College

Multiply:

\[ \left(-\frac{12}{25}\right) \cdot \frac{5}{9} \]

What is the product?

Enter your answer as a fraction in simplified form in the box.

Answer :

Sure, let's find the product of the fractions [tex]\(\left(-\frac{12}{25}\right) \cdot \frac{5}{9}\)[/tex].

### Step-by-Step Solution

1. Multiply the Numerators:
- First, multiply the numerators of the fractions.
[tex]\[
-12 \times 5 = -60
\][/tex]

2. Multiply the Denominators:
- Next, multiply the denominators of the fractions.
[tex]\[
25 \times 9 = 225
\][/tex]

3. Form the New Fraction:
- Combine the results from the previous steps to form a new fraction.
[tex]\[
\frac{-60}{225}
\][/tex]

4. Simplify the Fraction:
- To simplify the fraction [tex]\(\frac{-60}{225}\)[/tex], find the greatest common divisor (GCD) of 60 and 225.
- The GCD of 60 and 225 is 15.

- Divide both the numerator and the denominator by their GCD to simplify the fraction.
[tex]\[
\frac{-60 \div 15}{225 \div 15} = \frac{-4}{15}
\][/tex]

So, the product of [tex]\(\left(-\frac{12}{25}\right) \cdot \frac{5}{9}\)[/tex] is [tex]\(\frac{-4}{15}\)[/tex].