cross multiplying proportions (the math behind it)

Question

I want to share a method i came up with that makes more since to me then cross multiplication. for example 6/x=2/4 if i take the reciprocal of 2/4 and multiply it on both sides i get 24/2x, when reduced it's 12/x, this works out as long as i remember to replace the division with an = sign. Is this a good way to look at it or is there a better way to think of it?

Answer 1

"rule of three" is the product of the means divided by the extreme

a/b = c/x

x = bc/a, b and c are the means, a = the extreme

still taught in French math courses, same procedure as cross multiplication

or multiplying by a common denominator

6/x = 2/4

x =(6)(4)/2 = 24/2 = 12

common denominator is 4x

(6/x)(4x) = (2/4)(4x)

24 = 2x

x = 24/2 = 12