Additive inverses are among the many pairs of numbers in Mathematics that show a special relationship. How do we get the additive inverse of a number? How is one number related to its additive inverse? In real life, where can we see additive inverses?

Additive Inverse is related to the operations, Addition and Subtraction. Inverse is synonymous to opposite, reverse, or flipped.

## Definition

- The additive inverse of a number is the opposite of the number.
- When a number is added to its additive inverse, it results to zero.
- In the number line, a number and its additive inverse have the same distance from zero.

To get the additive inverse of a number, simply change its sign. The additive inverse of a positive number is a negative number, and vice versa.

**Examples**

- The additive inverse of 4 is -4.
- The additive inverse of -7 is 7.
- The additive inverse of $\frac{2}{3}$ is-$\frac{2}{3}$.
- The additive inverse of $\frac{1}{5}$ is -$\frac{1}{5}$
- The additive inverse of 10.68 is -10.68.
- The additive inverse of -5.25 is 5.25.

## Additive Inverse Property

The sum of a number and its additive inverse is zero (0).

**Examples**

- 4 + (-4) = 0
- $\frac{1}{5}$ + (-$\frac{1}{5}$) = 0
- (-7) + 7 = 0
- 10.68 + (-10.68) = 0
- $\frac{2}{3}$ + (-$\frac{2}{3}$) = 0
- (-5.25) + 5.25 = 0

## Additive Inverse In Real Life

As we learn that Additive Inverse shows the Opposites, let us relate it to real-life situations.

- If you traveled 200m going to school, you would travel the same distance of 200m going home, even though you traveled in opposite directions..
- If you loan \$20 from your friend, you will need \$20 to settle the borrowed amount.

## Exercise: Additive Inverse

A. Determine if the underlined number is the additive inverse of the given number. Write a heckmark if it is correct and a crossmark if not.

—1) 0.2, -0.2

—2) $\frac{4}{1}$.$\frac{1}{4}$

—3) $\frac{7}{2}$, $\frac{-2}{7}$

—4) $\frac{-3}{9}$, $\frac{3}{9}$

—5) -9, 6

B. Write the additive inverse of the given numbers.

—1) 11

—2) -24

—3) $\frac{6}{5}$

—4)-7.75

—5) 3.14159…

—6)-439

—7) 0.008

—8) $\frac{-1}{7}$

—9) 802

—10) $\frac{5}{13}$

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