Which of the following uses the reciprocal property to rewrite [tex]\frac{x}{5}=\frac{72}{4}[/tex]?
A. [tex]\frac{x}{4}=\frac{5}{72}[/tex] B. [tex]\frac{5}{x}=\frac{4}{72}[/tex] C. [tex]\frac{x}{72}=\frac{4}{5}[/tex] D. [tex]\frac{x}{5}=\frac{72}{4}[/tex]
To find which option correctly uses the reciprocal property to rewrite [tex]\(\frac{x}{5} = \frac{72}{4}\)[/tex], we should understand what the reciprocal property entails.
The reciprocal property states that if [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], then [tex]\(\frac{b}{a} = \frac{d}{c}\)[/tex].
Given the equation [tex]\(\frac{x}{5} = \frac{72}{4}\)[/tex], we can apply the reciprocal property to this equation.
By taking the reciprocal of both sides of the equation [tex]\(\frac{x}{5} = \frac{72}{4}\)[/tex], we get: [tex]\[
\frac{5}{x} = \frac{4}{72}
\][/tex]
Now, let's check the given options to see which one matches [tex]\(\frac{5}{x} = \frac{4}{72}\)[/tex]:
From these options, the second one, [tex]\(\frac{5}{x} = \frac{4}{72}\)[/tex], correctly uses the reciprocal property to rewrite the original equation.
So, the correct answer is: [tex]\[
\boxed{\frac{5}{x} = \frac{4}{72}}
\][/tex]
