Question

insert two rational number between 1 upon 2 and 1 upon 3

Answer 1

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1/2 and 1/3

Let x = 1/3 ; y = 1/2

y > x ; n = 2

d = y - x / n + 1

$= \frac{ \frac{1}{2} - \frac{1}{3} }{2 + 1} \\ \\ = \frac{ \frac{3 - 2}{6} }{3} \\ \\ = \frac{ \frac{1}{6} }{3} \\ \\ = \frac{1}{6} \div 3 \\ \\ = \frac{1}{6} \times \frac{1}{3} \\ \\ = \frac{1}{18}$


1st rational number = x + d

= 1/3 + 1/18

= 6 + 1/18

= 7/18

2nd rational number = x + 2d

= 1/3 + 2 × 1/18

= 1/3 + 1/9

= 3 + 1/9

= 4/9





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