Q43. - Algebra 2

Question

Identify the additive inverse and multiplicative inverse for each number 

$-10$

Step-by-Step Solution

Answer

Additive inverse of $-10$ is 10 and multiplicative inverse of $-10$ is $-\frac{1}{10}$

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 - 10

Substitute $-10$ for a

$a=-10$

Multiply both sides by $-1$ 

$\begin{array}{c}\left(-1\right)\times a=\left(-1\right)\times \left(-10\right)\\ -a=10\end{array}$

Thus additive inverse of $-10$ is 10

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 - 10

Substitute $-10$ for a 

 $a=-10$ 

Reciprocal on both sides

$\begin{array}{c}\frac{1}{a}=\frac{1}{-10}\\ \frac{1}{a}=-\frac{1}{10}\end{array}$

Thus multiplicative inverse of $-10$ is $-\frac{1}{10}$