To solve $4 \frac{8}{12} + 5 \frac{7}{24}$, we will first convert the mixed fractions into improper fractions and then add them.

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Step 1: Convert mixed numbers to improper fractions.

1. $4 \frac{8}{12} = \frac{48}{12} + \frac{8}{12} = \frac{56}{12}$.
2. $5 \frac{7}{24} = \frac{120}{24} + \frac{7}{24} = \frac{127}{24}$.

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Step 2: Find the least common denominator (LCD).

The denominators are 12 and 24. The LCD is $24$.

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Step 3: Rewrite fractions with the LCD.

1. Rewrite $\frac{56}{12}$ with a denominator of 24: $\frac{56}{12} = \frac{56 \times 2}{12 \times 2} = \frac{112}{24}.$
2. $\frac{127}{24}$ remains the same.

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Step 4: Add the fractions.

$\frac{112}{24} + \frac{127}{24} = \frac{112 + 127}{24} = \frac{239}{24}.$

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Step 5: Convert back to a mixed number.

Divide $239$ by $24$:

• Quotient: $9$ (whole number part),
• Remainder: $239 - 24 \times 9 = 23$ (numerator of the fraction).

Thus, $\frac{239}{24} = 9 \frac{23}{24}$.

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Final Answer:

$9 \frac{23}{24}$

Would you like me to explain this in further detail or cover related examples?

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Related Questions:

1. How do you find the least common denominator for fractions?
2. How do you convert improper fractions back to mixed numbers?
3. Can you demonstrate how to subtract mixed fractions?
4. What are some tips for simplifying fractions during addition?
5. How do you solve problems involving fractions with three terms?

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Tip:

When adding fractions, always simplify each term first to make calculations easier and reduce potential errors.