Question:
Tick (✓) the correct answer
The product of two rational numbers is $\frac{-28}{81}$. If one of the numbers is $\frac{14}{27}$ then the other one is
(a) $\frac{-2}{3}$
(b) $\frac{2}{3}$
(c) $\frac{3}{2}$
(d) $\frac{-3}{2}$
Solution:
(a) $\frac{-2}{3}$
Let the other number be x.
Now,
$x \times \frac{14}{27}=\frac{-28}{81}$
$\Rightarrow x=\frac{-28}{81} \div \frac{14}{27}$
$=\frac{-28}{81} \times \frac{27}{14}$
$=\frac{(-28) \times 27}{81 \times 14}$
$=\frac{-(28 \times 27)}{81 \times 14}$
$=\frac{-(2 \times 3)}{9 \times 1}$
$=\frac{-6}{9}$
$=\frac{-2}{3}$
Thus, the other number is $\frac{-2}{3}$
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