On the planet Flarp... Please advice.

[maximkononov]

On the planet Flarp, 3 floops equal 5 fleeps, 4 fleeps equal 7 flaaps, and 2 flaaps equal 3 fliips. How many floops are equal to 35 fliips?

Solution (from the MGMT SG book):
35 fliips x 2 flaaps/3 fliips x 4 fleeps/7 flaaps x 3 floops/5 fleeps = 8 floops

How do I know that I need to multiply all the ratios? The problem states equalities, such as 3 floops = 5 fleeps and etc. Why equalities did become ratios? More detailed explanation would be helpful for me. When I was doing this problem, I expressed each unit from the beginning (floops) to the end (fliips) separately to find out how many floops are equal to 35 fliips.

[tim]

if you got to the correct answer, the approach you used will probably work. the idea behind the ratios is that if you want to change units, you can multiply what you have by some ratio that is equal to 1, which will preserve the overall quantity but express it in different units. consider the following example:

how many feet are there in 36 inches?
remember 12 inches = 1 foot

36 inches * 1 foot/12 inches = 3 feet