1. **State the problem:** We need to find the ratio of purple to white to blue marbles given 12 purple, 8 white, and 16 blue marbles. 2. **Write the ratio:** The ratio is $12:8:16$. 3. **Find the greatest common divisor (GCD):** To simplify the ratio, find the GCD of 12, 8, and 16. - Factors of 12: 1, 2, 3, 4, 6, 12 - Factors of 8: 1, 2, 4, 8 - Factors of 16: 1, 2, 4, 8, 16 The greatest common factor is 4. 4. **Divide each term by the GCD:** $$\frac{12}{\cancel{4}}:\frac{8}{\cancel{4}}:\frac{16}{\cancel{4}} = 3:2:4$$ 5. **Final answer:** The simplest form of the ratio of purple to white to blue marbles is $3:2:4$.