In seventh grade, Emile grew $\displaystyle{3}\frac{{9}}{{10}}\usepackage{cmbright}\Huge\$ cm, and in eighth grade he grew $\displaystyle{4}\frac{{2}}{{5}}\usepackage{cmbright}\Huge\$ cm. How much did his height increase during these two years?

The answer should be written as a proper mixed number and should be simplified, if possible.