Question
List five rational numbers between $-\frac{1}{2}$ and $\frac{2}{3}$
✓
Answer
Firstly we need to have common denominators in both the rational numbers
Thus we multiply $2$ with $6$ and $3$ with $4$ to get the common denominator $12$
We have $-\frac{1}{2}=-\frac{1 \times 6}{2 \times 6}=-\frac{6}{12}$
$\frac{2}{3}=\frac{2 \times 4}{3 \times 4}=\frac{8}{12}$
Now, we write the rational numbers between$-6\over 12$and$8\over 12$
So, $-\frac{6}{12}<-\frac{4}{12}<-\frac{3}{12}<0<\frac{4}{12}<\frac{6}{12}<\frac{8}{12}$
$\Rightarrow$ $-\frac{1}{2}<-\frac{1}{3}<-\frac{1}{4}<0<\frac{1}{3}<\frac{1}{2}<\frac{2}{3}$
$\therefore $ five rational numbers between $-\frac{1}{2}$and $\frac{2}{3}$are $-\frac{1}{3},-\frac{1}{4}, 0, \frac{1}{3}$and $\frac{1}{2}$.
Thus we multiply $2$ with $6$ and $3$ with $4$ to get the common denominator $12$
We have $-\frac{1}{2}=-\frac{1 \times 6}{2 \times 6}=-\frac{6}{12}$
$\frac{2}{3}=\frac{2 \times 4}{3 \times 4}=\frac{8}{12}$
Now, we write the rational numbers between$-6\over 12$and$8\over 12$
So, $-\frac{6}{12}<-\frac{4}{12}<-\frac{3}{12}<0<\frac{4}{12}<\frac{6}{12}<\frac{8}{12}$
$\Rightarrow$ $-\frac{1}{2}<-\frac{1}{3}<-\frac{1}{4}<0<\frac{1}{3}<\frac{1}{2}<\frac{2}{3}$
$\therefore $ five rational numbers between $-\frac{1}{2}$and $\frac{2}{3}$are $-\frac{1}{3},-\frac{1}{4}, 0, \frac{1}{3}$and $\frac{1}{2}$.
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