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

 Jun 8, 2024
 #1
avatar+806 
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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! :)

 Jun 8, 2024

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