Multiply −1.7

Question

by 2 1/2
. Write the answer as a mixed number in simplest form.(1 point)
Responses

−17/4
negative Start Fraction 17 over 4 End Fraction

−4 5/20
negative 4 Start Fraction 5 over 20 End Fraction

−2 34/100
negative 2 Start Fraction 34 over 100 End Fraction

−4 1/4

Answer 1

To multiply \(-1.7\) by \(2 \frac{1}{2}\), we first convert the mixed number \(2 \frac{1}{2}\) into an improper fraction.

1. Convert \(2 \frac{1}{2}\) to an improper fraction: \[ 2 \frac{1}{2} = 2 \cdot 2 + 1 = 4 + 1 = 5 \] Thus, \[ 2 \frac{1}{2} = \frac{5}{2} \]

2. Now perform the multiplication: \[ -1.7 \times \frac{5}{2} \] First, convert \(-1.7\) to a fraction: \[ -1.7 = -\frac{17}{10} \]

3. Now multiply: \[ -\frac{17}{10} \times \frac{5}{2} = -\frac{17 \cdot 5}{10 \cdot 2} = -\frac{85}{20} \]

4. Now simplify \(-\frac{85}{20}\): The greatest common divisor of 85 and 20 is 5. \[ -\frac{85 \div 5}{20 \div 5} = -\frac{17}{4} \]

5. Convert \(-\frac{17}{4}\) to a mixed number: \(-\frac{17}{4}\) can be written as: \[ -4 \frac{1}{4} \text{ (since } 17 \div 4 = 4 \text{ remainder } 1\text{)} \]

Thus, the answer is: \[ -\mathbf{4\frac{1}{4}} \]