Question
Find six rational numbers between 3 and 4.
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Answer
Given that to find out six rational numbers between 3 and 4 We have,$3\times\frac{7}{7}=\frac{21}{7}$ and
$4\times\frac{6}{6}=\frac{28}{7}$
We know 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28$\frac{21}{7}<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<\frac{28}{7}$
$3<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<4$
Therefore, 6 rational numbers between 3 and 4 are$\frac{22}{7},\frac{23}{7},\frac{24}{7},\frac{25}{7},\frac{26}{7},\frac{27}{7}$
Similarly to find 5 rational numbers between 3 and 4, multiply 3 and 4 respectively with $\frac{6}{6}$ and in order to find 8 rational numbers between 3 and 4 multiply 3 and 4 respectively with $\frac{8}{8}$ and so on.
$4\times\frac{6}{6}=\frac{28}{7}$
We know 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28$\frac{21}{7}<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<\frac{28}{7}$
$3<\frac{22}{7}<\frac{23}{7}<\frac{24}{7}<\frac{25}{7}<\frac{26}{7}<\frac{27}{7}<4$
Therefore, 6 rational numbers between 3 and 4 are$\frac{22}{7},\frac{23}{7},\frac{24}{7},\frac{25}{7},\frac{26}{7},\frac{27}{7}$
Similarly to find 5 rational numbers between 3 and 4, multiply 3 and 4 respectively with $\frac{6}{6}$ and in order to find 8 rational numbers between 3 and 4 multiply 3 and 4 respectively with $\frac{8}{8}$ and so on.
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