In Patty's room, 1/2 of her award ribbons are for horse riding and 1/6 are for ballet. What fraction of the awards are for another activity?

This is a relatively easy one to answer, it just needs to be looked at. If we change 1/2 to 3/6 (equal) we can add them together (easier) and get 4/6. Since 6/6 is obviously 1 we can fill in the fraction by adding 2/6 which simplified is 1/3. So the answer to this question is 1/3.

1/2 = 3/6

So,

(1/2) + (1/6) = (3/6) + (1/6)

(1/2) + (1/6) = (3+1) / 6

(1/2) + (1/6) = 4/6

(1/2) + (1/6) = 2/3

2/3 of the awards are for horse riding or ballet

So 1/3 is for the rest since 1 - (2/3) = (3/3) - (2/3) = (3-2) / 3 = 1/3

Answer: 1/3