Find the reciprocal of
11 `1/11`

Answer

To find the reciprocal of the mixed number \( 11 \frac{1}{11} \), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
A mixed number consists of a whole number and a fraction. To convert \( 11 \frac{1}{11} \) to an improper fraction, we use the formula:

\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} \div \text{Denominator} \]

For \( 11 \frac{1}{11} \):

\[ \text{Improper Fraction} = \left(11 \times 11\right) + 1 \div 11 = \frac{121 + 1}{11} = \frac{122}{11} \]

### Step 2: Find the reciprocal of the improper fraction.
The reciprocal of a fraction is obtained by swapping its numerator and denominator. So, the reciprocal of \( \frac{122}{11} \) is:

\[ \text{Reciprocal} = \frac{11}{122} \]

### Final Answer:
The reciprocal of \( 11 \frac{1}{11} \) is \( \frac{11}{122} \).

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