To solve [tex]\(\frac{6}{9} \times \frac{2}{3}\)[/tex], follow these steps:
1. Multiply the numerators:
[tex]\[
6 \times 2 = 12
\][/tex]
So, the product of the numerators is 12.
2. Multiply the denominators:
[tex]\[
9 \times 3 = 27
\][/tex]
So, the product of the denominators is 27.
3. Combine these to form a new fraction:
[tex]\[
\frac{12}{27}
\][/tex]
4. Simplify the fraction. To do this, we find the greatest common divisor (GCD) of 12 and 27, and then divide both the numerator and the denominator by this GCD.
The GCD of 12 and 27 is 3.
[tex]\[
\text{Numerator}: \frac{12}{3} = 4
\text{Denominator}: \frac{27}{3} = 9
\][/tex]
So, the fraction simplifies to:
[tex]\[
\frac{4}{9}
\][/tex]
Hence, the final answer is:
[tex]\[
\frac{6}{9} \times \frac{2}{3} = \frac{4}{9}
\][/tex]
