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 \[\left( \frac{-3}{4} \right)\] \[=\left[ \frac{1}{2}+\left( -\frac{3}{4} \right) \right]\div 2\] \[=\left[ \frac{2-3}{4} \right]\times \frac{1}{2}\] \[=-\frac{1}{4}\times \frac{1}{2}=-\frac{1}{8}\]
Thus, the three rational numbers are \[\left( -\frac{3}{4} \right),\left( -\frac{1}{8} \right)\] and \[\left( -\frac{11}{8} \right).\] A rational number between \[\left( -\frac{3}{4} \right)\] and \[\left( -\text{ }2 \right)\] \[=\left[ \left( -\frac{3}{4} \right)+(-2) \right]\div 2\] \[=\left[ \frac{(-3)+(-8)}{4} \right]\times \frac{1}{2}\] \[=\frac{-11}{4}\times \frac{1}{2}=\frac{-11}{8}\]
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