Q12. - Algebra 2

Question

Identify the additive inverse and multiplicative inverse for each number 

$1.5$

Step-by-Step Solution

Answer

Additive inverse of $1.5$ is $-1.5$ and multiplicative inverse of 1.5 is $\frac{2}{3}$

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 1 . 5

Substitute $1.5$ for a

$a=1.5$

Multiply both sides by $-1$ 

$\begin{array}{c}\left(-1\right)\times a=\left(-1\right)\times \left(1.5\right)\\ -a=-1.5\end{array}$

Thus additive inverse of 1.5 is -1.5

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 1 . 5

Substitute $1.5$ for $a$ 

Convert it from decimal form to fraction 

 $\begin{array}{c}a=1.5\\ =\frac{15}{10}\\ =\frac{3}{2}\end{array}$

Reciprocal on both sides

 $\begin{array}{c}\frac{1}{a}=\frac{1}{\frac{3}{2}}\\ \frac{1}{a}=\frac{2}{3}\end{array}$

Thus multiplicative inverse of $\frac{3}{2}$ is $\frac{2}{3}$