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Question
By what number should (−15)−1 be divided so that the quotient may be equal to (−5)−1?
Solution
Expressing in fractional form, we get:
(−15)−1 = −1/15, → (a−1 = 1/a)
and
(−5)−1 = −1/5 → (a−1 = 1/a)
We have to find a number x such that
`-1/15divx=-1/5`
Solving this equation, we get:
`-1/15xx1/x=-1/5`
`-1/15=-x/5`
`(-5)/(-15)=x`
`thereforex=1/3`
Hence, (−15)−1 should be divided by 1/3 to obtain (−5)−1.
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