To express \( 11 \frac{9}{18} \) as a mixed number in simplest form, we first simplify the fractional part \( \frac{9}{18} \).
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Simplify \( \frac{9}{18} \):
- The greatest common divisor (GCD) of 9 and 18 is 9.
- Divide both the numerator and the denominator by their GCD: \[ \frac{9 \div 9}{18 \div 9} = \frac{1}{2} \]
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Now, we replace \( \frac{9}{18} \) with \( \frac{1}{2} \) in the mixed number: \[ 11 \frac{9}{18} = 11 \frac{1}{2} \]
Thus, \( 11 \frac{9}{18} \) as a mixed number in simplest form is \( 11 \frac{1}{2} \).