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The problem in the image asks to find the quotient of the fractions \( 2 \frac{1}{2} \div 1 \frac{3}{10} \) and reduce it to the lowest terms.

Let's go through the steps to solve this:

1. **Convert Mixed Numbers to Improper Fractions**:
   - \( 2 \frac{1}{2} = \frac{5}{2} \)
   - \( 1 \frac{3}{10} = \frac{13}{10} \)

2. **Rewrite the Division as Multiplication**:
   - Dividing by a fraction is the same as multiplying by its reciprocal.
   - So, \( \frac{5}{2} \div \frac{13}{10} = \frac{5}{2} \times \frac{10}{13} \).

3. **Multiply the Fractions**:
   - \( \frac{5 \times 10}{2 \times 13} = \frac{50}{26} \).

4. **Simplify the Fraction**:
   - Divide the numerator and denominator by their greatest common divisor, which is 2.
   - \( \frac{50}{26} = \frac{25}{13} \).

5. **Convert to a Mixed Number (if necessary)**:
   - \( \frac{25}{13} = 1 \frac{12}{13} \).

The answer is **\( 1 \frac{12}{13} \)**.

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Would you like further clarification on any step, or have any additional questions?

Here are some additional questions to explore this topic further:
1. How do you convert a mixed number to an improper fraction?
2. What is the process for dividing fractions?
3. How do you find the greatest common divisor to simplify fractions?
4. Why is dividing by a fraction equivalent to multiplying by its reciprocal?
5. What are some examples of converting improper fractions back into mixed numbers?

**Tip**: Remember, for division of fractions, always multiply by the reciprocal of the divisor!

Find the quotient for the problem below and reduce to lowest terms: 2 1/2 ÷ 1 3/10

Learn how to divide mixed fractions with the example 2 1/2 ÷ 1 3/10. This problem includes converting mixed numbers to improper fractions, using the reciprocal to divide, and simplifying to lowest terms. Perfect for students in Grades 5-7.

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