How much is

3 1/2 - 2 2/3 = ?

$$3 \frac12 - 2 \frac23 \\\\ =3 +\frac12 - 2 -\frac23 \\\\ =3-2 +\frac12-\frac23 \\\\ =1+\frac12-\frac23 \\\\ =1\cdot \frac22 \cdot \frac33 +\frac12\cdot\frac33- \frac23\cdot \frac22\\\\ =\frac{1\cdot 2 \cdot 3+ 1\cdot 3 - 2 \cdot 2}{2\cdot 3}\\\\ =\frac{6+3-4}{6}\\\\ =\frac{5}{6}$$

or

$$3 \frac12 - 2 \frac23 \\\\ =\frac{3\cdot2+1} {2}-\frac{2\cdot 3+2}{3}\\\\ =\frac{7} {2}-\frac{8}{3}\\\\ =\frac{3\cdot 7-2\cdot 8}{2\cdot 3}\\\\ =\frac{21-16}{6}\\\\ =\frac{5}{6}$$