College

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

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

Answer :

To solve for the product of [tex]\( \frac{3}{4} \times \frac{12}{25} \)[/tex], follow these steps:

1. Multiply the numerators: Start by multiplying the numerators of the two fractions:
[tex]\[
3 \times 12 = 36
\][/tex]

2. Multiply the denominators: Next, multiply the denominators of the two fractions:
[tex]\[
4 \times 25 = 100
\][/tex]

3. Form a new fraction: Combine these two results to form a new fraction:
[tex]\[
\frac{36}{100}
\][/tex]

4. Simplify the fraction: Simplify [tex]\(\frac{36}{100}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
[tex]\[
\frac{36 \div 4}{100 \div 4} = \frac{9}{25}
\][/tex]

Now, since we calculated [tex]\(\frac{9}{25} = 0.36\)[/tex] in decimal form, we compare this with the provided options:

- (a) [tex]\(\frac{-125}{16}\)[/tex] is incorrect.
- (b) [tex]\(-\frac{9}{5}\)[/tex] is incorrect.
- (c) [tex]\(\frac{9}{5}\)[/tex] is incorrect and not equal to 0.36.

It seems there might be confusion in the options as none represent the calculated result of 0.36. Therefore, [tex]\(\frac{9}{25}\)[/tex] is the correct simplified answer for the multiplication of the fractions given.