Tic to tocs ratio problem

kn2130 wrote:If 1 tick equals 3 tacs and 2 tacs equal 5 tocs, what is the ratio of 1 tic to one toc?

1) 15/2

2) 6/5

3) 5/6

4) 3/10

5) 1/15



The explanation says: Get both tics and tocs in terms of the same number of tacs. Since we are given the value of tics in terms of 3 tacs, and tocs in terms of 2 tacs, let's use the LCM of 2 and 3, or 6. If 1 tic equals 3 tacs, then 2 tics equal 5 tacs. If 2 tacs equal 5 tocs, then 6 tocs equals 3x5 or 15 tocs. Therefore 2 tics = 6 tacs = 16 tocs. We don't care about tacs anymore, just tics and tocs.

I completely understand it till this point. the following is where I get lost:

Divide to get the ratio of units on one side, and the numbers on the other side.

2 tics = 15 tocs

1 tic/1 toc = 15/2

I would think the ratio of tics to tocs is 2:15, not 15:2. Please help!

Thanks sooo much!

kn2130 wrote:haha! thanks so much! sometimes i get stuck on the simplest things (usually after several hours of studying.) i stared at your response for a long time, quite blankly, until it suddenly came to me! many thanks!