Simplify the following ratios: (1) \( 3: 6 \) (4) \( 6: 8 \)

Certainly! Let's simplify each of the given ratios by finding the greatest common divisor (GCD) for each pair of numbers and then dividing both terms by that GCD. ### (1) Simplify \( 3 : 6 \) 1. **Find the GCD of 3 and 6:** - The factors of 3 are: 1, 3 - The factors of 6 are: 1, 2, 3, 6 - **GCD = 3** 2. **Divide both terms by the GCD:** \[ \frac{3}{3} : \frac{6}{3} = 1 : 2 \] **Simplified Ratio:** \( 1 : 2 \) --- ### (4) Simplify \( 6 : 8 \) 1. **Find the GCD of 6 and 8:** - The factors of 6 are: 1, 2, 3, 6 - The factors of 8 are: 1, 2, 4, 8 - **GCD = 2** 2. **Divide both terms by the GCD:** \[ \frac{6}{2} : \frac{8}{2} = 3 : 4 \] **Simplified Ratio:** \( 3 : 4 \) --- **Summary of Simplified Ratios:** 1. \( 3 : 6 \) simplifies to \( 1 : 2 \) 4. \( 6 : 8 \) simplifies to \( 3 : 4 \)