Question

insert three fractions between 4/7,2/3​

Answer 1

${ \huge{\frac{4}{7}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \huge{\frac{2}{3}}}$

Now,

$1st \: \: fraction = \frac{ \frac{4}{7} + \frac{2}{3} }{2} = \frac{ \frac{26}{21} }{2} = \frac{26}{21 \times 2} = \frac{13}{21}$

$2nd \: fraction = \frac{ \frac{4}{7} + \frac{13}{21} }{2} = \frac{ \frac{25}{21} }{2} = \frac{25}{42}$

$3rd \: \: fraction = \frac{ \frac{13}{21} + \frac{2}{3} }{2} = \frac{ \frac{27}{21} }{2} = \frac{27}{42}$