Q47. - Algebra 2

Question

Identify the additive inverse and multiplicative inverse for each number 

47. $\frac{4}{3}$

Step-by-Step Solution

Answer

Additive inverse of $\frac{4}{3}$ is $-\frac{4}{3}$ and multiplicative inverse of $\frac{4}{3}$ is $\frac{3}{4}$

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 4 3

Substitute $\frac{4}{3}$ for a 

$a=\frac{4}{3}$

Multiply both sides by $-1$

$\begin{array}{c}\left(-1\right)\times a=\left(-1\right)\times \left(\frac{4}{3}\right)\\ -a=-\frac{4}{3}\end{array}$ 

Thus additive inverse of $\frac{4}{3}$ is $-\frac{4}{3}$

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 4 3

Substitute $\frac{4}{3}$ for a 

$a=\frac{4}{3}$

Take reciprocal on both sides

 $\begin{array}{c}\frac{1}{a}=\frac{1}{\frac{4}{3}}\\ \frac{1}{a}=\frac{3}{4}\end{array}$

Thus multiplicative inverse of $\frac{4}{3}$ is $\frac{3}{4}$