Let's break down the phrase "the quotient of 5 times a number and 2" step by step to determine which variable expression correctly represents it.
1. Identify the parts of the phrase:
- "5 times a number": This suggests that we need to multiply 5 by some variable. Let's use [tex]\( n \)[/tex] to represent this unknown number. Therefore, [tex]\( 5 \cdot n \)[/tex] (or simply [tex]\( 5n \)[/tex]) represents "5 times a number".
- "the quotient of ... and 2": A quotient indicates division. So, we need to place the expression [tex]\( 5n \)[/tex] into the numerator of a fraction and 2 in the denominator.
2. Form the fraction:
- The phrase "the quotient of 5 times a number and 2" means we need to divide [tex]\( 5n \)[/tex] by 2.
Putting this together, the expression that represents "the quotient of 5 times a number and 2" is:
[tex]\[ \frac{5n}{2} \][/tex]
Thus, the correct choice among the options provided is:
[tex]\[ \frac{5n}{2} \][/tex]
