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

To do:  

We have to find the number that should be multiplied by $(\frac{1}{2})^{-1}$ so that the product is equal to $(\frac{-4}{7})^{-1}$.

Solution:

Let the number that should be multiplied by $(\frac{1}{2})^{-1}$ so that the product is equal to $(\frac{-4}{7})^{-1}$ be $x$.

Therefore,

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

$\frac{2}{1}\times x=\frac{7}{-4}$

$x=\frac{7}{-4\times2}$

$x=\frac{-7}{8}$

Hence, the number that should be multiplied by $(\frac{1}{2})^{-1}$ so that the product is equal to $(\frac{-4}{7})^{-1}$ is $\frac{-7}{8}$. 

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Updated on: 10-Oct-2022

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