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

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: $2\frac{1}{3} + 1\frac{1}{2} = \frac{7}{3} + \frac{3}{2}$

$\frac{1}{4} = \frac{3}{12}$

Add: $\frac{8}{12} + \frac{3}{12} = \frac{11}{12}$

Answer: $\frac{11}{12}$

Find common denominator (LCM of 4 and 6 is 12): $\frac{11}{4} = \frac{33}{12}, \quad \frac{11}{6} = \frac{22}{12}$

Add: $\frac{33}{12} + \frac{22}{12} = \frac{55}{12} = 4\frac{7}{12}$

Answer: $4\frac{7}{12}$ miles