Question

Write three rational number between 2/3 and 5/7

Answer 1

2/3 =   2*7/3*7
      = 14/21

5/7 = 5*3/7*3
      = 15/21

Now, 14/21 = 14*4/21*4 = 56/84
and, 15/21 = 15*4/21*4 = 60/84

so, three rational nos. are 57/84, 58/84 and 59/84

Answer 2

Given:

Two fractions 2/3 and 5/7

To find:

Three rational numbers between the given two fractions.

Solution:

The three rational numbers between 2/3 and 5/7 are 57/84, 58/84 and 59/84.

To answer this question, we will follow the following steps:

First of all, we should know that a number is said to be a rational number if it can be written in the form of p/q.

Now,

as given

we have two fractions 2/3 and 5/7.

First of all, we will make the denominators of given fractions the same.

So,

On multiplying 7 and 3 in both numerator and denominator of 2/3 and 5/7 respectively, we get

$\frac{2 \times 7}{3 \times 7} \: and \: \frac{5 \times 3}{7 \times 3}$

$= \frac{14}{21} \: and \: \frac{15}{21}$

Now, to find 'n' rational numbers between two numbers, we will multiply n + 1 in both the numerator and denominator of the given two numbers.

So,

Three rational numbers between 14/21 and 15/21 are

$\frac{14 \times 4}{21 \times 4} \: and \: \frac{15 \times 4}{21 \times 4}$

$= \frac{56}{84} \: and \: \frac{60}{84}$

$= \frac{57}{84}, \: \frac{58}{84} \: and \: \frac{59}{84}$

Hence, three rational numbers between 2/3 and 5/7 are 57/84, 58/84 and 59/84.