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We are tasked with finding the variable expression that represents the phrase: **"the quotient of 5 times a number and 2"**.

### Step 1: Break down the phrase.

- **"5 times a number"**: This can be written as \( 5n \), where \( n \) represents the number.
- **"Quotient"**: This indicates division.
- **"And 2"**: This tells us that the number \( 5n \) is divided by 2.

Thus, the expression for **"the quotient of 5 times a number and 2"** is:

\[
\frac{5n}{2}
\]

### Step 2: Analyze the options.

- **A. \( \frac{5n}{2} \)**: This matches the expression we just derived.
- **B. \( \frac{2}{5n} \)**: This is incorrect because it reverses the terms.
- **C. \( \frac{2n}{5} \)**: This is also incorrect because it changes the order of multiplication and division.
- **D. \( \frac{5}{2n} \)**: This is incorrect as the number being divided by 2 should be \( 5n \), not just 5.

### Final Answer:

The correct expression is:

\[
\boxed{\frac{5n}{2}}
\]

Would you like any more explanation on this? Here are some related questions:

1. How would you express "the quotient of a number and 3" in variable form?
2. What is the difference between "quotient" and "product" in algebraic expressions?
3. How can we represent "the quotient of 10 and the sum of a number and 5"?
4. What does "5 times the quotient of a number and 2" look like?
5. How do we translate complex word phrases into algebraic expressions?

**Tip:** Always remember that "quotient" refers to division!

Which variable expression represents the phrase 'the quotient of 5 times a number and 2'?

Learn how to express the phrase 'the quotient of 5 times a number and 2' using algebraic notation. Understand key concepts like quotients and variables, and solve with step-by-step guidance for students in Grades 6-8.

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