To solve the given expression, we need to evaluate it step by step. The expression is:

$\frac{\frac{1}{16}}{\frac{1}{12}} + \frac{12}{11}$

Step 1: Simplify the division of fractions

Simplify $\frac{\frac{1}{16}}{\frac{1}{12}}$.

This can be rewritten as:

$\frac{1}{16} \div \frac{1}{12} = \frac{1}{16} \times \frac{12}{1} = \frac{12}{16}$

Simplify $\frac{12}{16}$ by dividing both the numerator and denominator by 4:

$\frac{12}{16} = \frac{3}{4}$

Step 2: Add $\frac{3}{4}$ and $\frac{12}{11}$

To add these fractions, find a common denominator. The least common denominator (LCD) of 4 and 11 is 44.

Convert $\frac{3}{4}$ and $\frac{12}{11}$ to have the same denominator:

$\frac{3}{4} = \frac{3 \times 11}{4 \times 11} = \frac{33}{44}$

$\frac{12}{11} = \frac{12 \times 4}{11 \times 4} = \frac{48}{44}$

Now add the fractions:

$\frac{33}{44} + \frac{48}{44} = \frac{33 + 48}{44} = \frac{81}{44}$

Final Answer

$\frac{81}{44}$

Would you like further details or explanations? Here are some related questions to expand your understanding:

1. How do you find the least common denominator of two fractions?
2. How can you simplify fractions quickly?
3. What is the process for dividing fractions?
4. How do you add fractions with different denominators?
5. What are some common mistakes when simplifying complex fractions?

Tip: Always simplify fractions to their lowest terms to make calculations easier!