To solve the expression \( 16 \frac{3}{7} - 4 \frac{3}{4} \), we first convert the mixed numbers into improper fractions.
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Convert \( 16 \frac{3}{7} \): \[ 16 \frac{3}{7} = 16 + \frac{3}{7} = \frac{16 \times 7 + 3}{7} = \frac{112 + 3}{7} = \frac{115}{7} \]
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Convert \( 4 \frac{3}{4} \): \[ 4 \frac{3}{4} = 4 + \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \]
Now we have: \[ 16 \frac{3}{7} - 4 \frac{3}{4} = \frac{115}{7} - \frac{19}{4} \]
Next, we need a common denominator to subtract these two fractions. The least common multiple of 7 and 4 is 28.
Convert both fractions:
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Convert \( \frac{115}{7} \) to have a denominator of 28: \[ \frac{115}{7} = \frac{115 \times 4}{7 \times 4} = \frac{460}{28} \]
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Convert \( \frac{19}{4} \) to have a denominator of 28: \[ \frac{19}{4} = \frac{19 \times 7}{4 \times 7} = \frac{133}{28} \]
Now the expression is: \[ \frac{460}{28} - \frac{133}{28} = \frac{460 - 133}{28} = \frac{327}{28} \]
Finally, we can convert \( \frac{327}{28} \) back to a mixed number:
- Divide 327 by 28: \[ 327 \div 28 = 11 \quad \text{(Since \( 28 \times 11 = 308 \))} \] Remainder: \( 327 - 308 = 19 \)
So, we have: \[ \frac{327}{28} = 11 \frac{19}{28} \]
Thus, the final answer is: \[ \boxed{11 \frac{19}{28}} \]