We ran into that logic in a young man at the building supply center years ago, and I've never forgotten how amazed I was.
Here's the lesson my daughter's teacher used back in the 80's when trying to teach fractions:
When they insisted a 1/4 was bigger than 1/2 she would ask, "How many cents in $1.00, one-half dollar, and a quarter?" She would get the coins out and show them to the kids, and it would dawn on them.
Sue