Question

Fill the box

$\frac{4}{13}÷\square =\frac{-4}{7}$

Answer 1

Given $\frac{4}{13}÷\square =\frac{-4}{7}$

Now, let $x$be the required rational number then,

$$\begin{gathered} \frac{4}{13}÷x=\frac{-4}{7} \\ \Rightarrow x=\frac{4}{13}÷\frac{-4}{7} \\ =\frac{4}{13}\times \frac{7}{-4} \\ =\frac{7}{-13}(cancellingthecommonfactor4) \end{gathered}$$

Since, $\frac{7}{-13}=\frac{7\times (-1)}{-13\times (-1)}=\frac{-7}{13}$

Therefore, $\frac{4}{13}÷\frac{-7}{13}=\frac{-4}{7}$

Hence, the required answer is $\frac{-7}{3}$.