First, make both fractions have same denominator. Change 1/3 to 10/30 and 1/2 to 15/30. Then you can pick numbers in between like 11/30, 12/30, 13/30, 14/30. See, it's a phijig.
But the real trick? My teacher, Sir, used to say to just add the numerators and denominators: (1+1)/(3+2)=2/5. Then find numbers between 1/3 and 2/5, and so on. In our school, we didn't always have fancy methods, we just made the denominators bigger with whatever number we could multiply easily.
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