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Find any five rational numbers between $-1$ and $-2$.
Given :
The given numbers are $-1$ and $-2$.
To find :
We have to find any five rational numbers between $-1$ and $-2$.
Solution:
To plot 5 rational numbers in between $-2$ and $-1$, divide the line segment between $-2$ and $-1$ into at least six parts.
For convenience, divide it into six equal parts.
As the total length of the line segment is 1 unit, the length of each part is $\frac{1}{6}$ units.
So, the first point is $-2 +\frac{1}{6}$ which is $\frac{-11}{6} = -1\frac{5}{6}$
Similarly,
The next 4 rational numbers are,
$-2 + \frac{2}{6} =\frac{-12 + 2}{6} = \frac{-10}{6} = -1 \frac{4}{6}$.
$-2 + \frac{3}{6} =\frac{-12 + 3}{6} = \frac{-9}{6} = -1 \frac{3}{6}$.
$-2 + \frac{4}{6} =\frac{-12 + 4}{6} = \frac{-8}{6} = -1 \frac{2}{6}$.
$-2 + \frac{5}{6} =\frac{-12 + 5}{6} = \frac{-7}{6} = -1 \frac{1}{6}$.
Therefore, five rational numbers between $-1$ and $-2$ are, $-1\frac{5}{6}, -1\frac{4}{6}, -1\frac{3}{6}, -1\frac{2}{6}, -1\frac{1}{6}$
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