Question

By what number should we multiply (−6)⁻¹ to obtain a product equal to 9⁻¹?

Answer 1

Let the required number be x.
(−6)^-1 × x = (9)^-1
⇒ $\frac{1}{-6}\times x=\frac{1}{9}$
∴ x = $\frac{1}{9}\times \left(-6\right)=\frac{\left(-2\right)}{3}$
Hence, the required number is $\frac{-2}{3}$.