To solve the problem of adding [tex]\(\frac{8}{9}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex], let's go through the steps in detail:
1. Add the Fractions: Since the denominators are the same (9), you can simply add the numerators.
[tex]\[
\frac{8}{9} + \frac{4}{9} = \frac{8+4}{9} = \frac{12}{9}
\][/tex]
2. Simplify the Fraction: The fraction [tex]\(\frac{12}{9}\)[/tex] can be simplified. To do this, find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 12 and 9 is 3.
[tex]\[
\frac{12}{9} = \frac{12 \div 3}{9 \div 3} = \frac{4}{3}
\][/tex]
3. Convert to Mixed Number: Now, convert the improper fraction [tex]\(\frac{4}{3}\)[/tex] to a mixed number. Divide 4 by 3 to get a whole number part and a remainder.
- Whole number part: [tex]\(4 \div 3 = 1\)[/tex] (quotient)
- Remainder: [tex]\(4 \mod 3 = 1\)[/tex]
Therefore, [tex]\(\frac{4}{3}\)[/tex] can be written as:
[tex]\[
1 \frac{1}{3}
\][/tex]
So, the simplified answer, in mixed number form, is:
[tex]\[
1 \frac{1}{3}
\][/tex]
Thus, the correct choice from the given options is:
[tex]\[
\boxed{1 \frac{1}{3}}
\][/tex]
