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To solve the given problem, we need to add the mixed number \( 5 \frac{1}{2} \) and the whole number 10.

### Step-by-Step Solution:

1. **Convert the Mixed Number to an Improper Fraction:**

   The mixed number \( 5 \frac{1}{2} \) can be converted to an improper fraction. The formula to convert a mixed number \( a \frac{b}{c} \) to an improper fraction is:

   \[
   \frac{ac + b}{c}
   \]

   For \( 5 \frac{1}{2} \):

   \[
   5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}
   \]

2. **Convert the Whole Number to a Fraction:**

   The number 10 can be written as a fraction:

   \[
   10 = \frac{10}{1}
   \]

3. **Find a Common Denominator:**

   To add fractions, we need a common denominator. The denominators are 2 and 1. The least common multiple (LCM) of 2 and 1 is 2.

   Rewrite both fractions with the common denominator:

   \[
   \frac{11}{2} + \frac{10 \times 2}{1 \times 2} = \frac{11}{2} + \frac{20}{2}
   \]

   This simplifies to:

   \[
   \frac{11}{2} + \frac{20}{2} = \frac{31}{2}
   \]

4. **Convert the Improper Fraction to a Mixed Number:**

   Now, convert the improper fraction \( \frac{31}{2} \) to a mixed number.

   Divide 31 by 2:

   \[
   31 \div 2 = 15 \text{ remainder } 1
   \]

   So, \( \frac{31}{2} = 15 \frac{1}{2} \).

### Final Answer:

\[
5 \frac{1}{2} + 10 = 15 \frac{1}{2}
\]

Would you like more details, or do you have any questions?

### Related Questions:

1. How do you convert a mixed number to an improper fraction?
2. What is the process for adding fractions with different denominators?
3. How do you find the least common multiple (LCM) of two numbers?
4. How do you simplify an improper fraction to a mixed number?
5. What are some real-life applications of adding mixed numbers?

### Tip:

Always remember to find a common denominator when adding or subtracting fractions, as this allows you to combine the fractions correctly!

Solve the problem 5 1/2 + 10 by converting the mixed number to an improper fraction and finding the least common denominator (LCD). This detailed step-by-step solution is suitable for students in Grades 4-6.

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