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.
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 = ?
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.