for problems 6–19, write an algebraic expression that represents the description. all variables are nonzero numbers.
6. triple the value of a number n
7. the quotient of t and 8.2
8. twice as much as n
9. a number x divided by 2\frac{1}{2}
10. a number p squared
11. \frac{1}{4} of f
12. a number m split evenly into 3 groups
13. one - half of the product of 2 and a number g

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Accepted Answer

Let's solve some of these algebraic expression problems. We'll take problem 6 first:

### Problem 6: Triple the value of a number $ n $
# Explanation:
## Step 1: Understand the operation
"Triple" means multiplying by 3. So we need to multiply the number $ n $ by 3.
## Step 2: Write the expression
The algebraic expression is $ 3 \times n $, which can be written as $ 3n $.
# Answer: $ 3n $

### Problem 8: Twice as much as $ n $
# Explanation:
## Step 1: Understand the operation
"Twice" means multiplying by 2. So we multiply the number $ n $ by 2.
## Step 2: Write the expression
The algebraic expression is $ 2 \times n $, or $ 2n $.
# Answer: $ 2n $

### Problem 10: A number $ p $ squared
# Explanation:
## Step 1: Understand the operation
"Squared" means raising the number to the power of 2. So we take $ p $ and raise it to the 2nd power.
## Step 2: Write the expression
The algebraic expression is $ p^2 $.
# Answer: $ p^2 $

### Problem 12: A number $ m $ split evenly into 3 groups
# Explanation:
## Step 1: Understand the operation
"Split evenly into 3 groups" means dividing the number $ m $ by 3.
## Step 2: Write the expression
The algebraic expression is $ \frac{m}{3} $.
# Answer: $ \frac{m}{3} $

### Problem 7: The quotient of $ t $ and 8.2
# Explanation:
## Step 1: Understand the operation
"Quotient" means division. So we divide $ t $ by 8.2.
## Step 2: Write the expression
The algebraic expression is $ \frac{t}{8.2} $.
# Answer: $ \frac{t}{8.2} $

### Problem 9: A number $ x $ divided by $ 2\frac{1}{2} $
# Explanation:
## Step 1: Convert the mixed number
First, convert $ 2\frac{1}{2} $ to an improper fraction. $ 2\frac{1}{2} = \frac{5}{2} $.
## Step 2: Write the division expression
Dividing $ x $ by $ \frac{5}{2} $ is the same as multiplying $ x $ by the reciprocal of $ \frac{5}{2} $, which is $ \frac{2}{5} $. So the expression is $ x \div \frac{5}{2} = x \times \frac{2}{5} = \frac{2x}{5} $, or we can also write it as $ \frac{x}{2\frac{1}{2}} $.
# Answer: $ \frac{x}{2\frac{1}{2}} $ (or $ \frac{2x}{5} $)

### Problem 11: $ \frac{1}{4} $ of $ f $
# Explanation:
## Step 1: Understand the operation
"Of" in mathematics (when dealing with fractions) means multiplication. So we multiply $ \frac{1}{4} $ by $ f $.
## Step 2: Write the expression
The algebraic expression is $ \frac{1}{4} \times f $, which can be written as $ \frac{1}{4}f $ or $ \frac{f}{4} $.
# Answer: $ \frac{1}{4}f $ (or $ \frac{f}{4} $)

### Problem 13: One - half of the product of 2 and a number $ g $
# Explanation:
## Step 1: Find the product of 2 and $ g $
The product of 2 and $ g $ is $ 2\times g=2g $.
## Step 2: Find one - half of that product
One - half of $ 2g $ is $ \frac{1}{2}\times2g $. Since $ \frac{1}{2}\times2 = 1 $, the expression simplifies to $ g $. We can also write the expression without simplifying first as $ \frac{1}{2}(2g) $.
# Answer: $ \frac{1}{2}(2g) $ (or $ g $)

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Question

Explanation:

Problem 6: Triple the value of a number \( n \)

Step 1: Understand the operation

Step 2: Write the expression

Step 1: Understand the operation

Step 2: Write the expression

Step 1: Understand the operation

Step 2: Write the expression

Answer:

Problem 8: Twice as much as \( n \)