18/11 : 15/22

To simplify the ratio 18/11 : 15/22, you can express it as a fraction: \[ \frac{18/11}{15/22} \] To divide by a fraction, multiply by its reciprocal: \[ \frac{18}{11} \times \frac{22}{15} \] Now, multiply the numerators and the denominators: \[ \frac{18 \times 22}{11 \times 15} \] Calculating the numerator and denominator: - \( 18 \times 22 = 396 \) - \( 11 \times 15 = 165 \) So the simplified ratio becomes: \[ \frac{396}{165} \] Now, we can simplify \( \frac{396}{165} \) by finding the greatest common divisor (GCD) of 396 and 165. The GCD of 396 and 165 is 33. Now divide both the numerator and denominator by 33: - \( 396 \div 33 = 12 \) - \( 165 \div 33 = 5 \) Thus, the simplified ratio is: \[ 12 : 5 \]