To solve the expression \( 13 \frac{7}{13} \times 15 \frac{8}{5} \), we first convert the mixed numbers to improper fractions.

1. Convert \( 13 \frac{7}{13} \) to an improper fraction:
   \[
   13 \frac{7}{13} = \frac{13 \times 13 + 7}{13} = \frac{169 + 7}{13} = \frac{176}{13}
   \]

2. Convert \( 15 \frac{8}{5} \) to an improper fraction:
   \[
   15 \frac{8}{5} = \frac{15 \times 5 + 8}{5} = \frac{75 + 8}{5} = \frac{83}{5}
   \]

Now, multiply the two improper fractions:
\[
\frac{176}{13} \times \frac{83}{5} = \frac{176 \times 83}{13 \times 5}
\]

Calculate the numerator and the denominator:
\[
176 \times 83 = 14608
\]
\[
13 \times 5 = 65
\]

So, the fraction is:
\[
\frac{14608}{65}
\]

Next, simplify the fraction by finding the greatest common divisor (GCD) of 14608 and 65, but since they have no common factors, the fraction is already in its simplest form.

Thus, the final answer is:
\[
\frac{14608}{65}
\]
Or, as a mixed number:
\[
224 \frac{8}{65}
\]

Would you like any further details or have any questions? 

Here are some related questions you might find interesting:

1. How do you simplify improper fractions?
2. What is the process for converting improper fractions to mixed numbers?
3. How do you multiply and divide mixed numbers directly?
4. What is the significance of finding the GCD when simplifying fractions?
5. How can you convert a fraction to a decimal?

**Tip:** When multiplying fractions, always simplify before multiplying if possible, to make the calculations easier.

Solve the multiplication of mixed numbers 13 7/13 × 15 8/5 by converting them to improper fractions and applying fraction multiplication rules. This detailed guide is perfect for students in Grades 5-7, covering key concepts like converting mixed numbers and simplifying fractions.

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