Multiply. Write your answer as a fraction in simplest form. 2/3 x 2/7 x 9/11

Answer 1

To multiply the fractions \( \frac{2}{3} \), \( \frac{2}{7} \), and \( \frac{9}{11} \), we follow these steps:

1. Multiply the numerators: \[ 2 \times 2 \times 9 = 36 \]

2. Multiply the denominators: \[ 3 \times 7 \times 11 = 231 \]

3. Combine the results to form the fraction: \[ \frac{36}{231} \]

4. Now, we need to simplify the fraction. First, we find the greatest common divisor (GCD) of 36 and 231. We can do this by finding the prime factors of each number:

   • The prime factors of 36 are \( 2^2 \times 3^2 \).
   • The prime factorization of 231 is \( 3 \times 7 \times 11 \).

   The common factor is \( 3 \).

5. Now we divide both the numerator and denominator by their GCD: \[ \frac{36 \div 3}{231 \div 3} = \frac{12}{77} \]

Thus, the product of \( \frac{2}{3} \times \frac{2}{7} \times \frac{9}{11} \) in simplest form is: \[ \frac{12}{77} \]