Question:
By what number should $\left(\frac{1}{2}\right)^{-1}$ be multiplied so that the product may be equal to $\left(\frac{-4}{7}\right)^{-1} ?$
Solution:
Expressing in fractional form, we get:
(1/2)−1 = 2, ---> (a−1 = 1/a)
and
(−4/7)−1 = −7/4 ---> (a−1 = 1/a)
We have to find a number x such that
$2 x=-\frac{7}{4}$
Dividing both sides by 2, we get:
$x=-\frac{7}{8}$
Hence, (1/2)−1 should be multiplied by −7/8 to obtain (−4/7)−1.
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