1. Subtract: [tex]\frac{8}{9} - \frac{2}{9}[/tex]. Express your final answer in simplest form.

A. [tex]\frac{1}{2}[/tex]
B. [tex]\frac{5}{9}[/tex]
C. [tex]\frac{1}{3}[/tex]
D. [tex]\frac{2}{3}[/tex]



Answer :

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]