College

What is the product of [tex]$3 \frac{3}{4} \times -\left(\frac{12}{25}\right)$[/tex]?

A. [tex]-\frac{125}{16}[/tex]
B. [tex]-\frac{9}{5}[/tex]
C. [tex]\frac{9}{5}[/tex]
D. [tex]\frac{125}{16}[/tex]

Answer :

To find 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 3 by the denominator 4:
[tex]\[
3 \times 4 = 12
\][/tex]
- Add the numerator 3:
[tex]\[
12 + 3 = 15
\][/tex]
- The improper fraction is:
[tex]\[
\frac{15}{4}
\][/tex]

2. Multiply the Fractions:

Next, multiply [tex]\(\frac{15}{4}\)[/tex] by [tex]\(-\frac{12}{25}\)[/tex]:

[tex]\[
\frac{15}{4} \times -\frac{12}{25} = -\left(\frac{15 \times 12}{4 \times 25}\right)
\][/tex]

- Multiply the numerators:
[tex]\[
15 \times 12 = 180
\][/tex]
- Multiply the denominators:
[tex]\[
4 \times 25 = 100
\][/tex]
- The fraction becomes:
[tex]\[
-\frac{180}{100}
\][/tex]

3. Simplify the Fraction:

Simplify [tex]\(-\frac{180}{100}\)[/tex] by finding the greatest common divisor (GCD) of 180 and 100, which is 20:

[tex]\[
\frac{180 \div 20}{100 \div 20} = \frac{9}{5}
\][/tex]

Thus, the simplified product is:

[tex]\[
-\frac{9}{5}
\][/tex]

Therefore, the product of [tex]\(3 \frac{3}{4} \times -\left(\frac{12}{25}\right)\)[/tex] is [tex]\(-\frac{9}{5}\)[/tex], corresponding to option B.