Question: Simplify the following ratios (a) 9 : 81
1. **State the problem:** Simplify the ratio $9 : 81$.
2. **Formula and rules:** To simplify a ratio, divide both terms by their greatest common divisor (GCD).
3. **Find the GCD:** The GCD of $9$ and $81$ is $9$.
4. **Divide both terms by the GCD:**
$$\frac{9}{\cancel{9}} : \frac{81}{\cancel{9}} = 1 : 9$$
5. **Final answer:** The simplified ratio is $1 : 9$.