Question

Find two rational and two irrational numbers between 1/8 and 2/9.

Answer 1

$d = \frac{ y - x}{n + 1} = \frac{ \frac{2}{9} - \frac{1}{8} }{3} = \frac{7}{72 \times 3} \\ x + d = \frac{1}{8} + \frac{7}{72 \times 3} = \frac{27 + 7}{216} \\ \: \: \: \: \: \: \: \: = \frac{34}{216} \\ x + 2d = \frac{27 + 14}{216} = \frac{41}{216}$