To convert the mixed number [tex]\(32 \frac{4}{5}\)[/tex] to an improper fraction, follow these steps:
1. Identify the whole number and the fraction part:
- The whole number part is [tex]\(32\)[/tex].
- The fractional part is [tex]\(\frac{4}{5}\)[/tex].
2. Convert the whole number to a fraction with the same denominator as the fractional part:
- Since the denominator of the fractional part is [tex]\(5\)[/tex], express [tex]\(32\)[/tex] as a fraction:
[tex]\[32 = \frac{32 \times 5}{5} = \frac{160}{5}\][/tex]
3. Add the fractional part to the converted whole number:
- The fractional part is [tex]\(\frac{4}{5}\)[/tex].
- Add this to the converted whole number:
[tex]\[\frac{160}{5} + \frac{4}{5} = \frac{160 + 4}{5} = \frac{164}{5}\][/tex]
Thus, the mixed number [tex]\(32 \frac{4}{5}\)[/tex] as an improper fraction is [tex]\(\frac{164}{5}\)[/tex].
The correct answer is [tex]\(\frac{164}{5}\)[/tex].
