https://file.aiquickdraw.com/mathbot/file/1726743820562pb5ju04x.jpg

The equation in the image is:

\[
6 \frac{5}{6} + 8 \frac{1}{4} = ?
\]

This is a sum of two mixed numbers.

### Step 1: Convert the mixed numbers to improper fractions
- \( 6 \frac{5}{6} = \frac{6 \times 6 + 5}{6} = \frac{36 + 5}{6} = \frac{41}{6} \)
- \( 8 \frac{1}{4} = \frac{8 \times 4 + 1}{4} = \frac{32 + 1}{4} = \frac{33}{4} \)

### Step 2: Find a common denominator
The least common denominator (LCD) of 6 and 4 is 12. We convert both fractions to have the denominator of 12:
- \( \frac{41}{6} = \frac{41 \times 2}{6 \times 2} = \frac{82}{12} \)
- \( \frac{33}{4} = \frac{33 \times 3}{4 \times 3} = \frac{99}{12} \)

### Step 3: Add the fractions
Now that both fractions have the same denominator, we can add them:
\[
\frac{82}{12} + \frac{99}{12} = \frac{82 + 99}{12} = \frac{181}{12}
\]

### Step 4: Convert the improper fraction back to a mixed number
To convert \( \frac{181}{12} \) to a mixed number, divide 181 by 12:
- \( 181 \div 12 = 15 \) with a remainder of 1.
Thus, \( \frac{181}{12} = 15 \frac{1}{12} \).

### Final Answer:
\[
6 \frac{5}{6} + 8 \frac{1}{4} = 15 \frac{1}{12}
\]

Would you like more details or have any questions about this solution?

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Here are five related questions to practice:
1. What is the sum of \( 7 \frac{2}{3} + 5 \frac{5}{9} \)?
2. Subtract \( 10 \frac{3}{5} - 4 \frac{7}{8} \).
3. Multiply \( 3 \frac{1}{4} \times 2 \frac{2}{3} \).
4. Convert \( 12 \frac{7}{8} \) to an improper fraction.
5. Simplify \( \frac{45}{12} \).

**Tip:** When adding or subtracting fractions, always find the least common denominator (LCD) for accuracy and ease.

Learn how to solve the addition of mixed numbers 6 5/6 and 8 1/4. This step-by-step guide covers converting mixed numbers to improper fractions, finding a common denominator, adding fractions, and converting the result back to a mixed number. Suitable for students in Grades 5-7.

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