Question:
By what number should (−3)−1 be multiplied so that the product becomes 6−1?
Solution:
Let the number be $x$.
$\therefore(-3)^{-1} \times x=(6)^{-1}$
$\Rightarrow \frac{1}{-3} \times x=\frac{1}{6}$
$\Rightarrow \frac{1 \times-1}{-3 \times-1} \times x=\frac{1}{6}$
$\therefore \frac{-x}{3}=\frac{1}{6}$
On cross multiplying:
$-x \times 6=1 \times 3$
$\Rightarrow-6 x=3$
$\Rightarrow 6 x=-3$
$\therefore x=\frac{-3}{6}=\frac{-1}{2}$