### Theory:

When a fractional number is added with another fractional number, based on the type of the fractions (like, unlike or mixed) added, different methods can be followed.

If all the fractions in the addition operation have the same denominator, then add the numerator and write the result as a fractional number with the same denominator.
Example:
$\frac{1}{2}+\frac{5}{2}+\frac{7}{2}=\frac{13}{2}$
$\begin{array}{l}\mathit{Find}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{value}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\frac{1}{2}+\frac{2}{3}\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}i\right)\phantom{\rule{0.147em}{0ex}}\mathit{LCM}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\left(2,3\phantom{\rule{0.147em}{0ex}}\right)=6\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}\mathit{ii}\right)\phantom{\rule{0.147em}{0ex}}\mathit{To}\phantom{\rule{0.147em}{0ex}}\mathit{change}\phantom{\rule{0.147em}{0ex}}2\phantom{\rule{0.147em}{0ex}}\mathit{to}\phantom{\rule{0.147em}{0ex}}6\phantom{\rule{0.147em}{0ex}}\mathit{multiply}\phantom{\rule{0.147em}{0ex}}\mathit{numerator}\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}\mathit{denominator}\phantom{\rule{0.147em}{0ex}}\mathit{by}\phantom{\rule{0.147em}{0ex}}3,\frac{1×3}{2×3}=\frac{3}{6}\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}\mathit{iii}\right) \mathit{Add}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{numerator}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{all}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{fractions},\frac{3}{6}+\frac{4}{6}=\frac{7}{6}\end{array}$
$\begin{array}{l}\mathit{Add}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}3\frac{6}{2}+2\frac{3}{2}\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}i\right)\phantom{\rule{0.147em}{0ex}}\mathit{Add}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{whole}\phantom{\rule{0.147em}{0ex}}\mathit{parts}\phantom{\rule{0.147em}{0ex}}\mathit{seperately}.\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}\mathit{ii}\right)\phantom{\rule{0.147em}{0ex}}\mathit{Add}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{proper}\phantom{\rule{0.147em}{0ex}}\mathit{fractions}\phantom{\rule{0.147em}{0ex}}\mathit{seperately}.\\ \\ 3+2\phantom{\rule{0.147em}{0ex}}=5;\frac{6}{2}+\frac{3}{2}=\frac{9}{2}\\ \\ =5+\frac{9}{2}=\frac{19}{2}\end{array}$