By what number should

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:

$-x \times 6=1 \times 3$

$\Rightarrow-6 x=3$

$\Rightarrow 6 x=-3$

$\therefore x=\frac{-3}{6}=\frac{-1}{2}$

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