4.8 Introduction and Key Insights

When we add or subtract fractions, it is helpful to consider two different cases: when the fractions have the same denominator and when the fractions have different denominators. We first focus on adding and subtracting fractions that have the same or common denominator. It is a relatively short process, as we simply combine the numerators.

For instance, consider adding $9/15 + 2/15$. Because the denominators match, we are able to compute:

$\frac{9}{15} + \frac{2}{15} = \frac{9+2}{15} = \frac{11}{15}$.

Similarly:

$\frac{9}{15} - \frac{2}{15} = \frac{9-2}{15} = \frac{7}{15}$.

More generally, we have:

$\frac{a}{b} \pm \frac{c}{b} = \frac{a\pm c}{b}$.