Question

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

Answer 1

If you have issues with knowing which fraction is bigger or smaller thing of them as a number with a decimal instead. Like 15/30 is .50(or 50%) and 1/3 is .33(or 33%) and 2/3 is .66(or 66%). So you know that 50 is between 33 and 66.

Answer 2

you convert 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 the fractions easily