Proper definition of the ratio a:b:c

If am given a ratio I understand that we make that

(so I guess I could write <--> )

I understand how we can prove when we just have two numbers that <--> because you can write = = and the x's just cancel. However after playing with it for a little while I realized we cannot write =

Is the proper definition the following: are in the ratio <--> = =

from which it would follow as a theorem that = ?

Re: Proper definition of the ratio a:b:c

Strictly speaking a "ratio" is a fraction so only a:b, which is the same a/b makes sense. However, a:b:c is often used as shorthand for the two ratios a:b and b:c. Saying "a:b:c= 1:2:3 means a/b= 1/2 and b/c= 2/3.

Re: Proper definition of the ratio a:b:c

Quote:

Originally Posted by

**HallsofIvy** Strictly speaking a "ratio" is a fraction so only a:b, which is the same a/b makes sense. However, a:b:c is often used as shorthand for the two ratios a:b and b:c. Saying "a:b:c= 1:2:3 means a/b= 1/2 and b/c= 2/3.

Thanks a lot, for some reason I still haven't been able to find this after searching through a bunch of textbooks or a quick google search.