By what number should (−5)⁻¹ be multiplied so that the product is (8)⁻¹?

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Solution

Let the required number be x.
(−5)^-1 $\times$ x = (8)^-1
⇒ $\frac{1}{- 5} \times x = \frac{1}{8}$
∴ x = $\frac{1}{8} \times (- 5)$ = $\frac{- 5}{8}$
Hence, the required number is $\frac{- 5}{8}$ .

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