find three rational number between 2/3 and 3/4?

Okay, you can start by finding the average between 2/3 and 3/4.

(2/3 + 3/4) / 2 = (8/12 + 9/12) / 2 = (17/12)/2 = 17/24

The average of two different numbers is always going to be *between* the two numbers, so we can say that 17/24 is definitely between 2/3 and 3/4.

Now you can find the average between 2/3 and 17/24, and between 17/24 and 3/4.

(2/3 + 17/24) / 2 = (16/24 + 17/24) / 2 = (33/24) / 2 = 33/48 = 11/16

(17/24 + 3/4) / 2 = (17/24 + 18/24) / 2 = (35/24) / 2 = 35/48

So three rational numbers between 2/3 and 3/4 are... 11/16, 17/24, and 35/48

Of course, those aren't the only three...there are *infinitely* many rational numbers between 2/3 and 3/4. By trying different combinations of numerators and denominators, I'm sure you can come up with some more fractions that fall between 2/3 and 3/4. I hope that helps. Good luck!

2/3 = (2×16)/(3×16) = 32/48
3/4 = (3×12)/(4×12) = 36/48

The three rational numbers can be :
33/48 = 11/16
34/48 = 17/24
35/48

Hence, the three rational numbers can be 11/16, 17/24 and 35/48.

32/48_______________________36/48
_______33/48__34/48__35/48_______

If you want n rational numbers between the rational numbers a and b, where a<b, you can use
a+k, a+2k, a+3k, a+nk
where a+(n+1)k = b, so that (n+1)k=b-a and giving k=(b-a)/(n+1).

Doing this with your numbers a=2/3, b=3/4, k=(3/4-2/3)/4 = 1/48 and you have

2/3 < 11/16 < 17/24 < 35/48 < 3/4

which is actually an arithmetic progression with common difference k=1/48

Just add the two now and divide them by 2.
(2/3+3/4)/2=17/12*1/2=17/24.
Find other two nos between 17/24 and3/4 and go on!

One way to do this is to change the

fractions to decimals:

2/3 = 0.666 . . . ; 3/4 = 0.7500 . . .

So three rational numbers in

between would be 0.67, 0.68, and 0.69

or, as fractions, 67/100, 68/100 = 17/25,

and 69/100. Obviously there's lots more.