Question

By what number should 5⁻¹ be multiplied so that the product may be equal to (−7)⁻¹?

Answer 1

Using the property a⁻¹ = 1/a for every natural number a, we have 5⁻¹ = 1/5 and (−7)⁻¹ = −1/7. We have to find a number x such that \[\frac{1}{5} \times x = \frac{- 1}{7}\] Multiplying both sides by 5, we get:

\[x = \frac{- 5}{7}\]

Hence, the required number is −5/7.