Question

Is $\frac{8}{9}$ the multiplication inverse of $-1\frac{1}{8}$. Why or why not?

Answer 1

Verify the multiplication inverse :

The multiplicative inverse of a number $N$ is represented by $\frac{1}{N}$

Therefore, $x$ is the number and $x\text{'}$ is the multiplicative inverse then $x\times x\text{'}=1$

Given that the the multiplication inverse of $-1\frac{1}{8}$ is $\frac{8}{9}$

Therefore the multiplicative inverse of $-1\frac{1}{8}=-\frac{9}{8}$ is

$$\begin{gathered} x\times x\text{'}=1 \\ \Rightarrow -\frac{9}{8}\times x\text{'}=1 \\ \Rightarrow x\text{'}=-\frac{8}{9} \end{gathered}$$

Therefore $x\text{'}=-\frac{8}{9}\ne \frac{8}{9}$

Hence $\frac{8}{9}$ is not a multiplication inverse of $-1\frac{1}{8}$