Question

Find four rational number between 1/6 and 1/3
​

Answer 1

$Let\: q_1, \: q_2, \: q_3, \: and \: q_4 \: be \: the \: \\ four \: required \: rational \: numbers.$

Then,

$q_1 = \frac{1}{2} ( \frac{1}{6} + \frac{1}{3} ) \\ \\ = \frac{1}{2} ( \frac{1 + 2}{6} ) \\ \\ = \frac{1}{4}$

$q_2 = \frac{1}{2} ( \frac{1}{4} + \frac{1}{3} ) \\ \\ = \frac{1}{2} ( \frac{3 + 4}{12} ) \\ \\ = \frac{7}{24}$

$q_3 = \frac{1}{2} ( \frac{7}{24} + \frac{1}{3} ) \\ \\ = \frac{1}{2} ( \frac{7 + 8}{24} ) \\ \\ = \frac{5}{16}$

$q_4 = \frac{1}{2} ( \frac{5}{16} + \frac{1}{3} ) \\ \\ = \frac{1}{2} ( \frac{15 + 16}{48} ) \\ \\ = \frac{31}{96}$

$\sf{Hence, the \: four \: rational number } \\ \sf between \frac{1}{6} \: and \: \frac{1}{3} are \: \frac{1}{4},\frac{7}{24} , \frac{5}{16} \: and \: \frac{31}{96} .$

Answer 2

Step-by-step explanation:

to find:-

rational number between

$\frac{1}{6} and \: \frac{1}{3} \\ lcm \: of3 \: and \: 6 \: is \: 6 \: \\ \frac{1}{6} \times \frac{1}{1} = \frac{1}{6} \\ \frac{1}{3} \times \frac{2}{2} = \frac{2}{6} \\ \\ \frac{1}{6} \times \frac{5}{5} = \frac{5}{30} \\ \frac{2}{6} \times \frac{5}{5} = \frac{10}{30} \\ rational \: number \: are \\ \frac{6}{10} \: \: \frac{7}{10} \: \: \frac{8}{10} \: \: \frac{9}{10}$

hope it help you

♡♡♡♡♡♡♡♡♡