### Addition of fractions with the different (related) denominators

To add fractions with different denominators we must first convert to equivalent fractions with the same denominator. Initially, students work with related fractions. 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.

\begin{align}\frac{3}{6} + \frac{9}{12} &= \frac{6}{12} + \frac{9}{12} \text{(convert to equivalent fractions with the 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}