By what number should \((\frac{1}{2})^{-1}\) be multiplied so that th

1.	By what number should \((\frac{1}{2})^{-1}\) be multiplied so that the product may be equal to \((-\frac{4}{7})^{-1}\)?
Answer» Let the number \((\frac{1}{2})^{-1}\) should be multiplied by x According to the question: \(x\times (\frac{1}{2})^{-1}=(-\frac{4}{7})^{-1}\) \(x\times 2=-\frac{7}{4}\)[Using \(a^{-n}\)=\(\frac{1}{a^{n}}\)] x = \(-\frac{7}{4}\times \frac{1}{2}=-\frac{7}{8}\) Therefore \((\frac{1}{2})^{-1}\) should be multiplied by \(-\frac{7}{8}\)

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

Answer»

Let the number \((\frac{1}{2})^{-1}\) should be multiplied by x

According to the question:

\(x\times (\frac{1}{2})^{-1}=(-\frac{4}{7})^{-1}\)

\(x\times 2=-\frac{7}{4}\)[Using \(a^{-n}\)=\(\frac{1}{a^{n}}\)]

x = \(-\frac{7}{4}\times \frac{1}{2}=-\frac{7}{8}\)

Therefore \((\frac{1}{2})^{-1}\) should be multiplied by \(-\frac{7}{8}\)

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