Adding and Subtracting Fractions

Same Denominator

When fractions have the same denominator, simply add or subtract the numerators:

$\frac{2}{7} + \frac{3}{7} = \frac{2 + 3}{7} = \frac{5}{7}$

$\frac{5}{9} - \frac{2}{9} = \frac{5 - 2}{9} = \frac{3}{9} = \frac{1}{3}$

Different Denominators

Steps:

1. Find a common denominator (usually the LCM)
2. Convert each fraction to an equivalent fraction
3. Add or subtract the numerators
4. Simplify if possible

Example: $\frac{1}{4} + \frac{1}{6}$

LCM of 4 and 6 is 12: $\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{6} = \frac{2}{12}$

$\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$

Mixed Numbers

Convert to improper fractions first, then add/subtract: $2\frac{1}{3} + 1\frac{1}{2} = \frac{7}{3} + \frac{3}{2}$