Simplify $\frac{100}{180}$.
Since $100$ and $180$ have a common factor of $20$, we can simplify as follows $$\frac{100}{180}=\frac{20\cdot 5}{20\cdot 9}=\frac{\cancel{20}\cdot 5}{\cancel{20}\cdot 9}=\boxed{\frac{5}{9}}.$$