Question

By what number should (−15)⁻¹ be divided so that the quotient may be equal to (−5)⁻¹?

Answer 1

Expressing in fractional form, we get:
(−15)⁻¹ = −1/15,      → (a⁻¹ = 1/a)
and
(−5)⁻¹ = −1/5          → (a⁻¹ = 1/a)
We have to find a number x such that

`-1/15divx=-1/5`
Solving this equation, we get:
`-1/15xx1/x=-1/5`
`-1/15=-x/5`

`(-5)/(-15)=x`

`thereforex=1/3`

Hence, (−15)⁻¹ should be divided by 1/3 to obtain (−5)⁻¹.