rational manipulation

[Ryan$]

Hi guys, I just want to verify about something:
why it's right that if I want to calculate x over this equation:

a:b
x:c

then to calculate x, I do (a*c)/b , why it's right? it makes no sense for me, any clue why that rule is always right?!

 

[Romsek]

\(\displaystyle \dfrac a b = \dfrac x c \)

multiply both sides by \(\displaystyle c\)

\(\displaystyle \dfrac{a c}{b} = \dfrac{c x}{c}\)

simplify the right-hand side

\(\displaystyle \dfrac{a c}{b} = x\)