Which is greater?

whichisbigger

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).

\frac{2}{5} \circ \frac{7}{21}

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

\frac{8}{20} \circ \frac{7}{21}

Him: “Oh, now I know that \frac{8}{20} is larger than \frac{7}{21}!”

Me: “How do you know that?”

Him: “If we had \frac{7}{20} we would know that is more than \frac{7}{21} since \frac{1}{20} is more than \frac{1}{21}. We just have 1 more \frac{1}{20} so for sure \frac{8}{20} is more than \frac{7}{21}.”

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.