Add, answer as a mixed number in simplest form.

3, 4/5 + 4, 4/15 = [__], [__]/[__]
Enter the whole number.

1 answer

To add the mixed numbers \(3 \frac{4}{5}\) and \(4 \frac{4}{15}\), we first convert each mixed number into an improper fraction.

  1. Convert \(3 \frac{4}{5}\):

    \[ 3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \]

  2. Convert \(4 \frac{4}{15}\):

    \[ 4 \frac{4}{15} = \frac{4 \times 15 + 4}{15} = \frac{60 + 4}{15} = \frac{64}{15} \]

  3. Find a common denominator:
    The denominators are \(5\) and \(15\). The least common denominator (LCD) is \(15\).

  4. Convert \( \frac{19}{5} \) to have a denominator of \(15\):

    \[ \frac{19}{5} = \frac{19 \times 3}{5 \times 3} = \frac{57}{15} \]

  5. Now add the two fractions:

    \[ \frac{57}{15} + \frac{64}{15} = \frac{57 + 64}{15} = \frac{121}{15} \]

  6. 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.