Question

please tell 5 rational numbers between ⅕ and ⅙​

Answer 1

Step-by-step explanation:

$let \: x = \frac{1}{5} \: \: \: y = \frac{1}{6} \: \: n = 5$

$d = \frac{y - x}{n + 1} = \frac{ \frac{1}{6} - \frac{1}{5} }{5 + 1} = \frac{ \frac{5 - 6}{30} }{6} = \frac{ \frac{ - 1}{30} }{6} \\ = \frac{ - 1}{30} \times \frac{1}{6} = \frac{ - 1}{180}$

Thus, the five rational numbers between 1/5 and 1/6 are (x+d) ,(x+2d),(x+3d),(x+4d),(x+5d)

$ie \: ( \frac{1}{5} + ( - \frac{1}{180} )) \: ( \frac{1}{5} + 2 \times ( \frac{ - 1}{180} )) \: \\ (\frac{1}{5} + 3 \times ( \frac{ - 1}{180} )) ( \frac{1}{5} + 4 \times ( \frac{ - 1}{180} )) \: ( \frac{1}{5} + 5( \frac{ - 1}{180} ))$

$( \frac{1}{5} - \frac{1}{180}) \: ( \frac{1}{5} - \frac{2}{180}) \: ( \frac{1}{5} - \frac{3}{180}) \: \\ ( \frac{1}{5} - \frac{4}{180}) \: ( \frac{1}{5} - \frac{5}{180})$

$( \frac{36 - 1}{180}) \: ( \frac{36 -2 }{180}) \: ( \frac{36 - 3}{180}) \: ( \frac{36 - 4}{180}) \: ( \frac{36 - 5}{180})$

(35/180),(34/180),(33/180),(32/180),(31/180)