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) $\frac{-3}{2}$

Answer 1

(a) $\frac{-2}{3}$
Let the other number be x.

Now,

$x\times \frac{14}{27}=\frac{-28}{81}$

$\Rightarrow x=\frac{-28}{81}÷\frac{14}{27}$

$$\begin{gathered} =\frac{-28}{81}\times \frac{27}{14} \\ =\frac{\left(-28\right)\times 27}{81\times 14} \\ =\frac{-\left(28\times 27\right)}{81\times 14} \\ =\frac{-\left(2\times 3\right)}{9\times 1} \\ =\frac{-6}{9} \\ =\frac{-2}{3} \end{gathered}$$
Thus, the other number is $\frac{-2}{3}$