By what number should

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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

$-\frac{1}{15} \div x=-\frac{1}{5}$

Solving this equation, we get:

$-\frac{1}{15} \times \frac{1}{x}=-\frac{1}{5}$

$-\frac{1}{15}=-\frac{x}{5}$

$\frac{-5}{-15}=x$

 

$\therefore x=\frac{1}{3}$

Hence, (−15)−1 should be divided by 1/3 to obtain (−5)−1.

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