Certainly! Let's break this down step-by-step.
First, convert the mixed fraction [tex]\(4 \frac{2}{3}\)[/tex] into an improper fraction. Here’s the detailed transformation:
[tex]\[ 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \][/tex]
Next, we need to add [tex]\(\frac{14}{3}\)[/tex] to [tex]\(\frac{7}{9}\)[/tex]. For this, we need a common denominator. The least common multiple (LCM) of 3 and 9 is 9. Thus, we convert [tex]\(\frac{14}{3}\)[/tex] to a fraction with the denominator 9:
[tex]\[ \frac{14}{3} = \frac{14 \times 3}{3 \times 3} = \frac{42}{9} \][/tex]
Now, add the fractions [tex]\(\frac{42}{9}\)[/tex] and [tex]\(\frac{7}{9}\)[/tex]:
[tex]\[ \frac{42}{9} + \frac{7}{9} = \frac{42 + 7}{9} = \frac{49}{9} \][/tex]
So, the solution to the problem is:
[tex]\[ \boxed{\frac{49}{9}} \][/tex]
