Given the proportion:
[tex]\[
\frac{a}{b} = \frac{c}{d}
\][/tex]
We need to determine which of the provided options is equal to [tex]\( b \)[/tex].
First, cross-multiply to eliminate the fractions:
[tex]\[
a \cdot d = b \cdot c
\][/tex]
Our goal is to solve for [tex]\( b \)[/tex]. Isolate [tex]\( b \)[/tex] on one side of the equation:
[tex]\[
b \cdot c = a \cdot d
\][/tex]
Next, divide both sides of the equation by [tex]\( c \)[/tex]:
[tex]\[
b = \frac{a \cdot d}{c}
\][/tex]
Thus, after isolating [tex]\( b \)[/tex], we find that:
[tex]\[
b = \frac{a \cdot d}{c}
\][/tex]
Given the options, the correct one that matches our derived expression is:
H. [tex]\(\frac{a d}{c}\)[/tex]
