https://file.aiquickdraw.com/mathbot/file/17287653770349r2kbchi.jpg

Let's solve the problem shown in the image.

The task is to multiply the fractions \( \frac{3}{8} \) and \( 5 \frac{5}{7} \), then simplify and write the result as a mixed number.

### Step 1: Convert the mixed number to an improper fraction
The number \( 5 \frac{5}{7} \) can be converted to an improper fraction:
\[
5 \frac{5}{7} = \frac{5 \times 7 + 5}{7} = \frac{35 + 5}{7} = \frac{40}{7}
\]

### Step 2: Multiply the fractions
Now we multiply \( \frac{3}{8} \) and \( \frac{40}{7} \):
\[
\frac{3}{8} \times \frac{40}{7} = \frac{3 \times 40}{8 \times 7} = \frac{120}{56}
\]

### Step 3: Simplify the fraction
The greatest common divisor (GCD) of 120 and 56 is 8, so we divide both the numerator and denominator by 8:
\[
\frac{120}{56} = \frac{120 \div 8}{56 \div 8} = \frac{15}{7}
\]

### Step 4: Convert the improper fraction to a mixed number
The fraction \( \frac{15}{7} \) can be expressed as a mixed number:
\[
\frac{15}{7} = 2 \frac{1}{7}
\]

### Conclusion
The answer is \( 2 \frac{1}{7} \), which matches the last option.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How do you find the greatest common divisor (GCD) of two numbers?
2. What are the steps to convert a mixed number into an improper fraction?
3. Why is it important to simplify fractions?
4. How can you check your multiplication of fractions for accuracy?
5. What are some other methods to solve fraction multiplication problems?

**Tip:** Always convert mixed numbers into improper fractions before performing arithmetic operations to simplify the calculations.

Multiply. Simplify and write as a mixed number: (3/8) * (5 5/7)

Learn how to multiply fractions and mixed numbers, using (3/8) * (5 5/7) as an example. This solution demonstrates the conversion of mixed numbers to improper fractions, multiplying fractions, and simplifying to a mixed number.

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