Question

Multiply −1.7
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:
\[
-\mathbf{4\frac{1}{4}}
\]