This is the equivalent problem in a different representation.

My son was comparing two fractions to decide which is bigger (a problem that appears in his Beast Academy workbook).

He looked at the fractions and noticed that if he changed the first fraction, he could get the denominators to be closer together.

Him: “Oh, now I know that is larger than !”

Me: “How do you know that?”

Him: “If we had we would know that is more than since is more than . We just have 1 more so for sure is more than .”

What I find interesting about this is that I was taught that in order to compare two fractions, one first needs to be able to find a common denominator. Obviously that’s not true.