Question

Fill in the boxes:

$\frac{\boxed{}}{8}+\frac{-3}{12}=\frac{-9}{24}$

Answer 1

First take $\mathrm{x}$ at the place of the box.

Now convert the given fractions on LHS into equivalent fractions.

To convert them into equivalent fractions, take LCM of the denominators.

LCM of $8$ and $12$ is $24$.

$$\begin{gathered} \Rightarrow \frac{\mathrm{x}\times 3}{8\times 3}+\frac{-3\times 2}{12\times 2}=\frac{-9}{24} \\ \Rightarrow \frac{3\mathrm{x}}{24}+\frac{-6}{24}=\frac{-9}{24} \\ \Rightarrow \frac{3\mathrm{x}-6}{24}=\frac{-9}{24} \end{gathered}$$

$$\begin{gathered} \Rightarrow 3\mathrm{x}-6=-9 \\ \Rightarrow 3\mathrm{x}=-9+6 \\ \Rightarrow 3\mathrm{x}=-3 \\ \Rightarrow \mathrm{x}=\frac{-3}{3} \\ \Rightarrow \mathrm{x}=-1 \end{gathered}$$

Hence, $\frac{\boxed{-1}}{8}+\frac{-3}{12}=\frac{-9}{24}$.