Question

find ten rational numbers between 2/3 and 4/5​

Answer 1

Answer:

1. (41/60 )(42/60 ) (43/60) (44/60) (45/60)

Answer 2

Solution :-

LCM of 3 and 5 is 15

Now,

$\frac{2}{3} = \frac{2}{3} \times \frac{5}{5} = \frac{10}{15} \: and \: \frac{4}{5} = \frac{4}{5} \times \frac{3}{3} = \frac{12}{15}$

Since,

There is only one integers between 10 and 12.

Therefore,

$We \: replace \: \frac{2}{3} \: and \: \frac{4}{5} \: by \: equivalent$

Rational number having sufficiently large common denominator, i.e.,

$\frac{2}{3} = \frac{10}{10} \times \frac{10}{10} = \frac{100}{150} \: and \: \frac{4}{5} = \frac{12}{15} \times \frac{10}{10} = \frac{120}{150}$

Therefore,

Integers 101, 102, ..., 119 lie between 100 and 120.

$\frac{100}{150} < \frac{101}{150} < \frac{102}{150} < \frac{103}{150} ..., < \frac{119}{150} < \frac{120}{150}$

Therefore,

Ten rational number between

$</p><p>Ten \: rational \: number \: between \: \frac{2}{3} \: and \: \frac{4}{5} \: are \: \: :$

$\frac{101}{150} , \frac{102}{150} , \frac{103}{150},\frac{104}{150} ,..., \frac{110}{150}$