To change the improper fraction [tex]\(\frac{493}{174}\)[/tex] into an equal mixed number, we proceed as follows:
1. Divide the numerator by the denominator:
[tex]\[
\frac{493}{174}
\][/tex]
2. Determine the integer part: By performing the division, the quotient is 2. This quotient represents the integer part of the mixed number. So,
[tex]\[
\frac{493}{174} = 2 \ldots
\][/tex]
3. Find the remainder: The remainder of the division gives the numerator for the fractional part of the mixed number. The remainder when 493 is divided by 174 is 145.
4. Express the remainder as the fractional part:
[tex]\[
\frac{493}{174} = 2 + \frac{145}{174}
\][/tex]
Therefore, the improper fraction [tex]\(\frac{493}{174}\)[/tex] as an equal mixed number is:
[tex]\[
2 \frac{145}{174}
\][/tex]
After examining the given options, we see that the correct answer is:
[tex]\[
2 \frac{145}{174}
\][/tex]
So, from the given choices, none of them match our initial fraction exactly. However, among the given choices, the fraction should match [tex]\(\frac{493}{174} = 2 + \frac{145}{174}\)[/tex]. It looks like a mix-up happened with available answers. Recalculation would have led us to this mixed number, but double-checking the solution, this might involve some mistake in available choices or further steps are needed to identify the closest one. The chosen given answer doesn't fit exactly here.
