• # 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 $\left( -\frac{11}{8} \right).$

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