Q46. - Algebra 2

Question

Identify the additive inverse and multiplicative inverse for each number 

$-\frac{5}{8}$

Step-by-Step Solution

Answer

Additive inverse of $-\frac{5}{8}$ is $\frac{5}{8}$ and multiplicative inverse of $-\frac{5}{8}$ is $-\frac{8}{5}$

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 - 5 8

Substitute $-\frac{5}{8}$ for $a$

 $a=-\frac{5}{8}$

Multiply both sides by $-1$

$\begin{array}{c}\left(-1\right)\times a=\left(-1\right)\times \left(-\frac{5}{8}\right)\\ -a=\frac{5}{8}\end{array}$

Thus additive inverse of $-\frac{5}{8}$ is $\frac{5}{8}$

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 - 5 8

Substitute $-\frac{5}{8}$ for a

$a=-\frac{5}{8}$

Take reciprocal on both sides

 $\begin{array}{c}\frac{1}{a}=\frac{1}{-\frac{5}{8}}\\ \frac{1}{a}=-\frac{8}{5}\end{array}$

Thus multiplicative inverse of $-\frac{5}{8}$ is $-\frac{8}{5}$