### Addition of fractions with different but related denominators

To add fractions with different denominators we must first convert to equivalent fractions with the same denominator.

\begin{align}\frac{3}{6} + \frac{9}{12} &= \frac{6}{12} + \frac{9}{12} \text{(convert each to equivalent fraction with same denominator)} \\&= \frac{15}{12} \\&= 1\frac{3}{12} \text{(convert the improper fraction to a mixed number)} \\&= 1\frac{1}{4} \text{(simplify)}\end{align}

Fractions are 'related' if the denominator of one is a multiple of another. For example, the fractions $$\dfrac{1}{3} \text{and} \dfrac{5}{9}$$ have related denominators because 9 is a multiple of 3.