Multiplication is the inverse operation of division.*

## Squaring and the Square Root

The inverse operation of squaring is taking the square root.

Imagine we **square** 3...

3** ^{2}** → 9

...we can reverse the operation by taking the **square root**:

3 ← **√9**

The square root has reversed the squaring. *The square root is the inverse operation of squaring...*

### ...and Vice Versa

If the square root is the inverse operation of squaring, the inverse operation of the square root is squaring.

Imagine we take the **square root** of 4...

**√**4 → 2

...we can reverse the operation by **squaring**:

4 ← 2^{2}

Squaring has reversed the square root. *Squaring is the inverse operation of the square root.*

## What Is an Inverse Operation Useful?

### Checking Your Answer

The inverse operation is useful for checking your answers.

Imagine you multiply 6 by 4:

6 × 4 = 24

The inverse operation of multiplication is division. Divide your answer by 4 to see if you get back to 6:

24 ÷ 4 = 6 ✔