Q45. - Algebra 2

Question

Identify the additive inverse and multiplicative inverse for each number 

$-0.125$

Step-by-Step Solution

Answer

Additive inverse of $-0.125$ is $0.125$ and multiplicative inverse of $-0.125$ is $-8$

Step 1 - 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’

Step 2 - 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 $0.125$

Step 3 - 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’

Step 4 - 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 $-8$