To solve $4 \frac{6}{8} + 7 \frac{4}{8}$, follow these steps:

Step 1: Convert the mixed numbers to improper fractions

1. $4 \frac{6}{8} = \frac{4 \times 8 + 6}{8} = \frac{32 + 6}{8} = \frac{38}{8}$
2. $7 \frac{4}{8} = \frac{7 \times 8 + 4}{8} = \frac{56 + 4}{8} = \frac{60}{8}$

Step 2: Add the improper fractions

Since the denominators are the same ($8$), add the numerators directly: $\frac{38}{8} + \frac{60}{8} = \frac{38 + 60}{8} = \frac{98}{8}$

Step 3: Simplify the fraction

Divide both the numerator and denominator by their greatest common divisor (GCD), which is $2$: $\frac{98}{8} = \frac{98 \div 2}{8 \div 2} = \frac{49}{4}$

Step 4: Convert back to a mixed number

Divide $49$ by $4$:

• Quotient: $12$ (whole number part)
• Remainder: $1$ (numerator of the fractional part)

Thus, the result is: $12 \frac{1}{4}$

Final Answer:

$12 \frac{1}{4}$

Would you like further clarification or a breakdown of any step?

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Related Questions:

1. How do you subtract mixed numbers with different denominators?
2. Can improper fractions always be simplified to mixed numbers?
3. What is the process to find the GCD of two numbers?
4. How do you add fractions with different denominators?
5. What is the quickest way to convert a mixed number into an improper fraction?

Tip: Always simplify your fractions in the final answer to make them easier to interpret!