Question

Identify the additive inverse and multiplicative inverse for each number

$-10$

Short answer

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

Step-by-step solution

- 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’

- 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

- 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’

- 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 $-\frac{1}{10}$