question_answer

The sum of two rational numbers is \[-\frac{4}{5}.\] if one of them is\[\frac{-11}{20}\], find the other.

Answer:

\[\because \]       \[-\frac{11}{20}\] + (a rational number) \[=-\frac{4}{5}\]

\[\therefore \]      The required rational number

\[=-\frac{4}{5}-\left( \frac{-11}{20} \right)\]

\[=-\frac{4}{5}+\frac{11}{20}\] \[\left[ \because \,\,Additive\text{ in}verse\text{ }of\frac{-11}{20}is\frac{11}{20} \right]\]

\[=\frac{-4\times 4+11}{20}\]     \[[\because \,\,LCM\,of\,5\,and\,20\,is\,20]\]

\[=\frac{-16+11}{20}\]

\[=\frac{-5}{20}\,\,or\,\,\frac{-1}{4}\]

Thus,   the other rational number\[=-\frac{1}{4}\].