Question

By what number should $(-15{)}^{-1}$ be divided so that the quotient may be equal to $(-5{)}^{-1}$ ?

Answer 1

Let x be the number divide $(-15{)}^{-1}$ to get $(-5{)}^{-1}$ as a quotient.
So,

$(-15{)}^{-1}÷x=(-5{)}^{-1}\Rightarrow \frac{1}{-15}\times \frac{1}{x}=\frac{1}{-5}[\because a^{-m}=\frac{1}{a^m}]\Rightarrow \frac{1}{x}=\frac{1}{-5}\times \frac{-15}{1}\Rightarrow x=\frac{1}{3}$