The problem asks for the total length of two boards with given lengths in mixed fractions:

• One board is $1 \frac{1}{2}$ meters long.
• The other board is $3 \frac{1}{2}$ meters long.

Step-by-step solution:

1. Convert mixed numbers to improper fractions:

   • $1 \frac{1}{2} = \frac{3}{2}$
   • $3 \frac{1}{2} = \frac{7}{2}$

2. Add the two fractions:

   • $\frac{3}{2} + \frac{7}{2} = \frac{3 + 7}{2} = \frac{10}{2}$

3. Simplify the result:

   • $\frac{10}{2} = 5$

So, the total length of the shelf is 5 meters.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. How would you add two fractions with different denominators?
2. What is the process for converting improper fractions to mixed numbers?
3. Can you subtract mixed numbers with unlike denominators?
4. What are real-life applications of adding mixed numbers?
5. How do you multiply mixed numbers?

Tip: Always simplify fractions when possible to make calculations easier!