To add [tex]\( 4 \frac{2}{3} + \frac{7}{9} \)[/tex], follow these steps:
1. Convert the mixed number [tex]\( 4 \frac{2}{3} \)[/tex] to an improper fraction:
- [tex]\( 4 = \frac{4 \times 3}{3} = \frac{12}{3} \)[/tex]
- Then, add the fractional part: [tex]\( \frac{12}{3} + \frac{2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \)[/tex]
2. Now add [tex]\( \frac{14}{3} + \frac{7}{9} \)[/tex]:
- Find a common denominator for the fractions. The least common multiple (LCM) of 3 and 9 is 9.
- Convert [tex]\( \frac{14}{3} \)[/tex] to a fraction with a denominator of 9:
[tex]\[ \frac{14}{3} = \frac{14 \times 3}{3 \times 3} = \frac{42}{9} \][/tex]
- Now add the fractions with a common denominator:
[tex]\[ \frac{42}{9} + \frac{7}{9} = \frac{42 + 7}{9} = \frac{49}{9} \][/tex]
Therefore,
[tex]\[ 4 \frac{2}{3} + \frac{7}{9} = \frac{49}{9} \][/tex]
So, the final answer is:
[tex]\[
\boxed{49/9}
\][/tex]
