Answer:
13/48, 7/24, and 15/48
Step-by-step 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
