To add the mixed numbers \(3 \frac{4}{5}\) and \(4 \frac{4}{15}\), we first convert each mixed number into an improper fraction.
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Convert \(3 \frac{4}{5}\):
\[ 3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \]
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Convert \(4 \frac{4}{15}\):
\[ 4 \frac{4}{15} = \frac{4 \times 15 + 4}{15} = \frac{60 + 4}{15} = \frac{64}{15} \]
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Find a common denominator:
The denominators are \(5\) and \(15\). The least common denominator (LCD) is \(15\). -
Convert \( \frac{19}{5} \) to have a denominator of \(15\):
\[ \frac{19}{5} = \frac{19 \times 3}{5 \times 3} = \frac{57}{15} \]
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Now add the two fractions:
\[ \frac{57}{15} + \frac{64}{15} = \frac{57 + 64}{15} = \frac{121}{15} \]
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Convert the improper fraction \( \frac{121}{15} \) to a mixed number:
Divide \(121\) by \(15\):
\[ 121 \div 15 = 8 \quad \text{ (with a remainder of } 1\text{)} \]
So, \(121 = 15 \times 8 + 1\).
Therefore,
\[ \frac{121}{15} = 8 \frac{1}{15} \]
In simplest form, the final answer is:
\[ 8 \frac{1}{15} \]
So the whole number is 8.
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