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\(-\frac{17}{12}\)
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The Deep Dive
To simplify \( -2 \frac{1}{6} + \frac{3}{4} \), first, convert the mixed number into an improper fraction: \(-2 \frac{1}{6} = -\frac{13}{6}\). Now, add it to \(\frac{3}{4}\). To do this, find a common denominator, which is 12: \(-\frac{13}{6} = -\frac{26}{12}\) and \(\frac{3}{4} = \frac{9}{12}\). Now add: \(-\frac{26}{12} + \frac{9}{12} = -\frac{17}{12}\), which can also be expressed as \(-1 \frac{5}{12}\). So, the answer is \(-1 \frac{5}{12}\).