Question
Find five rational numbers between $\frac{-3}{5}\text{ and }\frac{-1}{2}$
✓
Answer
$LCM$ of $5$ and $2 = 10$
Now $\frac{-3}{5}=\frac{-3\times2}{5\times2}=\frac{-6}{10}$
$=\frac{-6\times6}{10\times6}=\frac{-36}{60}$
and $\frac{-1}{2}=\frac{-1\times5}{2\times5}=\frac{-5}{10}$
$=\frac{-5\times6}{10\times6}=\frac{-30}{60}$
and $\frac{-36}{60}<\frac{-35}{60}<\frac{-34}{60}<\frac{-33}{60}$
$<\frac{-32}{60}<\frac{-31}{60}<\frac{-30}{60}$
$\therefore$ five rational numbers between $\frac{-3}{5}$ and $\frac{-1}{2}$ are $\frac{-36}{60}<\frac{-34}{60}<\frac{-33}{60}<\frac{-32}{60}<\frac{-31}{60}$
Now $\frac{-3}{5}=\frac{-3\times2}{5\times2}=\frac{-6}{10}$
$=\frac{-6\times6}{10\times6}=\frac{-36}{60}$
and $\frac{-1}{2}=\frac{-1\times5}{2\times5}=\frac{-5}{10}$
$=\frac{-5\times6}{10\times6}=\frac{-30}{60}$
and $\frac{-36}{60}<\frac{-35}{60}<\frac{-34}{60}<\frac{-33}{60}$
$<\frac{-32}{60}<\frac{-31}{60}<\frac{-30}{60}$
$\therefore$ five rational numbers between $\frac{-3}{5}$ and $\frac{-1}{2}$ are $\frac{-36}{60}<\frac{-34}{60}<\frac{-33}{60}<\frac{-32}{60}<\frac{-31}{60}$
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