Question

By what number should (−15)⁻¹ be divided so that the quotient may be equal to (−5)⁻¹?

Answer 1

Using the property a⁻¹ = 1/a for every natural number a, we have (−15)⁻¹ = −1/15 and (−5)⁻¹ = −1/5. We have to find a number x such that
$$\begin{gathered} \frac{{\displaystyle \frac{-1}{15}}}{{\displaystyle \frac{\mathrm{x}}{1}}}=\frac{-1}{5} \\ \mathrm{or}\frac{-1}{15}\times \frac{1}{\mathrm{x}}=\frac{-1}{5} \\ \mathrm{or}x=\frac{1}{3} \end{gathered}$$
Hence, (−15)⁻¹ should be divided by $\frac{1}{3}$ to obtain (−5)⁻¹.