To reduce the mixed number \(10 \frac{15}{10}\), we first simplify the fraction part and then combine it with the whole number.

### Step-by-step Solution:

1. **Convert the mixed number into an improper fraction:**
   \[
   10 \frac{15}{10} = 10 + \frac{15}{10}
   \]

2. **Simplify the fraction \(\frac{15}{10}\):**

   \[
   \frac{15}{10} = \frac{15 \div 5}{10 \div 5} = \frac{3}{2}
   \]

3. **Rewrite the mixed number:**
   \[
   10 + \frac{3}{2}
   \]

   To combine these, we need a common denominator:

   \[
   10 = \frac{20}{2}
   \]

   So,

   \[
   10 + \frac{3}{2} = \frac{20}{2} + \frac{3}{2} = \frac{23}{2}
   \]

4. **Convert back to a mixed number (if needed):**
   \[
   \frac{23}{2} = 11 \frac{1}{2}
   \]

### Conclusion:
The reduced form of \(10 \frac{15}{10}\) is \(11 \frac{1}{2}\).

Would you like more details or have any questions?

### Related Questions:
1. How do you convert improper fractions to mixed numbers?
2. What are the steps to simplify a fraction?
3. How can you find the greatest common divisor of two numbers?
4. What is the process to add fractions with different denominators?
5. How do you convert between mixed numbers and improper fractions?

**Tip:** Always simplify fractions before combining them with whole numbers to make calculations easier.

Learn how to simplify the mixed number 10 15/10 step by step. This guide covers the conversion of mixed numbers to improper fractions, fraction simplification, and the addition of fractions with common denominators. Ideal for students in Grades 4-6.

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