question_answer

Find the three rational numbers between \[\frac{1}{2}\]and \[-\text{ }2.\]

Answer:

A rational number between  \[\frac{1}{2}\]and \[-\text{ }2\]

\[=\left[ \frac{1}{2}+(-2) \right]\div 2\]

\[=\left[ \frac{1-4}{2} \right]\div 2\]

\[=\left[ -\frac{3}{2} \right]\times \frac{1}{2}=-\frac{3}{4}\]

A rational number between \[\frac{1}{2}\] and \[\left( \frac{-3}{4} \right)\]

\[=\left[ \frac{1}{2}+\left( -\frac{3}{4} \right) \right]\div 2\]

\[=\left[ \frac{2-3}{4} \right]\times \frac{1}{2}\]

\[=-\frac{1}{4}\times \frac{1}{2}=-\frac{1}{8}\]

                                                                                                                                                                                   

A rational number between \[\left( -\frac{3}{4} \right)\] and \[\left( -\text{ }2 \right)\]

\[=\left[ \left( -\frac{3}{4} \right)+(-2) \right]\div 2\]

\[=\left[ \frac{(-3)+(-8)}{4} \right]\times \frac{1}{2}\]

\[=\frac{-11}{4}\times \frac{1}{2}=\frac{-11}{8}\]

                                                                                                                                                Thus, the three rational numbers are \[\left( -\frac{3}{4} \right),\left( -\frac{1}{8} \right)\] and \[\left( -\frac{11}{8} \right).\]