To evaluate the expression -5 7/12 + 3 9/12 - 2 5/12, we can first convert all the mixed numbers to improper fractions.
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Convert -5 7/12 to an improper fraction: \[ -5 \frac{7}{12} = -\left(5 \times 12 + 7\right)/12 = -\left(60 + 7\right)/12 = -67/12 \]
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Convert 3 9/12 to an improper fraction: \[ 3 \frac{9}{12} = (3 \times 12 + 9)/12 = (36 + 9)/12 = 45/12 \]
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Convert -2 5/12 to an improper fraction: \[ -2 \frac{5}{12} = -\left(2 \times 12 + 5\right)/12 = -\left(24 + 5\right)/12 = -29/12 \]
Now we can rewrite the original expression using the improper fractions: \[ -67/12 + 45/12 - 29/12 \]
Combine the fractions by adding and subtracting the numerators: \[ = \frac{-67 + 45 - 29}{12} = \frac{-67 + 45 - 29}{12} = \frac{-67 + 45 - 29}{12} \] Let's perform the addition and subtraction step by step:
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Add -67 and 45: \[ -67 + 45 = -22 \]
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Now subtract 29: \[ -22 - 29 = -51 \]
So, we have: \[ \frac{-51}{12} \]
Now, we can convert this improper fraction back to a mixed number. Divide -51 by 12: -51 divided by 12 equals -4 with a remainder of 3.
Thus: \[ -51/12 = -4 \frac{3}{12} \]
We can simplify the fraction \( \frac{3}{12} \) to \( \frac{1}{4} \): \[ -4 \frac{1}{4} \]
Therefore, the final answer is: \[ \boxed{-4 \frac{1}{4}} \]
The correct choice is D. -4 1/4.