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5. Find five rational numbers between.

(i) $\frac{2}{3}$ and $\frac{4}{5}$ (ii) $\frac{-3}{2}$ and $\frac{5}{3}$ (iii) $\frac{1}{4}$ and $\frac{1}{2}$

Answers (1)

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(i) For finding rational numbers between 2 numbers one method is to find means between the numbers repeatedly.

Another method is:- For $\frac{2}{3}$ and $\frac{4}{5}$

$\frac{2}{3}$ can be written as $\frac{10}{15}$ $\left ( \frac{2}{3}\times \frac{5}{5} = \frac{10}{15}\right )$

and $\frac{4}{5}$ can be written as $\frac{12}{15}$ $\left ( \frac{4}{5}\times \frac{3}{3} = \frac{12}{15}\right )$

Thus numbers between $\frac{10}{15}$ and $\frac{12}{15}$ are the required numbers.

Now since we require 5 numbers in between, thus we multiply numerator and denominator both by 4.

It becomes numbers between $\frac{40}{60}$ and $\frac{48}{60}$ .

Thus numbers are $\frac{41}{60}, \frac{42}{60}, \frac{43}{60}, \frac{44}{60}, \frac{45}{60}$ .

(ii) Similarly for $\frac{-3}{2}$ and $\frac{5}{3}$

Required numbers fall between $\frac{-9}{6}$ and $\frac{10}{6}$ $\left \{ \left ( \frac{-3}{2}\times \frac{3}{3} \right )= \frac{-9}{6} \right \}$

Thus numbers are $\frac{-8}{6}, \frac{-7}{6}, \frac{-6}{6}, \frac{-5}{6}, \frac{-4}{6}$

(iii) For $\frac{1}{4}$ and $\frac{1}{2}$

Required numbers lie between $\frac{1}{4}$ and $\frac{2}{4}$ or we can say between $\frac{8}{32}$ and $\frac{16}{32}$

Thus numbers are $\frac{9}{32}, \frac{10}{32}, \frac{11}{32}, \frac{12}{32}, \frac{13}{32}$

Posted by

Divya Prakash Singh

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