Question

3/5 x 2/5 x 4/9

Answer 1

To multiply the fractions \( \frac{3}{5} \), \( \frac{2}{5} \), and \( \frac{4}{9} \), you multiply the numerators together and the denominators together.

1. Multiply the numerators:
\[
3 \times 2 \times 4 = 24
\]

2. Multiply the denominators:
\[
5 \times 5 \times 9 = 225
\]

Putting it all together, you get:
\[
\frac{24}{225}
\]

Now, to simplify \( \frac{24}{225} \), we can find the greatest common divisor (GCD) of 24 and 225. The prime factorization of 24 is \( 2^3 \times 3 \), and the prime factorization of 225 is \( 3^2 \times 5^2 \). The GCD is \( 3 \).

Now, divide both the numerator and the denominator by 3:
\[
\frac{24 \div 3}{225 \div 3} = \frac{8}{75}
\]

So, the simplified result is:
\[
\frac{8}{75}
\]