Question

Find 6 rational numbers between 3 and 4.

Find 5 rational numbers between 2/5 and 3/5.

Find 5 rational numbers between 1/6 and 2/5.

Let a = 7/12 and b = 5/6. Express both a and b in the form k₁/m and k₂/m where k₁, k₂ and m are integers and k₂ – k₁ > 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 k₂ – k₁ > n + 1 is necessary to find n such rational numbers between the two rational numbers a and b using this method.