Question

Fill in the blanks:

$\frac{3}{4}+\frac{-5}{12}=\_\_\_$

Answer 1

Let $\mathrm{X}$ be filled at the blank;

So according to given condition,

$\Rightarrow \frac{3}{4}+\frac{-5}{12}=\mathrm{X}$

$\Rightarrow \mathrm{X}=\frac{3}{4}+\frac{-5}{12}$

LCM of denominator $4$ and $12$ is $12$.

Now convert both the rational numbers into equivalent rational numbers with denominator $12$,

$$\begin{gathered} \Rightarrow \mathrm{X}=\frac{3\times 3}{4\times 3}+\frac{-5\times 1}{12\times 1} \\ \Rightarrow \mathrm{X}=\frac{9}{12}-\frac{5}{12} \\ \Rightarrow \mathrm{X}=\frac{9-5}{12} \\ \Rightarrow \mathrm{X}=\frac{4}{12} \\ \Rightarrow \mathrm{X}=\frac{\cancel{4}}{{\displaystyle \underset{3}{\cancel{12}}}} \\ \Rightarrow \mathrm{X}=\frac{1}{3} \end{gathered}$$

Hence, $\frac{3}{4}+\frac{-5}{12}=\boxed{\frac{1}{3}}$.