College

Multiply. Write your answer in lowest terms as a proper or improper fraction.

[tex]\[\frac{12}{25} \times \left(-\frac{5}{4}\right)\][/tex]

Answer :

Sure! Let's go through the steps to multiply the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(-\frac{5}{4}\)[/tex] and then simplify the result.

1. Multiply the Numerators:

Take the numerators of each fraction and multiply them.
[tex]\[
12 \times (-5) = -60
\][/tex]

2. Multiply the Denominators:

Take the denominators of each fraction and multiply them.
[tex]\[
25 \times 4 = 100
\][/tex]

3. Form the New Fraction:

Combine the results from the two steps above to form a new fraction.
[tex]\[
\frac{-60}{100}
\][/tex]

4. Simplify the Fraction:

To simplify the fraction, find the greatest common divisor (GCD) of 60 and 100, which is 20. Use this to divide both the numerator and the denominator.

- Divide the numerator by the GCD: [tex]\(-60 \div 20 = -3\)[/tex]
- Divide the denominator by the GCD: [tex]\(100 \div 20 = 5\)[/tex]

5. Write the Simplified Fraction:

The simplified form of the fraction is:
[tex]\[
\frac{-3}{5}
\][/tex]

So, the answer is [tex]\(\frac{-3}{5}\)[/tex].

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