To evaluate the expression \( 26.95 \div -5 \frac{1}{2} \), we first need to convert the mixed number \(-5 \frac{1}{2}\) into an improper fraction.
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Convert \(-5 \frac{1}{2}\) to an improper fraction: \[ -5 \frac{1}{2} = -\left(5 \times 2 + 1\right)/2 = -\frac{10 + 1}{2} = -\frac{11}{2} \]
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Now, rewrite the division problem: \[ 26.95 \div -5 \frac{1}{2} = 26.95 \div -\frac{11}{2} \]
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Dividing by a fraction is the same as multiplying by its reciprocal: \[ 26.95 \div -\frac{11}{2} = 26.95 \times -\frac{2}{11} \]
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Next, calculate \( 26.95 \times -\frac{2}{11} \): \[ 26.95 \times -\frac{2}{11} = \frac{26.95 \times -2}{11} \]
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First, calculate \( 26.95 \times -2 \): \[ 26.95 \times -2 = -53.90 \]
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Now divide \(-53.90\) by \(11\): \[ -53.90 \div 11 = -4.9 \]
Thus, the value of the expression \( 26.95 \div -5 \frac{1}{2} \) is \(\boxed{-4.9}\).
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