Inverse Property of Addition

Use the Inverse Properties of Addition and Multiplication

Notice that in each case, the missing number was the opposite of the number.

We call \(-a \) the additive inverse of \(a \). The opposite of a number is its additive inverse. A number and its opposite add to \(0 \), which is the additive identity.

Source: Rice University, https://openstax.org/books/prealgebra/pages/7-4-properties-of-identity-inverses-and-zero
This work is licensed under a Creative Commons Attribution 4.0 License.

EXAMPLE 7.34

Find the additive inverse of each expression: (a) \( 13 \)

(b) \( -\frac {5}{8} \)

(c) \( 0.6 \)

TRY IT 7.67

Find the additive inverse:

(a) \( 18 \)

(b) \( \frac {7}{9} \)

(c) \( 1.2 \)

TRY IT 7.68

Find the additive inverse:

(a) \( 47 \)

(b) \( \frac {7}{13}\)

(c) \( 8.4 \)

Example 7.34

To find the additive inverse, we find the opposite.

(a) The additive inverse of \(13\) is its opposite, \(-13\).

(b) The additive inverse of \(-\frac{5}{8}\) is its opposite, \(\frac{5}{8}\).

(c) The additive inverse of \(0.6\) is its opposite, \(-0.6\).

Try It 7.67

(a) \(-18\)

(b) \(-\frac{7}{9}\)

(c) \(-1.2\)

Try It 7.68

(a) \(-47\)

(b) \(-\frac{7}{13}\)

(c) \(-8.4\)