Answer :
To solve the problem of finding the product of [tex]\(3 \frac{3}{4} \times -\left(\frac{12}{25}\right)\)[/tex], we start by converting the mixed number into an improper fraction:
1. Convert the Mixed Number:
[tex]\(3 \frac{3}{4}\)[/tex] can be converted to an improper fraction.
- Multiply the whole number 3 by the denominator 4: [tex]\(3 \times 4 = 12\)[/tex].
- Add the numerator 3 to this result: [tex]\(12 + 3 = 15\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{15}{4}\)[/tex].
Thus, [tex]\(3 \frac{3}{4} = \frac{15}{4}\)[/tex].
2. Multiply the Fractions:
- We need to multiply [tex]\(\frac{15}{4}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex].
- The multiplication of two fractions involves multiplying the numerators and the denominators:
[tex]\[
\frac{15}{4} \times -\frac{12}{25} = \frac{15 \times -12}{4 \times 25}
\][/tex]
3. Calculate the Numerator and Denominator:
- Multiply the numerators: [tex]\(15 \times -12 = -180\)[/tex].
- Multiply the denominators: [tex]\(4 \times 25 = 100\)[/tex].
4. Write the Result as a Fraction:
- So, the product is [tex]\(\frac{-180}{100}\)[/tex].
5. Simplify the Fraction:
- Divide both the numerator and the denominator by their greatest common divisor, which is 20 in this case:
[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].
None of the provided options exactly match the simplified form directly. However, if there is a possibility of considering any other factor or typographical issue in options, [tex]\(-\frac{9}{5}\)[/tex] should indeed be an aim for correctness in simplification at this point, derived sending a review toward option formatting.
1. Convert the Mixed Number:
[tex]\(3 \frac{3}{4}\)[/tex] can be converted to an improper fraction.
- Multiply the whole number 3 by the denominator 4: [tex]\(3 \times 4 = 12\)[/tex].
- Add the numerator 3 to this result: [tex]\(12 + 3 = 15\)[/tex].
- Place this result over the original denominator: [tex]\(\frac{15}{4}\)[/tex].
Thus, [tex]\(3 \frac{3}{4} = \frac{15}{4}\)[/tex].
2. Multiply the Fractions:
- We need to multiply [tex]\(\frac{15}{4}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex].
- The multiplication of two fractions involves multiplying the numerators and the denominators:
[tex]\[
\frac{15}{4} \times -\frac{12}{25} = \frac{15 \times -12}{4 \times 25}
\][/tex]
3. Calculate the Numerator and Denominator:
- Multiply the numerators: [tex]\(15 \times -12 = -180\)[/tex].
- Multiply the denominators: [tex]\(4 \times 25 = 100\)[/tex].
4. Write the Result as a Fraction:
- So, the product is [tex]\(\frac{-180}{100}\)[/tex].
5. Simplify the Fraction:
- Divide both the numerator and the denominator by their greatest common divisor, which is 20 in this case:
[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].
None of the provided options exactly match the simplified form directly. However, if there is a possibility of considering any other factor or typographical issue in options, [tex]\(-\frac{9}{5}\)[/tex] should indeed be an aim for correctness in simplification at this point, derived sending a review toward option formatting.