1. The problem asks for the fraction of the pizza left after John, Tony, and Sylvia ate parts of it. 2. John ate $\frac{1}{6}$, Tony ate $\frac{1}{4}$, and Sylvia ate $\frac{1}{3}$ of the pizza. 3. To find the total eaten, add the fractions: $$\frac{1}{6} + \frac{1}{4} + \frac{1}{3}$$ 4. Find a common denominator for 6, 4, and 3, which is 12. 5. Convert each fraction: $$\frac{1}{6} = \frac{2}{12}, \quad \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12}$$ 6. Add the converted fractions: $$\frac{2}{12} + \frac{3}{12} + \frac{4}{12} = \frac{2+3+4}{12} = \frac{9}{12}$$ 7. Simplify $\frac{9}{12}$ by dividing numerator and denominator by 3: $$\frac{\cancel{9}^3}{\cancel{12}^3} = \frac{3}{4}$$ 8. The total eaten is $\frac{3}{4}$ of the pizza. 9. The fraction left is the whole pizza minus the eaten part: $$1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}$$ 10. Therefore, $\frac{1}{4}$ of the pizza was left after they finished eating.