To evaluate the expression \((-5 \frac{1}{2} - 8.75) / 1 \frac{1}{2}\), we will follow these steps:
- Convert mixed numbers to improper fractions or decimals for easier calculation.
- Compute the numerator by performing the subtraction.
- Divide by the denominator.
Step 1: Convert mixed numbers to improper fractions or decimals.
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The mixed number \(-5 \frac{1}{2}\): \[ -5 \frac{1}{2} = -\left(5 + \frac{1}{2}\right) = -\frac{10}{2} - \frac{1}{2} = -\frac{11}{2} \]
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The decimal \(8.75\) can stay as it is because it's already a decimal.
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The mixed number \(1 \frac{1}{2}\): \[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \]
Step 2: Compute the numerator.
Now, substitute the values into the expression:
\[ (-5 \frac{1}{2} - 8.75) = \left(-\frac{11}{2} - 8.75\right) \]
Convert \(8.75\) to a fraction: \[ 8.75 = \frac{875}{100} = \frac{35}{4} \]
Now, we will compute \(-\frac{11}{2} - \frac{35}{4}\). To subtract these fractions, we need a common denominator. The least common multiple of \(2\) and \(4\) is \(4\).
Convert \(-\frac{11}{2}\) to a fraction with a denominator of \(4\): \[ -\frac{11}{2} = -\frac{11 \times 2}{2 \times 2} = -\frac{22}{4} \]
Now perform the subtraction: \[ -\frac{22}{4} - \frac{35}{4} = \frac{-22 - 35}{4} = \frac{-57}{4} \]
Step 3: Divide by the denominator \(\frac{3}{2}\).
Now, we need to divide by \(\frac{3}{2}\): \[ \frac{-57}{4} \div \frac{3}{2} = \frac{-57}{4} \times \frac{2}{3} = \frac{-57 \times 2}{4 \times 3} = \frac{-114}{12} \]
Now simplify \(\frac{-114}{12}\):
- Determine the GCD of \(114\) and \(12\), which is \(6\). \[ \frac{-114 \div 6}{12 \div 6} = \frac{-19}{2} \]
Step 4: Convert to a mixed number.
\(-\frac{19}{2}\) is an improper fraction, which can be converted to a mixed number: \[ -\frac{19}{2} = -9 \frac{1}{2} \]
Thus, the evaluated expression in simplest form is: \[ \boxed{-9 \frac{1}{2}} \]