What is the sum of all positive common fractions (in simplest terms) less than $5$ whose denominator is 3?

BRAINBOLT Jun 8, 2024

#1**+1 **

It's actually not hard to just list all the numbers out.

We have

\(\frac{1}{3}, \frac{2}{3}, \frac{4}{3},\frac{5}{3}, \frac{7}{3}, \frac{8}{3}, \frac{10}{3}, \frac{11}{3}, \frac{13}{3}, \frac{14}{3}\)

The ones we excluded from this list, like 3/3 and 6/3 are not in simplest form, therefore eliminated.

Now, adding all these values up, we get \(75/3=25\)

That means 25 is our answer!

Thanks! :)

NotThatSmart Jun 8, 2024