To multiply \(-1.7\) by \(212\), we start with the calculation:
\[ -1.7 \times 212 = -359.4 \]
Next, we convert \(-359.4\) to a mixed number.
First, we know that \(-359\) is the whole number part.
Now we look at the decimal part, \(0.4\). To express \(0.4\) as a fraction, we recognize that:
\[ 0.4 = \frac{4}{10} = \frac{2}{5} \]
Thus, we can express \(-359.4\) as:
\[ -359.4 = -359 - \frac{2}{5} \]
This can also be written as:
\[ -359 \frac{2}{5} \]
So the mixed number in simplest form is:
\[ -359 \frac{2}{5} \]
However, this option is not among those you’ve provided.
It looks like I misunderstood, as the original problem did not include options for \(-359 \frac{2}{5}\). Let us ensure we've correctly interpreted your provided options.
Here are the options by simplifying:
- \(-414\) can be expressed as \(-414\)
- \(-174\) is \(-174\)
- \(-234100\) seems like an error; however it could mean \(-234\frac{100}{100}\) or similar (if numbers are misquoted).
- \(-4520\) is \(-4520\)
Since there's no true option for \(-359.4\) (or \(-359 \frac{2}{5}\)), it seems there might be a misunderstanding with the calculation vs the provided options.
If we recheck: The calculation was accurate for \(−1.7 \times 212 = −359.4\)
Please let me know if there’s any adjustment to the questions or different aspects to consider!