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Answer :

There can be infinitely many rational numbers between \(\frac{3}{5} \) and \(\frac{4}{5} \) , one way to take them is

\(\frac{3}{5} = \frac{3×10}{5×10} = \frac{30}{50} \)

\(\frac{4}{5} = \frac{4×10}{5×10} = \frac{40}{50} \)

Therefore the rational number between \(\frac{30}{50} \) and \(\frac{40}{50} \) are

\(\frac{31}{50} ,\frac{32}{50} \frac{33}{50} ,\frac{34}{50} ,
\frac{35}{50} \)

Another way to find middle rational number between two number \(\frac{3}{5} \) and \(\frac{4}{5} \)is

\(\Rightarrow \) \(\frac{\frac{3}{5} + \frac{4}{5} }{2} \)

= \( \frac{\frac{7}{5} }{2} \)

= \(\frac{7}{10} \) .

As, \( \frac{3}{5} < \frac{7}{10} < \frac{4}{5} \) .

Now,a rational number between \(\frac{3}{5} \) and \(\frac{7}{10} \) is

\(\Rightarrow \)\(\frac{\frac{3}{5} + \frac{7}{10} }{2} \)

=\( \frac{\frac{13}{10} }{2} \)

= \(\frac{13}{20} \).

As, \(\frac{3}{5} < \frac{13}{20} < \frac{7}{10} < \frac{4}{5} \).

Similarly, \(\frac{25}{40} , \frac{27}{40} , \frac{15}{20} \) are rational numbers between \(\frac{3}{5} \) and \(\frac{4}{5} \).

Therefore, five rationals between numbers\(\frac{3}{5} \) and \(\frac{4}{5} \)are

\( \frac{25}{40} , \frac{13}{20} , \frac{27}{40} , \frac{7}{10} , \frac{15}{20} \).

- Is zero a rational number?Can you write it in the form \(\frac{p}{q} \),where p and q are integers and \(q \ne 0\).
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- State whether the following statements are true or false.Give reasons for your answers. i)Every natural number is a whole number. ii) Every integer is a whole number. iii) Every rational number is a whole number.

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