# Which is greater?

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.