To solve the subtraction of the fractions [tex]\(\frac{8}{9} - \frac{2}{9}\)[/tex], we can follow these steps:
1. Ensure the denominators are the same: Both fractions [tex]\(\frac{8}{9}\)[/tex] and [tex]\(\frac{2}{9}\)[/tex] have the same denominator ([tex]\(9\)[/tex]). Since the denominators are already the same, we can simply subtract the numerators.
2. Subtract the numerators:
[tex]\[
8 - 2 = 6
\][/tex]
3. Keep the common denominator: The denominator remains [tex]\(9\)[/tex], as both fractions have the same denominator.
4. Form the resulting fraction:
[tex]\[
\frac{6}{9}
\][/tex]
5. Simplify the fraction:
- To simplify [tex]\(\frac{6}{9}\)[/tex], we find the greatest common divisor (GCD) of [tex]\(6\)[/tex] and [tex]\(9\)[/tex].
- The GCD of [tex]\(6\)[/tex] and [tex]\(9\)[/tex] is [tex]\(3\)[/tex].
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\][/tex]
Therefore, the simplified form of [tex]\(\frac{8}{9} - \frac{2}{9}\)[/tex] is [tex]\(\frac{2}{3}\)[/tex].
So, the final answer is:
[tex]\(\frac{2}{3}\)[/tex]
The correct answer, based on the given multiple choices, is:
[tex]\(\boxed{\frac{2}{3}}\)[/tex]
