Answer :
To solve the problem of finding the product of [tex]\(3 \frac{3}{4} \times-\left(\frac{12}{25}\right)\)[/tex], follow these steps:
1. Convert the Mixed Number to an Improper Fraction:
- The mixed number [tex]\(3 \frac{3}{4}\)[/tex] can be converted to an improper fraction.
- Multiply the whole number part (3) by the denominator of the fraction part ([tex]\(4\)[/tex]), and add the numerator of the fraction part ([tex]\(3\)[/tex]).
- This gives: [tex]\(3 \times 4 + 3 = 12 + 3 = 15\)[/tex].
- Therefore, [tex]\(3 \frac{3}{4}\)[/tex] becomes [tex]\(\frac{15}{4}\)[/tex].
2. Determine the Product:
- Multiply the improper fraction [tex]\(\frac{15}{4}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex].
- The product of two fractions is calculated by multiplying their numerators and their denominators:
[tex]\[
\text{Product} = \left(\frac{15}{4}\right) \times \left(-\frac{12}{25}\right) = \frac{15 \times (-12)}{4 \times 25}
\][/tex]
- This simplifies to:
[tex]\[
\frac{-180}{100}
\][/tex]
3. Simplify the Fraction:
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20:
[tex]\[
\frac{-180 \div 20}{100 \div 20} = \frac{-9}{5}
\][/tex]
Therefore, the product of [tex]\(3 \frac{3}{4} \times-\left(\frac{12}{25}\right)\)[/tex] is [tex]\(-\frac{9}{5}\)[/tex].
The correct answer is:
B. [tex]\(-\frac{9}{5}\)[/tex]
1. Convert the Mixed Number to an Improper Fraction:
- The mixed number [tex]\(3 \frac{3}{4}\)[/tex] can be converted to an improper fraction.
- Multiply the whole number part (3) by the denominator of the fraction part ([tex]\(4\)[/tex]), and add the numerator of the fraction part ([tex]\(3\)[/tex]).
- This gives: [tex]\(3 \times 4 + 3 = 12 + 3 = 15\)[/tex].
- Therefore, [tex]\(3 \frac{3}{4}\)[/tex] becomes [tex]\(\frac{15}{4}\)[/tex].
2. Determine the Product:
- Multiply the improper fraction [tex]\(\frac{15}{4}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex].
- The product of two fractions is calculated by multiplying their numerators and their denominators:
[tex]\[
\text{Product} = \left(\frac{15}{4}\right) \times \left(-\frac{12}{25}\right) = \frac{15 \times (-12)}{4 \times 25}
\][/tex]
- This simplifies to:
[tex]\[
\frac{-180}{100}
\][/tex]
3. Simplify the Fraction:
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20:
[tex]\[
\frac{-180 \div 20}{100 \div 20} = \frac{-9}{5}
\][/tex]
Therefore, the product of [tex]\(3 \frac{3}{4} \times-\left(\frac{12}{25}\right)\)[/tex] is [tex]\(-\frac{9}{5}\)[/tex].
The correct answer is:
B. [tex]\(-\frac{9}{5}\)[/tex]