nine more than the quotient of a number and 6

The expression "nine more than the quotient of a number and 6" can be represented mathematically as:

\[
\frac{x}{6} + 9
\]

Here:
- \( x \) represents the unknown number.
- \(\frac{x}{6}\) is the quotient of the number and 6.
- Adding 9 to this quotient gives the final expression.

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Here are five related questions:

1. How would you express "nine less than the quotient of a number and 6"?
2. What is the value of the expression if the number is 12?
3. How would you write an equation if this expression equals 15?
4. Can you solve for \( x \) if the expression equals 20?
5. How does the expression change if instead of 9 more, it's 5 more?

**Tip:** When translating word problems into algebraic expressions, identify keywords like "more than," "less than," and "quotient" to set up the correct mathematical operation.

Explore the mathematical expression "nine more than the quotient of a number and 6" with detailed explanations and examples. Learn how to translate word problems into algebraic expressions and solve related equations. Suitable for students in Grades 6-8.

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