Let's analyze the given phrase: "the quotient of 5 times a number and 2."
1. Identify the unknown variable:
Let's denote the unknown number by the variable [tex]\( n \)[/tex].
2. Express "5 times a number":
The phrase "5 times a number" translates to [tex]\( 5 \times n \)[/tex], which can be written as [tex]\( 5n \)[/tex].
3. Express "the quotient of 5 times a number and 2":
A quotient indicates a division operation. Therefore, "the quotient of 5 times a number and 2" translates to dividing [tex]\( 5n \)[/tex] by 2.
Thus, the expression can be written algebraically as:
[tex]\[
\frac{5n}{2}
\][/tex]
Given the multiple-choice options:
1. [tex]\(\frac{2n}{5} \)[/tex]
2. [tex]\(\frac{5}{2n} \)[/tex]
3. [tex]\(\frac{5n}{2} \)[/tex]
4. [tex]\(\frac{2}{5n} \)[/tex]
The correct variable expression that represents the phrase "the quotient of 5 times a number and 2" is:
[tex]\[
\boxed{\frac{5n}{2}}
\][/tex]
