Let \(a = \frac{7}{12}\), \(b = \frac{5}{6}\). Express both \(a\) and \(b\) in the form \(\frac{k_1}{m}\) and \(\frac{k_2}{m}\) where \(k_1, k_2\) and \(m\) are integers and \(k_2 − k_1 = 6\). Using the same denominator m, write exactly five distinct rational numbers lying between \(a\) and \(b\) keeping an integer numerator. Explain why the condition \(k_2 − k_1 > n + 1\) is necessary to find \(n\) such rational numbers between the two rational numbers \(a\) and \(b\) using this method.