Answer :
To find the product of the fractions and write it in its lowest terms, follow these steps:
1. Identify the fractions: You are given [tex]\(-\frac{12}{45}\)[/tex] and [tex]\(\frac{18}{20}\)[/tex].
2. Multiply the numerators: The numerator will be the product of [tex]\(-12\)[/tex] and [tex]\(18\)[/tex], which is [tex]\(-12 \times 18 = -216\)[/tex].
3. Multiply the denominators: The denominator will be the product of [tex]\(45\)[/tex] and [tex]\(20\)[/tex], which is [tex]\(45 \times 20 = 900\)[/tex].
4. Write the product of the fractions: The product is [tex]\(-\frac{216}{900}\)[/tex].
5. Simplify the fraction: To simplify, find the greatest common divisor (GCD) of 216 and 900. The GCD is 36.
6. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{-216}{900} = \frac{-216 \div 36}{900 \div 36} = \frac{-6}{25}
\][/tex]
So, the product of [tex]\(-\frac{12}{45}\)[/tex] and [tex]\(\frac{18}{20}\)[/tex] in lowest terms is [tex]\(-\frac{6}{25}\)[/tex].
1. Identify the fractions: You are given [tex]\(-\frac{12}{45}\)[/tex] and [tex]\(\frac{18}{20}\)[/tex].
2. Multiply the numerators: The numerator will be the product of [tex]\(-12\)[/tex] and [tex]\(18\)[/tex], which is [tex]\(-12 \times 18 = -216\)[/tex].
3. Multiply the denominators: The denominator will be the product of [tex]\(45\)[/tex] and [tex]\(20\)[/tex], which is [tex]\(45 \times 20 = 900\)[/tex].
4. Write the product of the fractions: The product is [tex]\(-\frac{216}{900}\)[/tex].
5. Simplify the fraction: To simplify, find the greatest common divisor (GCD) of 216 and 900. The GCD is 36.
6. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{-216}{900} = \frac{-216 \div 36}{900 \div 36} = \frac{-6}{25}
\][/tex]
So, the product of [tex]\(-\frac{12}{45}\)[/tex] and [tex]\(\frac{18}{20}\)[/tex] in lowest terms is [tex]\(-\frac{6}{25}\)[/tex].
