Question

Find 3 rational number number between 1/2 & 2/3​

Answer 1

Answer:

Step-by-step explanation:

Given rationals numbers are, 1/2 & 3/4

We know that, Between two given rational numbers, there exists infinite number of rational numbers. We are required to find out 3 such.

Changing to equivalent fractions.

1/2 = 12/24

3/4 = 18/24

We changed the rationals to have equal denominators.

So now rational numbers between 12/24 & 18/24 would be rational numbers between 1/2, 3/4 ( Because they are equivalent fractions 1/2 = 12/24, 3/4 = 18/24)

Now, Rationals between 1/2 & 3/4 are

13/24

14/24

15/24

16/24

17/24

We can also find many such rational numbers. And If we wish to find exactly equidistant rational numbers,

Then We can use the Arithmetic progression.

Between two rationals a & b ( b > a), we need to find n equidistant rationals then the distance between consecutive rationals is

d = b - a / n +1

After finding the distance,

The required rationals will be a + d, a + 2d,a + 3d,.....

Hope helped !

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Answer 2

LCM of 2 and 3 = 6

1/2 = 1 ×3 / 2×3

= 3/6

2/3 = 2× 2 / 3×2

= 4/6

Three rational number between 3/6 and 4/6