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:
Using the property a−1 = 1/a for every natural number a, we have (1/2)−1 = 2 and (−4/7)−1 = −7/4. 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, the required number is −7/8.
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