[tex] \frac{a}{c} = \frac{d}{a}[/tex] is changed to [tex] a^{2} = cd[/tex] by multiplying by the product of the denominators.
[tex] \frac{a}{c} \times ac = ac \times \frac{d}{a}[/tex]
Because the end result looks like the numerator on the left is multiplied by the denominator on the right, and vice versa, the process is often referred to as "cross multiplying." That is an illusion. The rules of algebra require the same thing be done to both sides of the equation. In this case, that is multiplication of both sides by the product of the denominators.
