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?

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.