Question

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

Answer 1

Answer with explanation:

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

Factors of 30 are=1,2,3,5,6,10,15,30.

So, all these fractions will begin from and has sum

   $\rightarrow\frac{1}{30}+\frac{7}{30}+\frac{11}{30}+\frac{13}{30}+\frac{17}{30}+\frac{19}{30}+\frac{23}{30}+\frac{29}{30}+\frac{31}{30}+\frac{37}{30}+\frac{41}{30}+\frac{43}{30}+\frac{47}{30}+\frac{49}{30}+\frac{53}{30}+\frac{59}{30}+\frac{61}{30}+\frac{67}{30}+\frac{71}{30}+\frac{73}{30}+\frac{77}{30}+\frac{79}{30}+\frac{83}{30}+\frac{89}{30}+\frac{91}{30}+\frac{97}{30}+\frac{101}{30}+\frac{103}{30}+\frac{107}{30}+\frac{109}{30}+\frac{113}{30}+\frac{119}{30}+\frac{121}{30}+\frac{127}{30}+\frac{131}{30}$

$\frac{133}{30}+\frac{137}{30}+\frac{139}{30}+\frac{143}{30}+\frac{147}{30}+\frac{149}{30}\\\\=\frac{3147}{30}\\\\=104.9$