Question

Multiply −1.7
by 212
. Write the answer as a mixed number in simplest form.(1 point)
Responses

−174
negative Start Fraction 17 over 4 End Fraction

−4520
negative 4 Start Fraction 5 over 20 End Fraction

−234100
negative 2 Start Fraction 34 over 100 End Fraction

−414

Answer 1

To solve \(-1.7 \times 212\), we first perform the multiplication:

\[
-1.7 \times 212 = -360.4
\]

Next, we convert \(-360.4\) into a mixed number. Start by recognizing that \(-360.4\) is composed of the whole number part and the decimal part:

1. The whole number part is \(-360\).
2. The decimal \(0.4\) can be converted to a fraction. Since \(0.4 = \frac{4}{10}\), we simplify this fraction:

\[
\frac{4}{10} = \frac{2}{5}
\]

Thus, we can rewrite \(-360.4\) as:

\[
-360 - 0.4 = -360 - \frac{2}{5} = -360 \frac{2}{5}
\]

So the final answer is:

\[
-360 \frac{2}{5}
\]

Now, let's look at the provided options:

- \(-174\)
- negative \(\frac{17}{4}\)
- \(-4520\)
- negative \(\frac{5}{20}\)
- \(-234100\)
- negative \(\frac{34}{100}\)
- \(-414\)

None of these options match the converted mixed number. Thus, the correct representation in simplest form should actually be:

\[
-360 \frac{2}{5}
\]

If we mean, to summarize:

The answer to the question, expressed in a comparable mixed number format, does not directly match the options provided. However, \(-360 \frac{2}{5}\) is indeed the simplest form derived from \(-360.4\).