Problems from Sum and subtraction of fractions

We begin by simplifying the first fraction: ${\displaystyle \frac{3}{6}}={\displaystyle \frac{3:3}{6:3}}={\displaystyle \frac{1}{2}}.$ Then, $\begin{array}{l}2=2\\ 15=3\cdot 5\end{array}\}\Rightarrow m.c.m(2,15)=2\cdot 3\cdot 5=30$

Now we find the value $m$ for the two fractions: $m_1={\displaystyle \frac{30}{2}}=15$ and $m_2={\displaystyle \frac{30}{15}}=2.$ Then: $${\displaystyle \frac{1}{2}}-{\displaystyle \frac{2}{15}}={\displaystyle \frac{1\cdot 15}{2\cdot 15}}-{\displaystyle \frac{2\cdot 2}{15\cdot 2}}={\displaystyle \frac{15}{30}}-{\displaystyle \frac{4}{30}}={\displaystyle \frac{15-4}{30}}={\displaystyle \frac{11}{30}}.$$

The fractions are already simplified, so we calculate the less common multiple: $${\displaystyle \frac{19}{24}}+{\displaystyle \frac{1}{18}}={\displaystyle \frac{19\cdot 3}{24\cdot 3}}+{\displaystyle \frac{1\cdot 4}{18\cdot 4}}={\displaystyle \frac{57}{72}}+{\displaystyle \frac{4}{72}}={\displaystyle \frac{57+4}{72}}={\displaystyle \frac{61}{72}}.$$