To solve the expression \( 3 \frac{1}{4} \cdot \frac{5}{8} \), let's follow these steps:

1. Convert the mixed number \( 3 \frac{1}{4} \) into an improper fraction:
   \[
   3 \frac{1}{4} = \frac{13}{4}
   \]
   (because \( 3 \cdot 4 + 1 = 13 \)).

2. Now, multiply the two fractions:
   \[
   \frac{13}{4} \cdot \frac{5}{8} = \frac{13 \cdot 5}{4 \cdot 8} = \frac{65}{32}
   \]

So, the product is \( \frac{65}{32} \), which is an improper fraction.

To convert \( \frac{65}{32} \) into a mixed number:
\[
\frac{65}{32} = 2 \frac{1}{32}
\]
This is the final answer.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you multiply two mixed numbers?
2. What are the steps to convert an improper fraction into a mixed number?
3. How can you simplify fractions before multiplying them?
4. What is the significance of using improper fractions in multiplication?
5. How do you divide two fractions?

**Tip:** When multiplying mixed numbers, always convert them to improper fractions first to simplify the process.

Learn how to multiply a mixed number by a fraction with this example: 3\frac{1}{4} \cdot \frac{5}{8}. This tutorial covers converting mixed numbers to improper fractions and multiplying fractions, suitable for students in Grades 5-6.

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