Question

insert a rational number between 2/3 and 5/7​

Answer 1

Answer:

L.C.M of 5 and 7 is 35.

⇒ 2/5 = 2×7/5×7 = 14 /35.

⇒ 3/7 = 3×5/7×5 = 15/35.

By multiplying the numerator and denominator of 14/35 and 15/35 by 4.

⇒ 14/35 = 14 × 4 /35 × 4 = 56/140

⇒15/35 = 15×4 / 35 × 4 = 60 / 140.

Three rational numbers = 57/140 , 58/140 ,59/140.

Note : There are infinite rational or irrational numbers between two numbers

Answer 2

Answer:

Required rational number is 29/42.

Step-by-step explanation:

Given rational numbers are 2/3 and 5/7.

First we have to make their denominators same.

Multiplying numerator and denominator of rational number 2/3 by 14.

Then, $\frac{2}{3} = \frac{2*14}{3*14} = \frac{28}{42}$

Now, multiplying numerator and denominator of rational number 5/7 by 6.

Then, $\frac{5}{7} = \frac{5*6}{7*6} = \frac{30}{42}$

Given rational numbers are transformed to 28/42 and 30/42.

A rational number between these two rational numbers is 29/42.

Thus, required rational number is 29/42.