If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 11 days. If he works at reduced efficiency, he can work without break and finish that same job in 11 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?

A)5/11
B)6/11
C)7/11
D)8/11
E)9/11

Here is the solution:
My question is how does 1/11:1/8 get reduced to 8/11? Doesn't the : mean they are multiplied??

If Dale needs to rest every third day at full efficiency, that means he'll rest on days 3, 6, and 9 before finishing the job on day 11. That means that he'll have worked a total of 8 days, accomplishing 1/8 of the job each day.

At reduced efficiency, he works a total of 11 days, completing 1/11 of the job each day.

Therefore, the ratio of his output at reduced to his output at full is 1/11 : 1/8. That reduces to 8/11.