Fractions

**theloser** · September 2nd 2011, 07:45 PM

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

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.

**SammyS** · September 2nd 2011, 08:17 PM

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

**Siron** · September 3rd 2011, 12:53 AM

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

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