Answer :
To solve the problem of multiplying the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(-\frac{5}{4}\)[/tex], let's go step-by-step:
1. Multiply the numerators:
Multiply the numerators of the fractions:
[tex]\[
12 \times (-5) = -60
\][/tex]
So, the numerator of the product is [tex]\(-60\)[/tex].
2. Multiply the denominators:
Multiply the denominators of the fractions:
[tex]\[
25 \times 4 = 100
\][/tex]
So, the denominator of the product is [tex]\(100\)[/tex].
3. Write the product of the fractions:
After multiplying, the product of the fractions is:
[tex]\[
\frac{-60}{100}
\][/tex]
4. Simplify the fraction:
To simplify, find the greatest common divisor (GCD) of [tex]\(-60\)[/tex] and [tex]\(100\)[/tex]. The GCD is [tex]\(20\)[/tex].
5. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{-60 \div 20}{100 \div 20} = \frac{-3}{5}
\][/tex]
So, the answer to [tex]\(\frac{12}{25} \times \left(-\frac{5}{4}\right)\)[/tex] in its simplest form is [tex]\(-\frac{3}{5}\)[/tex].
1. Multiply the numerators:
Multiply the numerators of the fractions:
[tex]\[
12 \times (-5) = -60
\][/tex]
So, the numerator of the product is [tex]\(-60\)[/tex].
2. Multiply the denominators:
Multiply the denominators of the fractions:
[tex]\[
25 \times 4 = 100
\][/tex]
So, the denominator of the product is [tex]\(100\)[/tex].
3. Write the product of the fractions:
After multiplying, the product of the fractions is:
[tex]\[
\frac{-60}{100}
\][/tex]
4. Simplify the fraction:
To simplify, find the greatest common divisor (GCD) of [tex]\(-60\)[/tex] and [tex]\(100\)[/tex]. The GCD is [tex]\(20\)[/tex].
5. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{-60 \div 20}{100 \div 20} = \frac{-3}{5}
\][/tex]
So, the answer to [tex]\(\frac{12}{25} \times \left(-\frac{5}{4}\right)\)[/tex] in its simplest form is [tex]\(-\frac{3}{5}\)[/tex].