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avatar+677 

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

 Jun 5, 2024

Best Answer 

 #1
avatar+1280 
+1

We can easily just list the values 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 numbers we excluded like 3/3 or 6/3 are not in simplest form, so we ignore them. 

 

Adding all these fractions up, we get \(75/3=25\)

 

So 25 is our answer. 

 

Thanks! :)

 Jun 5, 2024
 #1
avatar+1280 
+1
Best Answer

We can easily just list the values 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 numbers we excluded like 3/3 or 6/3 are not in simplest form, so we ignore them. 

 

Adding all these fractions up, we get \(75/3=25\)

 

So 25 is our answer. 

 

Thanks! :)

NotThatSmart Jun 5, 2024

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