List five rational numbers between:
(i) $-1$ and $0$
(ii) $-2$ and $-1$

Given:

The given numbers are

(i) $-1$ and $0$ (ii) $-2$ and $-1$

To do :

We have to list five rational numbers between the given numbers.

Solution :

(i) Five rational numbers between $-1$ and 0

We can write $-1, 0$ as $\frac{-6}{6}, \frac{0}{6}$

So 5 rational numbers between $\frac{-6}{6}$, and $\frac{0}{6}$ are

$\frac{-5}{6}, \frac{-4}{6}, \frac{-3}{6}, \frac{-2}{6}, \frac{-1}{6}$.

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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Updated on: 10-Oct-2022

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