Math Help - Fractions

1. Fractions

$\frac{3}{5}x=\frac{5}{2}$

Can I do this?

$5(\frac{3}{5}x=\frac{5}{2})5$

$3x=\frac{25}{2}$

$\frac{3x}{3}=\frac{25/2}{3}$

$x=\frac{75}{2}$

Please tell me why it doesn't work.

2. Re: Fractions

... because $\frac{25/2}{3}=\frac{25}{2}\cdot \frac{1}{3}$

3. Re: Fractions

It can be useful to multiply each side with 10 (LCM of 2 and 5), and so you get:
$10\cdot \left(\frac{3}{5}x\right)=10\cdot \left(\frac{5}{2}\right)$
$\Leftrightarrow \frac{30}{5}x=\frac{50}{2}$
$\Leftrightarrow 6x=25$
$\Leftrightarrow x=\frac{25}{6}$