Addition and Subtraction of fractions

When adding or subtracting fractions, the denominators must be the same

Example:

\begin{equation*} \begin{split} &\text{Evaluate}\:\: 1\frac{1}{2} + 2\frac{3}{5} - \frac{4}{7}\\\\ &1 + \frac{1}{2} +  2 + \frac{3}{5} - \frac{4}{7}\\\\ &3 + \left(\frac{1}{2} + \frac{3}{5} - \frac{4}{7}\right)\:\:\:\:\: \color {blue} \text{Change the fractions so they have the same denominator}\\\\ &3 + \left(\frac{1 \times \color{red} 35}{2 \times \color{red} 35} + \frac{3 \times \color{red} 14}{5 \times \color{red} 14 } - \frac{4 \times\color{red} 10 }{7\times \color{red} 10}\right)\:\:\:\:\: \color {blue} \text{The LCM of 2, 5, and 7 is 70}\\\\ &3 + \left(\frac{35}{70} + \frac{42}{70} - \frac{40}{70}\right)\\\\ &3 + \frac{35 + 42 - 40}{70}\\\\ &3 + \frac{37}{70}\\\\ &3 \frac{37}{70} \end{split} \end{equation*}