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Find five rational numbers between \(1\) and \(2\).
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Question

Find five rational numbers between \(1\) and \(2\).

Answer

 \(\frac{7}{6}, \frac{4}{3}, \frac{3}{2}, \frac{5}{3}\) and \(\frac{11}{6}\).
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Solution

We have to find five rational numbers between \(1\) and \(2\).
So, we write \(1\) and \(2\) as rational numbers \(\frac{1}{1}\) and \(\frac{2}{1}\).
As the difference between the numerators is less than \(5\) ( rational number to be found)
Therefore, we  multiplying numerator and denominator by \(6\), so that difference between their  numerator become  is greater than \(5\).
i.e.  \(\frac{1}{1}=\frac{1\times 6}{1\times 6}=\frac{6}{6}\)
 and \(\frac{2}{1}=\frac{2\times 6}{1\times 6}=\frac{12}{6}\).
Thus, five rational numbers between \(\frac{6}{6}\) and \(\frac{12}{6}\) are \(\frac{7}{6}, \frac{8}{6}, \frac{9}{6}, \frac{10}{6}\) and \(\frac{11}{6}\).
So, the five rational numbers between \(1\) and \(2\) are \(\frac{7}{6}, \frac{4}{3}, \frac{3}{2}, \frac{5}{3}\) and \(\frac{11}{6}\).
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