To multiply \(-1.7\) by \(2 \frac{1}{2}\), we first convert \(2 \frac{1}{2}\) into an improper fraction.
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Convert \(2 \frac{1}{2}\): \[ 2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \] So, \[ 2 \frac{1}{2} = \frac{5}{2} \]
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Now multiply \(-1.7\) by \(\frac{5}{2}\). First, convert \(-1.7\) to a fraction: \[ -1.7 = -\frac{17}{10} \]
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Multiply the two fractions: \[ -\frac{17}{10} \times \frac{5}{2} = -\frac{17 \times 5}{10 \times 2} = -\frac{85}{20} \]
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Simplify \(-\frac{85}{20}\): \[ \text{The GCD of 85 and 20 is 5.} \] So, \[ -\frac{85 \div 5}{20 \div 5} = -\frac{17}{4} \]
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Convert \(-\frac{17}{4}\) to a mixed number:
- Divide \(17\) by \(4\): \[ 17 \div 4 = 4 \quad \text{(whole number)} \] \[ 17 - 4 \times 4 = 1 \quad \text{(remainder)} \]
- So, \(-\frac{17}{4} = -4 \frac{1}{4}\).
Thus, the final answer is: \[ \boxed{-4 \frac{1}{4}} \]