To find the reciprocal of \( 12 \frac{9}{11} \), we can follow these steps:
### Step 1: Convert the mixed number to an improper fraction
To convert the mixed number \( 12 \frac{9}{11} \) into an improper fraction, we use the formula:
\[
\text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator}
\]
Here, the whole number is 12, the numerator is 9, and the denominator is 11.
Calculating this gives:
\[
12 \frac{9}{11} = \frac{(12 \times 11) + 9}{11} = \frac{132 + 9}{11} = \frac{141}{11}
\]
### Step 2: Find the reciprocal of the improper fraction
The reciprocal of a fraction is obtained by swapping its numerator and denominator. Thus, the reciprocal of \( \frac{141}{11} \) is:
\[
\frac{11}{141}
\]
### Final Answer
The reciprocal of \( 12 \frac{9}{11} \) is \( \frac{11}{141} \).
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