Subtract

Explanation

Since the smallest number the denominators 2 and 3 divide exactly is 6, the LCD is 6

To build \(\frac52\) and \(\frac73\) so that their denominators are 6.  multiply each by a form of 1.

$\frac52 - \frac73 = \frac52 \color{red}{\cdot \frac33} - \frac73 \color{blue}{\cdot \frac22}$

Multiply the numerators.  Multiply the denominators.  The denominators are now the same

$= \frac{15}{6} = \frac{14}{6}$

Subtract the numerators and write the difference over the common denominator 6

$= \frac{15 - 14}{6}$

This fraction is in simplest form

$= \frac16$