Question:
By what number should $(-6)^{-1}$ be multiplied so that the product becomes $9^{-1} ?$
Solution:
Let the required number be $x$.
$\therefore x \times(-6)^{-1}=9^{-1}$
$x \times \frac{1}{-6}=\frac{1}{9} \Rightarrow \frac{x}{-6}=\frac{1}{9}$
or $x=\frac{-6}{9}$
The greatest common divisor for the numerator and the denominator is 3.
$\therefore x=\frac{-6}{9}=\frac{(-6) \div 3}{9 \div 3}=\frac{-2}{3}$
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