Write the expression. Then, check all that apply.

six times the sum of nine and a number

A 2-column table with 5 rows. Column 1 is labeled Key Words with entries six, times, the sum of, nine, a number. Column 2 is labeled Replace with entries 6, times, (+), 9, n.

Replace “a number” with the variable, n.
The two operations are multiplication and addition.
The two operations are multiplication and subtraction.
The constants are 6 and 9.
The expression is written as 6n + 9.
The expression is written as 6(9 + n).

Given the description "six times the sum of nine and a number," we need to write the corresponding expression using the information provided in the table and then check all the applicable statements.

### Step 1: Writing the Expression

Based on the keywords provided in the table:

- **six**: Replaced by `6`
- **times**: Implies multiplication
- **the sum of**: Implies addition, represented by `(+)`
- **nine**: Replaced by `9`
- **a number**: Replaced by `n`

Therefore, the expression for "six times the sum of nine and a number" is:

\[
6 \times (9 + n)
\]

Or simply:

\[
6(9 + n)
\]

### Step 2: Checking Each Statement

1. **Replace “a number” with the variable, n.**  
   - Correct, as the variable `n` is used for "a number."

2. **The two operations are multiplication and addition.**  
   - Correct, since the expression involves multiplication (`6 times`) and addition (`the sum of`).

3. **The two operations are multiplication and subtraction.**  
   - Incorrect, as there is no subtraction in the expression.

4. **The constants are 6 and 9.**  
   - Correct, as the constants in the expression are `6` and `9`.

5. **The expression is written as 6n + 9.**  
   - Incorrect, as this expression would not correctly represent "six times the sum of nine and a number."

6. **The expression is written as 6(9 + n).**  
   - Correct, as this matches the intended expression.

### Final Correct Statements

- Replace “a number” with the variable, n.
- The two operations are multiplication and addition.
- The constants are 6 and 9.
- The expression is written as 6(9 + n).

Would you like more details on any step, or do you have any questions?

### Related Questions

1. How do you simplify the expression \(6(9 + n)\)?
2. What happens if you replace addition with subtraction in the expression?
3. How would you write the expression for "six times the difference of nine and a number"?
4. How do you identify the constants and variables in an expression?
5. What are the steps to distribute multiplication over addition in an expression?

**Tip:** When translating word phrases to algebraic expressions, pay close attention to operation keywords like "sum," "difference," "product," and "quotient."

Learn how to translate the phrase 'six times the sum of nine and a number' into an algebraic expression. This lesson covers key algebraic concepts, focusing on writing and understanding expressions involving multiplication and addition. Suitable for students in Grades 6-8.

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