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.
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Here, we have to find the all positive rational numbers that are less than 5 having denominator 30 when written in lowest terms.
So, fractions :
1/ 30 + 7/ 30 + 11/ 30 + 13/ 30 + 17/ 30 + 19/ 30 + 23/ 30 + 29/ 30 + 31/ 30 + 37/ 30 + 41/ 30 + 43/ 30 + 47/30 + 49/30 + 53/30 + 59/30 + 61/ 30 + 67/30 + 71/30 + 73/30 + 77/30 + 79/30 + 83/30 + 89/30 + 91/ 30 + 97/30 + 101/ 30 + 103/30 + 107/30 + 109/30 + 113/30 + 119/30 + 121/ 30 + 127/30 + 131/ 30 + 133/30 + 137/30 + 139/30 + 141/ 30 + 143/30 + 147/30 + 149/30
= 3147/30
= 104.9
Hence, sum of all positive rational numbers that are less than 5 is 104.9