3 4/7 • 9 16/17 + 3 4/7 • 7 1/17

To solve the expression \(3 \frac{4}{7} \cdot 9 \frac{16}{17} + 3 \frac{4}{7} \cdot 7 \frac{1}{17}\), we can start by converting the mixed numbers into improper fractions.

1. Convert the mixed numbers to improper fractions:

   • \( 3 \frac{4}{7} = \frac{3 \times 7 + 4}{7} = \frac{21 + 4}{7} = \frac{25}{7} \)
   • \( 9 \frac{16}{17} = \frac{9 \times 17 + 16}{17} = \frac{153 + 16}{17} = \frac{169}{17} \)
   • \( 7 \frac{1}{17} = \frac{7 \times 17 + 1}{17} = \frac{119 + 1}{17} = \frac{120}{17} \)

2. Rewrite the expression using the improper fractions: \[ \frac{25}{7} \cdot \frac{169}{17} + \frac{25}{7} \cdot \frac{120}{17} \]

3. Factor out \(\frac{25}{7}\): \[ \frac{25}{7} \left(\frac{169}{17} + \frac{120}{17}\right) \]

4. Combine the fractions inside the parentheses: \[ \frac{169 + 120}{17} = \frac{289}{17} \]

5. Now we have: \[ \frac{25}{7} \cdot \frac{289}{17} \]

6. Multiply the fractions: \[ = \frac{25 \cdot 289}{7 \cdot 17} = \frac{7225}{119} \]

7. Convert the improper fraction back to a mixed number if necessary: Divide \(7225\) by \(119\): \[ 7225 \div 119 = 60 \quad \text{(the whole number)} \] To find the remainder: \[ 7225 - (60 \cdot 119) = 7225 - 7140 = 85 \] Thus, the mixed number is: \[ 60 \frac{85}{119} \]

8. Final answer: The result of the expression \(3 \frac{4}{7} \cdot 9 \frac{16}{17} + 3 \frac{4}{7} \cdot 7 \frac{1}{17}\) is: \[ 60 \frac{85}{119} \]