Question

Multiply −1.7 by 2 1/2 . Write the answer as a mixed number in simplest form.(1 point)
Responses

−414
negative 4 Start Fraction 1 over 4 End Fraction

−234100
negative 2 Start Fraction 34 over 100 End Fraction

−4520
negative 4 Start Fraction 5 over 20 End Fraction

−174

Answer 1

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

\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\]

Now we multiply \(-1.7\) by \(\frac{5}{2}\):

First, convert \(-1.7\) to a fraction:

\[
-1.7 = -\frac{17}{10}
\]

Now multiply the two fractions:

\[
-\frac{17}{10} \times \frac{5}{2} = -\frac{17 \times 5}{10 \times 2} = -\frac{85}{20}
\]

Next, we simplify \(-\frac{85}{20}\):

Both 85 and 20 can be divided by 5:

\[
-\frac{85 \div 5}{20 \div 5} = -\frac{17}{4}
\]

Now, convert \(-\frac{17}{4}\) to a mixed number:

To convert \(-\frac{17}{4}\) to a mixed number, divide:

17 divided by 4 is 4 with a remainder of 1, so:

\[
-\frac{17}{4} = -4 \frac{1}{4}
\]

Thus, the answer in simplest form is:

\[
\text{negative } 4 \frac{1}{4}
\]

The correct response is:

**negative 4 Start Fraction 1 over 4 End Fraction**