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