Sure! Let's solve this step-by-step.
First, convert the mixed number [tex]\( 4 \frac{2}{3} \)[/tex] to an improper fraction.
A mixed number consists of an integer part and a fractional part. In our case, the integer part is 4 and the fractional part is [tex]\( \frac{2}{3} \)[/tex].
To convert [tex]\( 4 \frac{2}{3} \)[/tex] to an improper fraction:
1. Multiply the integer part (4) by the denominator of the fraction (3):
[tex]\[
4 \times 3 = 12
\][/tex]
2. Add the result to the numerator of the fractional part:
[tex]\[
12 + 2 = 14
\][/tex]
So, the mixed number [tex]\( 4 \frac{2}{3} \)[/tex] as an improper fraction is:
[tex]\[
\frac{14}{3}
\][/tex]
Now, we need to add this fraction to [tex]\( \frac{7}{9} \)[/tex].
To add fractions, we need a common denominator. The denominators are 3 and 9. 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 we have:
[tex]\[
\frac{42}{9} + \frac{7}{9}
\][/tex]
Add the numerators together:
[tex]\[
42 + 7 = 49
\][/tex]
So, the resulting fraction is:
[tex]\[
\frac{49}{9}
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{\frac{49}{9}}
\][/tex]
