List five rational numbers between:
$(i)$. $-1$ and $0$
$(ii)$. $-2$ and $-1$
$(iii)$. $\frac{-4}{5}$ and $\frac{-2}{3}$
$(iv)$.$-\frac{1}{2}$ and $\frac{2}{3}$

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

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

(ii) Five rational numbers between  -2 and -1

We can write -2, -1 as $\frac{-12}{6}$, $\frac{-6}{6}$

So 5 rational numbers between $\frac{-12}{6}$ and $\frac{-6}{6}$ are

$\frac{-11}{6}$, $\frac{-10}{6}$, $\frac{-9}{6}$,$ \frac{-8}{6}$,$ \frac{-7}{6}$

(iii) Five rational numbers between -4/5 and -2/3

We can write $\frac{-4}{5}$, $\frac{-2}{3}$ as $\frac{-12}{15}$, $\frac{-10}{15}$ or $\frac{-48}{60}$, $\frac{-40}{60}$

So 5 rational numbers between $\frac{-48}{60}$ and $\frac{-40}{60}$ are

$\frac{-47}{60}$, $\frac{-46}{60}$, $\frac{-45}{60}$, $\frac{-44}{60}$, $\frac{-43}{60}$

(iv) Five rational numbers between -1/2 and 2/3

$-1/2 < (-1/6) < (0) < (1/3) < (1/2) < (20/36) < 2/3$

So 5 rational numbers between the given numbers are $(-1/6), (0), (1/3), (1/2), (20/36)$

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Updated on: 10-Oct-2022

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