rite the following ratios in its simplest form. (a) \( 9: 15 \) (b) \( 21: 35 \) (c) \( 12: 24: 48 \) (d) \( 18: 54: 81 \)

Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{21}{35}=x\) - step1: Reduce the fraction: \(\frac{3}{5}=x\) - step2: Swap the sides: \(x=\frac{3}{5}\) Solve the equation \( 9/15=x \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{9}{15}=x\) - step1: Reduce the fraction: \(\frac{3}{5}=x\) - step2: Swap the sides: \(x=\frac{3}{5}\) Solve the equation \( 18/54=x \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{18}{54}=x\) - step1: Reduce the fraction: \(\frac{1}{3}=x\) - step2: Swap the sides: \(x=\frac{1}{3}\) Solve the equation \( 12/24=x \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{12}{24}=x\) - step1: Reduce the fraction: \(\frac{1}{2}=x\) - step2: Swap the sides: \(x=\frac{1}{2}\) Let's simplify each of the given ratios step by step. ### (a) \( 9: 15 \) To simplify the ratio \( 9:15 \), we divide both numbers by their greatest common divisor (GCD), which is 3. \[ \frac{9 \div 3}{15 \div 3} = \frac{3}{5} \] So, the simplest form of \( 9:15 \) is \( 3:5 \). ### (b) \( 21: 35 \) For the ratio \( 21:35 \), we also divide both numbers by their GCD, which is 7. \[ \frac{21 \div 7}{35 \div 7} = \frac{3}{5} \] Thus, the simplest form of \( 21:35 \) is \( 3:5 \). ### (c) \( 12: 24: 48 \) For the ratio \( 12:24:48 \), we find the GCD of all three numbers, which is 12. \[ \frac{12 \div 12}{24 \div 12}{48 \div 12} = \frac{1}{2}{4} \] Therefore, the simplest form of \( 12:24:48 \) is \( 1:2:4 \). ### (d) \( 18: 54: 81 \) For the ratio \( 18:54:81 \), the GCD is 9. \[ \frac{18 \div 9}{54 \div 9}{81 \div 9} = \frac{2}{6}{9} \] Thus, the simplest form of \( 18:54:81 \) is \( 2:6:9 \). ### Summary of Simplified Ratios: - (a) \( 9:15 \) simplifies to \( 3:5 \) - (b) \( 21:35 \) simplifies to \( 3:5 \) - (c) \( 12:24:48 \) simplifies to \( 1:2:4 \) - (d) \( 18:54:81 \) simplifies to \( 2:6:9 \)