To convert the mixed number [tex]\(3 \frac{8}{9}\)[/tex] to an improper fraction, follow these steps:
1. Identify the whole number and the fraction part. Here, the whole number is 3, and the fraction part is [tex]\(\frac{8}{9}\)[/tex].
2. Convert the whole number into a fraction with the same denominator as the given fraction. This means converting 3 into [tex]\(\frac{3 \times 9}{9} = \frac{27}{9}\)[/tex].
3. Add the converted whole number fraction to the given fraction. This results in:
[tex]\[ \frac{27}{9} + \frac{8}{9} \][/tex]
4. Since the denominators are the same, you can add the numerators directly:
[tex]\[ \frac{27 + 8}{9} = \frac{35}{9} \][/tex]
Thus, the improper fraction is [tex]\(\frac{35}{9}\)[/tex].
The numerator of the improper fraction is [tex]\(\boxed{35}\)[/tex].
