Question

By what number should \[\left( \frac{1}{2} \right)^{- 1}\] be multiplied so that the product may be equal to \[\left( - \frac{4}{7} \right)^{- 1} ?\]

Answer 1

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 \[2x = \frac{- 7}{4}\] Dividing both sides by 2, we get:

\[x = \frac{- 7}{8}\]

Hence, the required number is −7/8.