Example  1
Evaluate and simplify the expression \(\frac{4}{5} + \frac{3}{4}\).


Step 1: Determine the Lowest Common Denominator.

Looking at the denominators, the LCD is \(4 \times 5 = 20\)

Step 2: Express each fraction with the LCD.

\[\frac{{4\left( {\color{red}4} \right)}}{{5\left( {\color{red}4} \right)}} + \frac{{3\left( {\color{red}5} \right)}}{{4\left( {\color{red}5} \right)}} = \frac{{16}}{{20}} + \frac{{15}}{{20}}\]

Step 3: Add/Subtract the numerators, and leave the denominator as the LCD. Simplify.

\[\begin{align}
 \frac{{16}}{{20}} + \frac{{15}}{{20}} &= \frac{{16 + 15}}{{20}} \\
  &= \frac{{31}}{{20}} \\
 \end{align}\]
Therefore, \(\frac{4}{5} + \frac{3}{4} = \frac{{31}}{{20}}\).