1. **State the problem:** Find the difference between the mixed numbers $10 \frac{1}{9}$ and $9 \frac{3}{4}$. 2. **Convert mixed numbers to improper fractions:** $10 \frac{1}{9} = \frac{10 \times 9 + 1}{9} = \frac{90 + 1}{9} = \frac{91}{9}$ $9 \frac{3}{4} = \frac{9 \times 4 + 3}{4} = \frac{36 + 3}{4} = \frac{39}{4}$ 3. **Find common denominator:** The denominators are 9 and 4. The least common denominator (LCD) is $36$. 4. **Rewrite fractions with common denominator:** $\frac{91}{9} = \frac{91 \times 4}{9 \times 4} = \frac{364}{36}$ $\frac{39}{4} = \frac{39 \times 9}{4 \times 9} = \frac{351}{36}$ 5. **Subtract the fractions:** $$\frac{364}{36} - \frac{351}{36} = \frac{364 - 351}{36} = \frac{13}{36}$$ 6. **Convert back to mixed number if needed:** $\frac{13}{36}$ is a proper fraction, so the difference is $\frac{13}{36}$. **Final answer:** $$10 \frac{1}{9} - 9 \frac{3}{4} = \frac{13}{36}$$