+1557 What is the sum of all positive common fractions (in simplest terms) less than $5$ whose denominator is 3?
+1632 You have 1/3, 2/3, 4/3, 5/3, 7/3, 8/3, 10/3, 11/3, 13/3, 14/3.
You have to skip 3/3, 6/3, 9/3, and 12/3 because they are not in simplest form, as they simplify to 1, 2, 3, and 4 respectively (in the same order). And you have to skip 15/3 = 5 because the problem states "less than 5".
Group by 2's for adding, like how 1/3 + 2/3 = 3/3 = 1
1/3 + 2/3 + 4/3 + 5/3 + 7/3 + 8/3 + 10/3 + 11/3 + 13/3 + 14/3 = 1 + 3 + 5 + 7 + 9 = 25.
Just a note: Notice how when I add the first 5 positive odd numbers, I get 5^2- can you generalize this?
+1632 You have 1/3, 2/3, 4/3, 5/3, 7/3, 8/3, 10/3, 11/3, 13/3, 14/3.
You have to skip 3/3, 6/3, 9/3, and 12/3 because they are not in simplest form, as they simplify to 1, 2, 3, and 4 respectively (in the same order). And you have to skip 15/3 = 5 because the problem states "less than 5".
Group by 2's for adding, like how 1/3 + 2/3 = 3/3 = 1
1/3 + 2/3 + 4/3 + 5/3 + 7/3 + 8/3 + 10/3 + 11/3 + 13/3 + 14/3 = 1 + 3 + 5 + 7 + 9 = 25.
Just a note: Notice how when I add the first 5 positive odd numbers, I get 5^2- can you generalize this?
