Question
What should be added to $-\frac{3}{6}$ to get $-\frac{11}{24} ?$
✓
Answer
Let the required rational number be $x$
Other number $=-\frac{3}{16}$
Sum of two number $=\frac{11}{24}$
According to question,
$ \begin{aligned} & -\frac{3}{16}+\mathrm{x}=\frac{11}{24} \\ & \Rightarrow \mathrm{x}=\frac{11}{24}+\frac{3}{16} \\ & \mathrm{x}=\frac{11 \times 2}{24 \times 2}+\frac{3 \times 3}{16 \times 3} \end{aligned} $
$(\because$ L.C.M. of 16 and $24=48)$
$ \begin{aligned} & x=\frac{22}{48}+\frac{9}{48} \\ & x=\frac{22+9}{48}=\frac{31}{48} \end{aligned} $
Other number $=-\frac{3}{16}$
Sum of two number $=\frac{11}{24}$
According to question,
$ \begin{aligned} & -\frac{3}{16}+\mathrm{x}=\frac{11}{24} \\ & \Rightarrow \mathrm{x}=\frac{11}{24}+\frac{3}{16} \\ & \mathrm{x}=\frac{11 \times 2}{24 \times 2}+\frac{3 \times 3}{16 \times 3} \end{aligned} $
$(\because$ L.C.M. of 16 and $24=48)$
$ \begin{aligned} & x=\frac{22}{48}+\frac{9}{48} \\ & x=\frac{22+9}{48}=\frac{31}{48} \end{aligned} $
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