To solve the expression \( 2 \frac{1}{6} \div 3 \frac{1}{10} \), follow these steps:

### 1. Convert mixed numbers to improper fractions:
- \( 2 \frac{1}{6} \) becomes \( \frac{2 \times 6 + 1}{6} = \frac{12 + 1}{6} = \frac{13}{6} \).
- \( 3 \frac{1}{10} \) becomes \( \frac{3 \times 10 + 1}{10} = \frac{30 + 1}{10} = \frac{31}{10} \).

### 2. Rewrite the division as multiplication by the reciprocal:
\[
\frac{13}{6} \div \frac{31}{10} = \frac{13}{6} \times \frac{10}{31}
\]

### 3. Multiply the fractions:
\[
\frac{13 \times 10}{6 \times 31} = \frac{130}{186}
\]

### 4. Simplify the fraction:
- The greatest common divisor (GCD) of 130 and 186 is 2.
- Divide the numerator and the denominator by 2:
\[
\frac{130 \div 2}{186 \div 2} = \frac{65}{93}
\]

Since \( \frac{65}{93} \) is already in its simplest form, the final answer is \( \frac{65}{93} \).

Would you like any further details or explanations?

Here are some related questions:
1. How do you convert a mixed number into an improper fraction?
2. What is the process of finding the reciprocal of a fraction?
3. How do you know when a fraction is in its simplest form?
4. What steps are involved in multiplying two fractions?
5. Can you explain how to compare fractions to determine which is larger?

**Tip**: After multiplying fractions, always check if you can simplify the result.

Learn how to divide mixed numbers 2 1/6 ÷ 3 1/10 using a step-by-step solution. This problem covers converting mixed numbers to improper fractions, multiplying fractions by their reciprocals, and simplifying fractions. Suitable for Grades 5-6.

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