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 
\[\frac{\frac{- 1}{15}}{\frac{x}{1}} = \frac{- 1}{5}\]
\[\text{ or }\frac{- 1}{15} \times \frac{1}{x} = \frac{- 1}{5}\]
\[\text{ or }x = \frac{1}{3}\]
Hence, (−15)⁻¹ should be divided by \[\frac{1}{3}\]

 to obtain (−5)⁻¹.