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:
- The whole number part is \(-360\).
- 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 \(-360.4\).