1. **State the problem:** We need to find the value of $\frac{5}{12} - \frac{1}{9}$. 2. **Formula and rules:** To subtract fractions, they must have a common denominator. The common denominator is the least common multiple (LCM) of the denominators. 3. **Find the LCM of 12 and 9:** $$\text{LCM}(12, 9) = 36$$ 4. **Convert each fraction to have denominator 36:** $$\frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}$$ $$\frac{1}{9} = \frac{1 \times 4}{9 \times 4} = \frac{4}{36}$$ 5. **Subtract the fractions:** $$\frac{15}{36} - \frac{4}{36} = \frac{15 - 4}{36} = \frac{11}{36}$$ 6. **Final answer:** $$\frac{5}{12} - \frac{1}{9} = \frac{11}{36}$$