To convert a mixed number to an improper fraction, follow these steps:
1. Identify the whole number and the fractional part of the mixed number. For [tex]\( 2 \frac{7}{9} \)[/tex], the whole number is [tex]\( 2 \)[/tex] and the fractional part is [tex]\( \frac{7}{9} \)[/tex].
2. Convert the whole number into a fraction with the same denominator as the fractional part. Since the denominator is [tex]\( 9 \)[/tex], we multiply the whole number [tex]\( 2 \)[/tex] by [tex]\( 9 \)[/tex] to get:
[tex]\[
2 \times 9 = 18
\][/tex]
3. Add the result to the numerator of the fractional part. The numerator of the fractional part is [tex]\( 7 \)[/tex], so we add:
[tex]\[
18 + 7 = 25
\][/tex]
4. Keep the same denominator, which is [tex]\( 9 \)[/tex].
Thus, the mixed number [tex]\( 2 \frac{7}{9} \)[/tex] as an improper fraction is:
[tex]\[
\frac{25}{9}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\frac{25}{9}
\][/tex]
