Question

Find the sum of all positive rational numbers that are less than 5, and that have a denominator of 30 when written in lowest terms.

Answer 1

1. find the factors of 30
2. (total number of fractions less than 5 with 30 as denominator)-(number of fractions less than 5 with 30 as denominator BUT not in lowest terms)

Answer 2

Factors of 30:1,2,3,5,6,10,15,30

\[\text{Answer}=150-[2,3,5,6,10,15,30]\times5=150-7\times5=115\]

Answer 3

Here are all possible numerators: 1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 133, 137, 139, 143, 149 They are the numbers less than 150 that are relatively prime with 30. Add them up and divide by 30.
Their sum is 3000. Divide 3000 by 30, you get 100. My answer is different than @kc_kennylau. Have I done something wrong?

Answer 4

@eliassaab sorry, it's me who didn't read the question carefully.

@JuanSalitras Disculpe por no haber leido la pregunta claramente... :/

Answer 5

No problem @kc_kennylau

Answer 6

http://openstudy.com/users/juansalitras#/updates/52ae253ae4b0b09acc7fb106
but he's not active anymore, and i think that it's due to his bad experience in not having anyone answering his questions in 13 days.

Answer 7

P.S. This question is posed 13 days ago.

Answer 8

I did not notice that.

Answer 9

If I had had this experience, I would have quitted OS immediately.