Question

By what number should (−30)⁻¹ be divided to get 6⁻¹?

Answer 1

Let the required number be x.
(-30)^-1 ÷ x = 6^-1
⇒ $\frac{1}{\left(-30\right)}\times \frac{1}{x}=\frac{1}{6}$
⇒ $\frac{1}{\left(-30x\right)}=\frac{1}{6}$
∴ x = $\frac{6}{\left(-30\right)}=\frac{1}{-5}$
=$\frac{-1}{5}$
Hence, the required number is $\frac{-1}{5}$.