Originally Posted by
dwsmith $\displaystyle \displaystyle\frac{2}{x}=\frac{7}{y}\cdot\frac{7}{ 7} \ \text{7 divided by 7 is 1 so we aren't changing the equality by multiplying by 1.}$
$\displaystyle \displaystyle\frac{1}{7}\cdot\frac{2}{x}=\frac{7}{ y}\cdot\frac{1}{7} \ \text{lets prove this is the same as the above equation.}$
If we multiply both sides by 7, we will have 1 and 7/7.
$\displaystyle \displaystyle 7\cdot\frac{1}{7}\Rightarrow\frac{7}{7}\Rightarrow 1\cdot\frac{2}{x}=\frac{7}{y}\cdot\frac{1}{7}\cdot 7\Rightarrow\frac{2}{y}\cdot\frac{7}{7} \ \text{as you can see, the 7 on the left hand side back to the right.}$
Same for the x.