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

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Solution

$L e t x b e m u l t i p l i e d, t h e x \times 5^{- 1} = (- 7)^{- 1} x = \frac{(- 7)^{- 1}}{(5)^{- 1}} = {(\frac{- 7}{5})}^{- 1} = {(\frac{5}{- 7})}^{1} = \frac{- 5}{7} ∴ R e q u i r e d n u m b e r = \frac{- 5}{7}$

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