Question

Tick (✓) the correct answer
The product of two numbers is $\frac{-16}{35}.$ If one of the numbers is $\frac{-15}{14}$, the other is
(a) $\frac{-2}{5}$
(b) $\frac{8}{15}$
(c) $\frac{32}{75}$
(d) $\frac{-8}{3}$

Answer 1

(c) $\frac{32}{75}$
Let the other number be x.

Now,

$x\times \frac{-15}{4}=\frac{-16}{35}$
$\Rightarrow x=\frac{-16}{35}÷\frac{-15}{14}$

$$\begin{gathered} =\frac{-16}{35}\times \frac{14}{-15} \\ =\frac{-\left(16\times 14\right)}{-\left(35\times 15\right)} \\ =\frac{16\times 14}{35\times 15}=\frac{224}{525}=\frac{32}{75} \end{gathered}$$

Thus, the other number is $\frac{32}{75}$