write a verbal description for each algebraic expression.
1. $100 - 5n$
2. $0.25r + 0.6s$
3. $\dfrac{3m - 8n}{13}$

write an algebraic expression for each verbal description.
4. half of the seventh graders and one third of the eighth graders were divided into ten teams.
5. thirty percent of the green house flowers are added to 25 ferns for the school garden.
6. four less than three times the number of egg orders and six more than two times the number of waffle orders.

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Question

write a verbal description for each algebraic expression.
1. $100 - 5n$
2. $0.25r + 0.6s$
3. $\dfrac{3m - 8n}{13}$

write an algebraic expression for each verbal description.
4. half of the seventh graders and one third of the eighth graders were divided into ten teams.
5. thirty percent of the green house flowers are added to 25 ferns for the school garden.
6. four less than three times the number of egg orders and six more than two times the number of waffle orders.

Accepted Answer

### 1. Verbal description of $100 - 5n$
# Explanation:
## Step1: Analyze the terms
The term $5n$ means 5 times a number $n$, and the expression is 100 minus that product.
## Step2: Formulate the description
So, a verbal description is "One hundred minus five times a number $n$".

### 2. Verbal description of $0.25r + 0.6s$
# Explanation:
## Step1: Analyze each term
$0.25r$ is 0.25 times a number $r$ (or a quarter of $r$), and $0.6s$ is 0.6 times a number $s$ (or three - fifths of $s$). The '+' sign means addition.
## Step2: Formulate the description
A verbal description is "Zero point two five times a number $r$ plus zero point six times a number $s$" (or "A quarter of $r$ plus three - fifths of $s$").

### 3. Verbal description of $\frac{3m - 8n}{13}$
# Explanation:
## Step1: Analyze the numerator
The numerator $3m-8n$ is three times a number $m$ minus eight times a number $n$. The entire expression is this difference divided by 13.
## Step2: Formulate the description
A verbal description is "The difference between three times a number $m$ and eight times a number $n$ divided by thirteen".

### 4. Algebraic expression for "Half of the seventh graders and one third of the eighth graders were divided into ten teams"
# Explanation:
## Step1: Define variables
Let the number of seventh graders be $s$ and the number of eighth graders be $e$.
## Step2: Translate the verbal description
Half of the seventh graders is $\frac{1}{2}s$, one third of the eighth graders is $\frac{1}{3}e$. The sum of these two quantities is $\frac{1}{2}s+\frac{1}{3}e$, and then we divide this sum by 10 (since they are divided into 10 teams).
## Step3: Write the algebraic expression
The algebraic expression is $\frac{\frac{1}{2}s+\frac{1}{3}e}{10}$ (or we can also write it as $\frac{s}{2}+\frac{e}{3}$ all over 10, and if we simplify the complex fraction, it can be $\frac{3s + 2e}{6\times10}=\frac{3s + 2e}{60}$, but the first form $\frac{\frac{1}{2}s+\frac{1}{3}e}{10}$ is also correct).

### 5. Algebraic expression for "Thirty percent of the green house flowers are added to 25 ferns for the school garden"
# Explanation:
## Step1: Define variable
Let the number of greenhouse flowers be $f$.
## Step2: Translate the verbal description
Thirty percent of the greenhouse flowers is $0.3f$ (or $\frac{30}{100}f=\frac{3}{10}f$). We add this to 25 ferns.
## Step3: Write the algebraic expression
The algebraic expression is $0.3f + 25$ (or $\frac{3}{10}f+25$).

### 6. Algebraic expression for "Four less than three times the number of egg orders and six more than two times the number of waffle orders"
# Explanation:
## Step1: Define variables
Let the number of egg orders be $e$ and the number of waffle orders be $w$.
## Step2: Translate each part
"Four less than three times the number of egg orders" is $3e - 4$, "six more than two times the number of waffle orders" is $2w+6$. The 'and' here means we are just stating both expressions, but if we assume it means the sum of these two expressions (since it's a bit ambiguous, but a common interpretation is to represent both parts together), the algebraic expression is $(3e - 4)+(2w + 6)$ which simplifies to $3e+2w + 2$. If we just need to represent the two phrases as separate expressions joined by 'and', we can write $3e - 4$ and $2w+6$, but a more likely interpretation (if we are to write a single algebraic expression for the combined idea) is $3e - 4+2w + 6=3e + 2w+2$.

# Answers:
1. One hundred minus five times a number $n$
2. Zero point two five times a number $r$ plus zero point six times a number $s$ (or "A quarter of $r$ plus three - fifths of $s$")
3. The difference between three times a number $m$ and eight times a number $n$ divided by thirteen
4. $\frac{\frac{1}{2}s+\frac{1}{3}e}{10}$ (where $s$ is the number of seventh graders and $e$ is the number of eighth graders)
5. $0.3f + 25$ (where $f$ is the number of greenhouse flowers)
6. $3e+2w + 2$ (where $e$ is the number of egg orders and $w$ is the number of waffle orders)

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QUESTION IMAGE

Question

Explanation:

1. Verbal description of \(100 - 5n\)

Step1: Analyze the terms

Step2: Formulate the description

2. Verbal description of \(0.25r + 0.6s\)

Step1: Analyze each term

Step2: Formulate the description

3. Verbal description of \(\frac{3m - 8n}{13}\)

Step1: Analyze the numerator

Step2: Formulate the description

4. Algebraic expression for "Half of the seventh graders and one third of the eighth graders were divided into ten teams"

Answer: