Choose the correct option. Write the reciprocal of the fraction 8 1⁄11 Options 89/11 11/89 11/80 80/11

1. Break Down the Problem

To find the reciprocal of the mixed fraction $8 \frac{1}{11}$, we first need to convert it into an improper fraction.

2. Relevant Concepts

The conversion from a mixed number $a \frac{b}{c}$ to an improper fraction is given by: $\text{Improper Fraction} = \frac{(a \times c) + b}{c}$

The reciprocal of a fraction $\frac{p}{q}$ is given by: $\text{Reciprocal} = \frac{q}{p}$

3. Analysis and Detail

1. Convert $8 \frac{1}{11}$ to an improper fraction:

   • Here, $a = 8$, $b = 1$, and $c = 11$.
   • Applying the formula: $\text{Improper Fraction} = \frac{(8 \times 11) + 1}{11} = \frac{88 + 1}{11} = \frac{89}{11}$

2. Now, find the reciprocal of $\frac{89}{11}$:

   • The reciprocal is: $\text{Reciprocal} = \frac{11}{89}$

4. Verify and Summarize

We have successfully converted the mixed number to an improper fraction and then found its reciprocal correctly. The steps were followed accurately as per mathematical rules.

Final Answer

The reciprocal of the fraction $8 \frac{1}{11}$ is $\frac{11}{89}$.

Correct Option

The correct option is 11/89.