Question

Insert 3 rational numbers between 1 /4 and 1/3 using mean method​

Answer 1

13/48, 7/24, and 15/48

Explanation:

When we have two numbers A and B (such that A < B), the mean between these numbers is:

mean = (A + B)/2

And we will always have that:

A < mean < B

In this case, we have the numbers 1/4 and 1/3

The mean between these numbers is:

M = (1/4 + 1/3)/2 = (3/12 + 4/12)/2 = (7/12)/2 = 7/24

we know that 7/24 is an integer that is between the numbers 1/4 and 1/3

Now we can take the mean between 1/4 and 7/24

M = (1/4 + 7/24)/2

= (6/24 + 7/24)/2 = (13/24)/2 = 13/48

And we have:

1/4 < 13/48 < 7/24

Now we can find the mean between 7/24 and 1/3:

M = ( 7/24 + 1/3)/2 = (7/24 + 8/24)/2 = (15/24)/2 = 15/48

then:

7/24 < 15/48 < 1/3

Then we can write:

1/4 < 13/48 < 7/24 < 15/48 < 1/3

Then the 3 rational numbers between 1/4 and 1/3 are:

13/48, 7/24, and 15/48