If [tex][tex]$\frac{A}{B}$[/tex][/tex] and [tex][tex]$\frac{C}{D}$[/tex][/tex] are rational expressions, then [tex][tex]$\frac{A}{B} \bullet \frac{C}{D}=\frac{A \bullet D}{B \bullet C}$[/tex][/tex].

A. True
B. False



Answer :

To determine whether the statement "If [tex]\(\frac{A}{B}\)[/tex] and [tex]\(\frac{C}{D}\)[/tex] are rational expressions, then [tex]\(\frac{A}{B} \cdot \frac{C}{D} = \frac{A \cdot D}{B \cdot C}\)[/tex]" is true or false, we need to analyze how rational expressions are multiplied.

When multiplying two rational expressions, the rule is:
[tex]\[ \frac{A}{B} \cdot \frac{C}{D} = \frac{A \cdot C}{B \cdot D} \][/tex]

Let’s demonstrate this rule with a general multiplication of rational expressions. Here’s a step-by-step breakdown:

1. Multiply the numerators: Take the numerator of the first fraction ([tex]\(A\)[/tex]) and multiply it by the numerator of the second fraction ([tex]\(C\)[/tex]).
[tex]\[ A \cdot C \][/tex]

2. Multiply the denominators: Take the denominator of the first fraction ([tex]\(B\)[/tex]) and multiply it by the denominator of the second fraction ([tex]\(D\)[/tex]).
[tex]\[ B \cdot D \][/tex]

3. Combine the fractions: Place the product of the numerators over the product of the denominators.
[tex]\[ \frac{A \cdot C}{B \cdot D} \][/tex]

Thus, the correct multiplication of [tex]\(\frac{A}{B}\)[/tex] and [tex]\(\frac{C}{D}\)[/tex] results in [tex]\(\frac{A \cdot C}{B \cdot D}\)[/tex].

However, the given statement is:
[tex]\[ \frac{A}{B} \cdot \frac{C}{D} = \frac{A \cdot D}{B \cdot C} \][/tex]

This statement claims that the product of the fractions results in [tex]\(\frac{A \cdot D}{B \cdot C}\)[/tex], which is incorrect based on the rules for multiplying rational expressions.

Therefore, the correct answer to the question is:

B. False