Question

Fill in the blanks $\frac{-2}{9}=\frac{?}{63}=\frac{?}{81}$

Answer 1

Given, $\frac{-2}{9}=\frac{?}{63}=\frac{?}{81}$

Let one number be $\text{x}$ and another number be $\text{y}$ .

$\therefore$ $\frac{-2}{9}=\frac{x}{63}=\frac{y}{81}$

Now, divide this into two parts: $\frac{-2}{9}=\frac{x}{63}$...(i) and $\frac{x}{63}=\frac{y}{81}$ ...(ii)

Now, lets take the first part and solve it by cross multiplication:

$\frac{-2}{9}=\frac{x}{63}\Rightarrow 63\times -2=9x\Rightarrow -126=9x\Rightarrow x=\frac{-126}{9}\Rightarrow x=-14$

Now, put $x=-14$ in the second part and solve it by cross multiplication:

$\frac{x}{63}=\frac{y}{81}\Rightarrow \frac{-14}{63}=\frac{y}{81}\Rightarrow 81\times -14=63y\Rightarrow -1134=63y\Rightarrow y=\frac{-1134}{63}\Rightarrow y=-18$

Therefore, $\frac{-2}{9}=\frac{?}{63}=\frac{?}{81}$ can be written as $\frac{-2}{9}=\frac{-14}{63}=\frac{-18}{81}$