To subtract the mixed numbers \( 13 \frac{5}{7} - 6 \frac{7}{8} \), follow these steps:

### Step 1: Convert the mixed numbers into improper fractions.
1. \( 13 \frac{5}{7} = \frac{(13 \times 7) + 5}{7} = \frac{91 + 5}{7} = \frac{96}{7} \)
2. \( 6 \frac{7}{8} = \frac{(6 \times 8) + 7}{8} = \frac{48 + 7}{8} = \frac{55}{8} \)

### Step 2: Find a common denominator.
The least common denominator (LCD) of 7 and 8 is 56.

1. Convert \( \frac{96}{7} \) to have a denominator of 56:
   \[
   \frac{96}{7} = \frac{96 \times 8}{7 \times 8} = \frac{768}{56}
   \]
2. Convert \( \frac{55}{8} \) to have a denominator of 56:
   \[
   \frac{55}{8} = \frac{55 \times 7}{8 \times 7} = \frac{385}{56}
   \]

### Step 3: Subtract the fractions.
\[
\frac{768}{56} - \frac{385}{56} = \frac{768 - 385}{56} = \frac{383}{56}
\]

### Step 4: Simplify, if possible.
\[
\frac{383}{56} \text{ cannot be simplified further. So, the result is } \frac{383}{56}.
\]

### Step 5: Convert back to a mixed number.
To convert \( \frac{383}{56} \) into a mixed number:
\[
383 \div 56 = 6 \text{ remainder } 47
\]
Thus, \( \frac{383}{56} = 6 \frac{47}{56} \).

### Final Answer:
\[
13 \frac{5}{7} - 6 \frac{7}{8} = 6 \frac{47}{56}
\]

Would you like further details or have any questions?

Here are some related questions for you:
1. How do you add mixed numbers?
2. What is the difference between proper and improper fractions?
3. How do you convert an improper fraction back to a mixed number?
4. How do you find the least common denominator?
5. What is the process for simplifying fractions?

**Tip:** When subtracting mixed numbers, always convert them to improper fractions first for easier calculations.

Learn how to subtract mixed numbers by converting them to improper fractions. This example problem (13 5/7 - 6 7/8) demonstrates key math concepts, including finding the least common denominator and simplifying fractions. Suitable for students in Grades 6-8.

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