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Additive Inverse calculator

Enter a number and the calculator will calculate its additive inverse.

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Use this online additive inverse calculator to instantly find the additive inverse of any number. This guide below explains how to calculate additive inverses manually or using our free calculator.

What's the Additive Inverse?

In arithmetic, the additive inverse of a number is defined as:

"A number that, when added to the given number, results in zero."

additive inverse

Whether working with fractions, decimals, or square roots, finding the additive inverse might seem tricky. But don’t worry! Our free calculator performs these calculations instantly and accurately.

How Do You Find the Additive Inverse of a Number?

Use this simple formula to calculate the additive inverse:

Additive Inverse = (-1) × Number

Additive Identity

In mathematics, zero (0) is called the additive identity because adding zero to any number—integer, fraction, or decimal—leaves the number unchanged. Interestingly, the additive inverse of zero is also zero.

Additive Inverse Table

Here is a table showing the additive inverses of some commonly used numbers:

Number	Additive Inverse
8	-8
7/8	-7/8
-4/5	4/5
4/5	-4/5
22	-22
15	-15
4	-4
17	-17
16	-16
13	-13
2	-2
0	0
55	-55

You can quickly verify any number’s additive inverse using this calculator.

Additive Inverse of Complex Numbers

For complex numbers, the additive inverse works similarly. Suppose:

Z = a + bi

Then its additive inverse is:

Additive Inverse = -Z = -(a + bi) = -a - bi

Additive Inverse of a Polynomial

The concept also applies to algebraic expressions. For a polynomial:

P(x) = ax² + bx + c

Its additive inverse is:

-P(x) = -ax² - bx - c

You can also simplify polynomials and algebraic expressions using our rational expression calculator.

Properties of Additive Inverse

-(-x) = x
(-x)² = x²
-(x + y) = (-x) + (-y)
-(x - y) = y - x
x - (-y) = x + y
(-x) × y = x × (-y) = -(x × y)
(-x) × (-y) = x × y

Numeric Examples

Example 1: Find the additive inverse of 23.

Solution:
Additive Inverse = (-1) × 23 = -23

Example 2: Find the additive inverse of -4.

Solution:
Additive Inverse = (-1) × (-4) = 4

How the Additive Inverse Calculator Works

Input:

Enter the number in the input field.
Click the calculate button.

Output:

Provides the additive inverse along with step-by-step calculations.

FAQ

What is the additive inverse of -2?

The additive inverse of -2 is 2. You can verify this using the calculator.

What is the additive inverse of 2 in Z10?

In modular arithmetic, additive inverse = n - a. Here, 10 - 2 = 8.

What is the sum of 12 ¼ and its additive inverse?

The sum is always 0.

What is the additive inverse of -9?

It is 9.

How is the additive inverse used in real life?

If you walk 20 steps forward and 20 steps back, your net movement is zero—illustrating the additive inverse concept.

Difference Between Additive Inverse and Absolute Value

Absolute value measures distance from zero (always non-negative). Additive inverse is the number that sums to zero with the original number.

What is the additive inverse of ab?

-ab, because ab + (-ab) = 0

What is the additive property of equality?

Adding or subtracting the same number on both sides of an equation preserves equality.

Conclusion

Additive inverses simplify calculations and help solve equations quickly. Use this free additive inverse calculator for accurate and instant results.

References

From Wikipedia: Additive identity, Common examples, Properties.
From Khan Academy: Inverse property.
From Lumen Learning: Identity and Inverse.

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