https://file.aiquickdraw.com/mathbot/file/1725936963655780w524b.jpg

The expression in the image is:

\[
10 \frac{1}{2} \div \frac{3}{4}
\]

### Step-by-Step Solution:

1. **Convert mixed number to improper fraction**:  
   \( 10 \frac{1}{2} \) can be written as an improper fraction:
   \[
   10 \frac{1}{2} = \frac{10 \times 2 + 1}{2} = \frac{21}{2}
   \]

2. **Division of fractions**:  
   To divide fractions, multiply by the reciprocal of the second fraction:
   \[
   \frac{21}{2} \div \frac{3}{4} = \frac{21}{2} \times \frac{4}{3}
   \]

3. **Simplify the multiplication**:
   Multiply the numerators and the denominators:
   \[
   \frac{21 \times 4}{2 \times 3} = \frac{84}{6} = 14
   \]

### Final Answer:
\[
10 \frac{1}{2} \div \frac{3}{4} = 14
\]

Would you like more details on any step or have any questions?

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Here are 5 related questions to explore further:
1. How do you multiply mixed numbers?
2. What is the reciprocal of a fraction and how is it used in division?
3. How do you convert improper fractions back to mixed numbers?
4. How would the answer change if the second fraction were \(\frac{3}{2}\) instead of \(\frac{3}{4}\)?
5. What are some strategies for simplifying fractions before multiplying?

**Tip**: Always simplify fractions whenever possible before multiplying or dividing to make calculations easier!

Learn how to divide mixed numbers and fractions with a step-by-step solution to 10 1/2 ÷ 3/4. Succeed in understanding key concepts such as converting mixed numbers to improper fractions and dividing fractions by multiplying by the reciprocal. Suitable for students in Grades 5-7.

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