Question:
By what number should 5−1 be multiplied so that the product may be equal to (−7)−1?
Solution:
Expressing in fraction form, we get:
5−1 = 1/5 (using the property a−1 = 1/a)
and
(−7)−1 = −1/7 (using the property a−1 = 1/a).
We have to find a number x such that
$\frac{1}{5} x=\frac{-1}{7}$
Multiplying both sides by 5, we get:
$x=-\frac{5}{7}$
Hence, 5−1 should be multiplied by −5/7 to obtain (−7)−1.
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