To solve the addition \( 63 \frac{5}{12} + \frac{12}{8} \), we will first convert everything into improper fractions.

### Step 1: Convert \( 63 \frac{5}{12} \) to an improper fraction

1. Convert the whole number 63 into a fraction with a denominator of 12:  
   \[
   63 = \frac{63 \times 12}{12} = \frac{756}{12}
   \]

2. Add the fractional part \(\frac{5}{12}\):  
   \[
   63 \frac{5}{12} = \frac{756}{12} + \frac{5}{12} = \frac{761}{12}
   \]

### Step 2: Simplify \(\frac{12}{8}\)

Simplify \(\frac{12}{8}\) by dividing both the numerator and the denominator by their greatest common divisor (4):

\[
\frac{12}{8} = \frac{12 \div 4}{8 \div 4} = \frac{3}{2}
\]

### Step 3: Convert \(\frac{3}{2}\) to have the same denominator as \(\frac{761}{12}\)

To add these fractions, they must have the same denominator. Convert \(\frac{3}{2}\) to a denominator of 12:

\[
\frac{3}{2} = \frac{3 \times 6}{2 \times 6} = \frac{18}{12}
\]

### Step 4: Add the fractions

Now, add \(\frac{761}{12}\) and \(\frac{18}{12}\):

\[
\frac{761}{12} + \frac{18}{12} = \frac{761 + 18}{12} = \frac{779}{12}
\]

### Step 5: Convert back to a mixed number

Convert \(\frac{779}{12}\) to a mixed number:

1. Divide 779 by 12:  
   \( 779 \div 12 = 64 \) remainder \( 11 \).
   
2. So, the mixed number is:  
   \[
   \frac{779}{12} = 64 \frac{11}{12}
   \]

### Final Answer

\[
63 \frac{5}{12} + \frac{12}{8} = 64 \frac{11}{12}
\]

Would you like more details or have any questions?

Here are some related questions:

1. How do you simplify fractions with different denominators?
2. What are improper fractions and how do you convert them to mixed numbers?
3. How can you find the greatest common divisor (GCD) of two numbers?
4. What steps are involved in adding mixed numbers?
5. How do you convert mixed numbers to improper fractions?

**Tip:** Always convert mixed numbers to improper fractions when adding or subtracting them for easier calculations!

Learn how to add mixed numbers and improper fractions by solving 63 5/12 + 12/8. This step-by-step guide covers key concepts like improper fractions, fraction simplification, and mixed number conversion. Suitable for students in Grades 5-7.

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