Explain how you know that 15/30 is greater than 1/3 but led than 2/3?

You covert them to a different fraction so that they all have the same denominator

15/30 stays the same

1/3 becomes 10/30 (multiply both numerator and denominator by 10)

and 2/3 becomes 20/30 (multiply both numerator and denominator by 10)

This way you can compare all fractions easily