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:

\[ 12 : 5 \]