https://file.aiquickdraw.com/mathbot/file/1726404291937bk9bf5on.jpg

The expression shown in the image is:

\[
8 \frac{2}{7} + 2 \frac{4}{5}
\]

### Step 1: Convert the mixed numbers to improper fractions.

1. \( 8 \frac{2}{7} \):
   - Multiply the whole number 8 by the denominator 7: \( 8 \times 7 = 56 \).
   - Add the numerator 2: \( 56 + 2 = 58 \).
   - So, \( 8 \frac{2}{7} = \frac{58}{7} \).

2. \( 2 \frac{4}{5} \):
   - Multiply the whole number 2 by the denominator 5: \( 2 \times 5 = 10 \).
   - Add the numerator 4: \( 10 + 4 = 14 \).
   - So, \( 2 \frac{4}{5} = \frac{14}{5} \).

### Step 2: Add the fractions.

To add \( \frac{58}{7} + \frac{14}{5} \), we need a common denominator.

- The least common denominator (LCD) of 7 and 5 is 35.
- Convert both fractions:

\[
\frac{58}{7} = \frac{58 \times 5}{7 \times 5} = \frac{290}{35}
\]
\[
\frac{14}{5} = \frac{14 \times 7}{5 \times 7} = \frac{98}{35}
\]

### Step 3: Perform the addition.

\[
\frac{290}{35} + \frac{98}{35} = \frac{290 + 98}{35} = \frac{388}{35}
\]

### Step 4: Simplify the fraction (if possible).

\(\frac{388}{35}\) is already in its simplest form.

### Final Answer:

\[
8 \frac{2}{7} + 2 \frac{4}{5} = \frac{388}{35} \approx 11.09
\]

Would you like to know more details or ask questions about this? Here are 5 related questions:

1. How do you convert improper fractions back into mixed numbers?
2. What is the method for finding the least common denominator of two fractions?
3. Can you explain more about simplifying fractions?
4. Why do we need a common denominator when adding fractions?
5. How would you subtract mixed numbers?

**Tip:** Always double-check your work when converting between mixed numbers and improper fractions to avoid mistakes!

Learn how to add the mixed numbers 8 2/7 and 2 4/5 with a step-by-step solution. This math problem covers key concepts like converting mixed numbers to improper fractions and adding fractions using a common denominator. Suitable for students in Grades 6-8.

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