Final answer:
To solve the presented expression, the mixed fractions are first converted to improper fractions, then the division is carried out by multiplying by the reciprocal. However, the final simplified answer 1/2 is not among the provided options, suggesting a possible misinterpretation of the question as written.
Step-by-step explanation:
When we evaluate the expression 1 2/3/9 divided by 1 1/9/3, we can simplify both mixed fractions and then divide the results. First, we convert the mixed fractions to improper fractions. To do this, for 1 2/3, we multiply the whole number by the denominator of the fraction (1 * 3 = 3), add the numerator (3 + 2 = 5), and place the result over the denominator (5/3). For 1 1/9, we follow the same process, resulting in 10/9. So we have (5/3) / 9 and (10/9) / 3. This simplifies to 5/27 and 10/27.
To divide these two fractions, we take the reciprocal of the second fraction and multiply. So, we have 5/27 * 27/10. The 27 in the numerator and denominator cancel each other out, and we are left with 5/10, which simplifies to 1/2. However, because 1/2 is not one of the provided options, it is possible there was a misunderstanding in interpreting the original question, which contains a mix of numbers and slashes that could represent complex fractions or division operations. If this is the case, please clarify the original question for a correct evaluation.