Question

find five rational numbers between 1/2 and 2/3

Answer 1

five rational numbers

1/2 and 2/3 first make denominator same.
1/2×3/3 and 2/3×2/2
3/6 and 4/6
3/6×7/7 and 4/6×7/7
21/42 and 28/42
then answer is 22/42 ,23/42,24/42,25/42,26/42

Answer 2

Firstly,we should make the rational numbers like(with same denominator).

For this, we will need their LCM.

LCM of 2 and 3 is 6.

1/2=1/2*3/3=3/6.
2/3=2/3*2/2=4/6.

Still we can't see any rational numbers between 1/2 and 2/3.

So we need to find equivalent numbers of 1/2 and 2/3.This can be done by multiplying the numbers with any number greater than or equal to 6.

Let's multiply by 6.

3/6=3/6*6/6=18/36.
46=4/6*6/6=24/36.

Now: 19/36,20/36(5/9),21/36(7/12),22/36(11/18) and 23/36 are 5 rational numbers between 1/2 and 2/3.

NOTE: We can find more numbers by multiplying them by other numbers like 7,8 and so on instead of 6.