Question

By what number should \[\left( \frac{1}{2} \right)^{- 1}\] be multiplied so that the product may be equal to \[\left( \frac{- 4}{7} \right)^{- 1} ?\]

Answer 1

Expressing in fractional form, we get:
(1/2)⁻¹ = 2,      → (a⁻¹ = 1/a)
and
(−4/7)⁻¹ = −7/4    → (a⁻¹ = 1/a)
We have to find a number x such that `2x=-7/4`
Dividing both sides by 2, we get: `x=-7/8`

Hence, (1/2)⁻¹ should be multiplied by −7/8 to obtain (−4/7)⁻¹.