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The problem asks to define a variable and write an expression for the phrase: **"the quotient of 6 times a number and 16."**

- Let's define the variable **x** to represent "a number."
- The phrase "6 times a number" can be written as **6x**.
- The phrase "the quotient of 6 times a number and 16" refers to the division of **6x** by **16**.

Thus, the correct mathematical expression is:

\[
\frac{6x}{16}
\]

Now, let's compare this to the provided choices:

1. \(\frac{16x}{6}\)
2. \(\frac{x}{96}\)
3. \(96x\)
4. \(\frac{6x}{16}\)

The correct answer is the last option: \(\frac{6x}{16}\).

Would you like further details or have any questions about this?

### Related Questions:
1. How would you express "the quotient of 10 times a number and 5"?
2. What is the value of \(\frac{6x}{16}\) when \(x = 2\)?
3. How do you simplify \(\frac{6x}{16}\)?
4. What is the difference between a quotient and a product in math?
5. Can you write an equation where the quotient of a number and 12 equals 5?

**Tip:** Always simplify fractions when possible to make expressions clearer!

Define a variable and write an expression for the phrase: the quotient of 6 times a number and 16.

Learn how to define a variable and write an algebraic expression for the phrase 'the quotient of 6 times a number and 16.' This solution covers the basics of algebra, focusing on quotients and variable expressions for students in grades 6-8.

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