To solve the problem [tex]\(4 \frac{2}{3} + \frac{7}{9}\)[/tex] and provide the answer as a fraction, follow these steps:
1. Convert the mixed fraction to an improper fraction:
- The mixed fraction [tex]\(4 \frac{2}{3}\)[/tex] can be written as [tex]\(4 + \frac{2}{3}\)[/tex].
- Convert [tex]\(4\)[/tex] to a fraction with the same denominator as [tex]\(\frac{2}{3}\)[/tex]. Thus, [tex]\(4 = \frac{12}{3}\)[/tex].
- Add the fractions: [tex]\(\frac{12}{3} + \frac{2}{3} = \frac{14}{3}\)[/tex].
2. Add the fractions [tex]\(\frac{14}{3}\)[/tex] and [tex]\(\frac{7}{9}\)[/tex]:
- To add these fractions, we need a common denominator. The least common denominator of 3 and 9 is 9.
- Convert [tex]\(\frac{14}{3}\)[/tex] to have a denominator of 9:
[tex]\[
\frac{14}{3} = \frac{14 \times 3}{3 \times 3} = \frac{42}{9}
\][/tex]
- Now add the two fractions with a common denominator:
[tex]\[
\frac{42}{9} + \frac{7}{9} = \frac{42 + 7}{9} = \frac{49}{9}
\][/tex]
Therefore, the result of adding [tex]\(4 \frac{2}{3} + \frac{7}{9}\)[/tex] is:
[tex]\[
\boxed{\frac{49}{9}}
\][/tex]
