Question

Find three rational numbers between 2/3 and 3/4

Answer 1

There are a variety of ways to do it.
I am just showing one-

1. 1/2(2/3 + 3/4)
=1/2(17/12)
=17/24

2.1/2(2/3 + 17/24)
=1/2(33/24)
=33/48

3.1/2(3/4 + 17/24)
=1/2(35/24)
=35/48

So, the required rational numbers are:- 17/24, 35/48, 33/48.

:)

Answer 2

Make the 2 denominators the same

2/3 = (2 x 4)/(3 x 4) = 8/12

3/4 = (3 x 3)/(4 x 3) = 9/12

⇒ The two factions are 8/12 and 9/12

To find 3 rational numbers, we multiply each fraction for 4 on both the numerator and denominator.

Multiply the fraction by the factor 4:

8/12 = (8 x 4) / (12 x 4) = 32/48

9/12 = (9 x 4) / ( 12 x 4) = 36/48

⇒ The two factions are 32/48 and 36/48

List the fractions in between:

32/48, 33/48, 34/48, 35/48, 36/48

⇒  The fractions are 33/48, 34/48, 35/48

Answer: 33/48, 34/48, 35/48