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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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