Question

Identify the additive inverse and multiplicative inverse for each number

$-0.125$

Short answer

Additive inverse of $-0.125$is$0.125$and multiplicative inverse of $-0.125$is localid="1647965937507" $-8$

Step-by-step solution

- Define additive inverse

Let ‘a’ be a real number such that

$a+\left(-a\right)=0=\left(-a\right)+a$

Then ‘$-a$’ is the additive inverse of ‘a’

- Additive inverse of -0.125

Substitute $-0.125$ for a

$a=-0.125$

Multiply both sides by $-1$

$\begin{array}{c}\left(-1\right)\times a=\left(-1\right)\times \left(-0.125\right)\\ -a=0.125\end{array}$

Thus additive inverse of $-0.125$is $0.125$

- Define multiplicative inverse

Let ‘a’ be a real number with$a\cancel{=}0$ such that

$a·\frac{1}{a}=1=\frac{1}{a}·a$

Then ‘$\frac{1}{a}$’ is the multiplicative inverse of ‘a’

- Multiplicative inverse of -0.125

Substitute $-0.125$ for a

$a=-0.125$

Convert decimal form of rational number to fraction form

$a=-\frac{1}{8}$

Take reciprocal on both sides

$\begin{array}{c}\frac{1}{a}=\frac{1}{-\frac{1}{8}}\\ \frac{1}{a}=-8\end{array}$

Thus multiplicative inverse of $-0.125$is $-8$