Question

By what number should (−6)⁻¹ be multiplied so that the product becomes 9⁻¹?

Answer 1

Let the required number be $x$.

$\therefore$ $x\times (-6{)}^{-1}=9^{-1}$

$$\begin{gathered} x\times \frac{1}{-6}=\frac{1}{9}\Rightarrow \frac{x}{-6}=\frac{1}{9} \\ \mathrm{or}x=\frac{-6}{9} \end{gathered}$$
The greatest common divisor for the numerator and the denominator is 3.

$\therefore x=\frac{-6}{9}=\frac{(-6)÷3}{9÷3}=\frac{-2}{3}$