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]



Answer :

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]:

1. [tex]\(\frac{x}{4} = \frac{5}{72}\)[/tex]
2. [tex]\(\frac{5}{x} = \frac{4}{72}\)[/tex]
3. [tex]\(\frac{x}{72} = \frac{4}{5}\)[/tex]
4. [tex]\(\frac{x}{5} = \frac{72}{4}\)[/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]