By what number should $5^{-1}$ be multiplied so that the product may be equal to $(-7)^{-1}$?

To do:  

We have to find the number that should be multiplied by $5^{-1}$ so that the product is equal to $(-7)^{-1}$.

Solution:

Let the number that should be multiplied by $5^{-1}$ so that the product is equal to $(-7)^{-1}$ be $x$.

Therefore,

$5^{-1}\times x=(-7)^{-1}$

$\frac{1}{5}\times x=\frac{1}{-7}$

$x=\frac{5}{-7}$

$x=\frac{-5}{7}$

Hence, the number that should be multiplied by $5^{-1}$ so that the product is equal to $(-7)^{-1}$ is $\frac{-5}{7}$.

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Updated on: 10-Oct-2022

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