My younger son was trying out some old AMC 8 problems this morning, and ran across this problem from the 1985 AMC 8 (or the AJHME as it was called then):

What number is the middle of 1/5 and 1/3?

He wanted to talk about this question for our math movie today. Great. He worked through the question fairly quickly and mentioned that one of the reasons the solution wasn’t that hard was that both 3 and 5 were odd.

That observation led me to ask what fraction was in between 1/3 and 1/2. It turned out that this question was much more challenging!