Question:
By what number should 5−1 be multiplied so that the product may be equal to (−7)−1?
Solution:
Using the property a−1 = 1/a for every natural number a, we have 5−1 = 1/5 and (−7)−1 = −1/7. We have to find a number x such that
$\frac{1}{5} \times x=\frac{-1}{7}$
Multiplying both sides by 5, we get:
$x=\frac{-5}{7}$
Hence, the required number is −5/7.
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