2/3 works here because its value is greater than 1/2 but less than 4/5. An easy way to visualize this is to take the decimal value of each number as decimals are often easier to understand than fractions.
1/2=.50
2/3=.67
4/5=.80
This inequality could be rewritten as .50 < .67 < .80 and would have the same value.
