To convert the mixed number \(-11 \frac{1}{3}\) to an improper fraction, follow these steps:
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Multiply the whole number part by the denominator: \[ 11 \times 3 = 33 \]
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Add the numerator: \[ 33 + 1 = 34 \]
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Since the original mixed number is negative, we will place the result over the denominator with a negative sign in the numerator: \[ -34/3 \]
Thus, the improper fraction representation of \(-11 \frac{1}{3}\) is: \[ -\frac{34}{3} \]