3. Write the following ratio in a simplified form: A. \( 1: \frac{1}{2} \) A. \( 1: 1 \frac{1}{2} \) C. \( 1: 2 \) D. \( 8: 9 \)

To simplify the given ratios, we will convert each ratio into a form where both parts are whole numbers. Let's go through each one step by step. ### A. \( 1: \frac{1}{2} \) To simplify this ratio, we can multiply both parts by 2 (the denominator of the fraction): \[ 1 \times 2 : \frac{1}{2} \times 2 = 2 : 1 \] So, the simplified form of \( 1: \frac{1}{2} \) is \( 2:1 \). ### B. \( 1: 1 \frac{1}{2} \) First, convert the mixed number \( 1 \frac{1}{2} \) into an improper fraction: \[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \] Now, we can write the ratio as: \[ 1 : \frac{3}{2} \] Next, multiply both parts by 2: \[ 1 \times 2 : \frac{3}{2} \times 2 = 2 : 3 \] So, the simplified form of \( 1: 1 \frac{1}{2} \) is \( 2:3 \). ### C. \( 1: 2 \) This ratio is already in a simple form. Therefore, the simplified form of \( 1: 2 \) is \( 1:2 \). ### D. \( 8: 9 \) This ratio is also already in a simple form. Therefore, the simplified form of \( 8: 9 \) is \( 8:9 \). ### Summary of Simplified Ratios: - A. \( 1: \frac{1}{2} \) → \( 2:1 \) - B. \( 1: 1 \frac{1}{2} \) → \( 2:3 \) - C. \( 1: 2 \) → \( 1:2 \) - D. \( 8: 9 \) → \( 8:9 \)