reteach
algebraic expressions can be written from verbal descriptions. likewise,
verbal descriptions can be written from algebraic expressions. in both
cases, it is important to look for word and number clues.
algebra from words
\one third of the participants increased by 25.\
clues
look for
umber words,\ like
- \one third.\
- \of\ means multiplied by.
- \increased by\ means add to.
combine the clues to produce the expression.
- \one third of the participants.\ $\frac{1}{3}p$ or $\frac{p}{3}$.
- \increased by 25.\ +25
\one third of the participants increased by 25.\
$\frac{1}{3}p + 25$ or $\frac{p}{3} + 25$
words from algebra
\write $0.75n - \frac{1}{2}m$ with words.\
clues
identify the number of parts of the problem.
- \0.75n\ means \three fourths of n\ or 75
hundredths of n. the exact meaning will
depend on the problem.
- \-\ means \minus,\ \decreased by,\ \less
than,\ etc., depending on the context.
- \$\frac{1}{2}m$\ is \one half of m\ or \m over 2.\
combine the clues to produce a description.
\75 hundredths of the population minus half
the men.\
write a verbal description for each algebraic expression.
1. $100 - 5n$
2. $0.25r + 0.6s$
3. $\frac{3m - 8n}{13}$

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.

original content copyright © by houghton mifflin harcourt. additions and changes to the original content are the responsibility of the instructor.
40

Question

reteach
algebraic expressions can be written from verbal descriptions. likewise,
verbal descriptions can be written from algebraic expressions. in both
cases, it is important to look for word and number clues.
algebra from words
\one third of the participants increased by 25.\
clues
look for
umber words,\ like
- \one third.\
- \of\ means multiplied by.
- \increased by\ means add to.
combine the clues to produce the expression.
- \one third of the participants.\ $\frac{1}{3}p$ or $\frac{p}{3}$.
- \increased by 25.\ +25
\one third of the participants increased by 25.\
$\frac{1}{3}p + 25$ or $\frac{p}{3} + 25$
words from algebra
\write $0.75n - \frac{1}{2}m$ with words.\
clues
identify the number of parts of the problem.
- \0.75n\ means \three fourths of n\ or 75
hundredths of n. the exact meaning will
depend on the problem.
- \-\ means \minus,\ \decreased by,\ \less
than,\ etc., depending on the context.
- \$\frac{1}{2}m$\ is \one half of m\ or \m over 2.\
combine the clues to produce a description.
\75 hundredths of the population minus half
the men.\
write a verbal description for each algebraic expression.
1. $100 - 5n$
2. $0.25r + 0.6s$
3. $\frac{3m - 8n}{13}$

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.

original content copyright © by houghton mifflin harcourt. additions and changes to the original content are the responsibility of the instructor.
40

Accepted Answer

### Problem 1: $100 - 5n$
# Explanation:
## Step1: Analyze each term
- $100$ is a constant.
- $5n$ means "5 times $n$" (since "of" or multiplication clue, here coefficient 5 with variable $n$ implies 5 multiplied by $n$).
- The subtraction sign "$-$" means "minus" or "decreased by" or "less than" (in context, we can say "100 minus 5 times $n$" or "5 times $n$ less than 100").

## Step2: Combine the clues
Combine the descriptions of each part. So, "One hundred minus five times $n$" (or "Five times $n$ less than one hundred").

# Answer: One hundred minus five times $n$ (or equivalent verbal description like "Five times $n$ less than one hundred")

### Problem 2: $0.25r + 0.6s$
# Explanation:
## Step1: Analyze each term
- $0.25r$: $0.25$ is "twenty - five hundredths" or "one fourth", and with $r$ it means "0.25 times $r$" or "one fourth of $r$" or "twenty - five hundredths of $r$".
- $0.6s$: $0.6$ is "six tenths" or "sixty hundredths", and with $s$ it means "0.6 times $s$" or "six tenths of $s$" or "sixty hundredths of $s$".
- The addition sign "$+$" means "plus" or "added to" or "and".

## Step2: Combine the clues
Combine the descriptions of each part. So, "Twenty - five hundredths of $r$ plus six tenths of $s$" (or "One fourth of $r$ plus six tenths of $s$" or other equivalent descriptions).

# Answer: Twenty - five hundredths of $r$ plus six tenths of $s$ (or equivalent like "One fourth of $r$ plus six tenths of $s$")

### Problem 3: $\frac{3m - 8n}{13}$
# Explanation:
## Step1: Analyze the numerator and denominator
- Numerator: $3m-8n$
    - $3m$ means "3 times $m$" or "three times $m$".
    - $8n$ means "8 times $n$" or "eight times $n$".
    - The subtraction sign "$-$" means "minus", so $3m - 8n$ is "three times $m$ minus eight times $n$".
- Denominator: $13$ means "thirteen", and the fraction bar means "divided by" or "the quotient of... and...".

## Step2: Combine the clues
The entire expression is "The quotient of (three times $m$ minus eight times $n$) and thirteen" (or "Thirteen divided into (three times $m$ minus eight times $n$)" or "Three times $m$ minus eight times $n$ divided by thirteen").

# Answer: The quotient of (three times $m$ minus eight times $n$) and thirteen (or equivalent verbal description)

### Problem 4: Half of the seventh graders and one third of the eighth graders were divided into ten teams.
# Explanation:
## Step1: Define variables
Let $s$ be the number of seventh graders and $e$ be the number of eighth graders.
## Step2: Translate each part
- "Half of the seventh graders": $\frac{1}{2}s$ (since "half" means $\frac{1}{2}$ and "of" means multiply).
- "One third of the eighth graders": $\frac{1}{3}e$ (since "one third" means $\frac{1}{3}$ and "of" means multiply).
- "and" means addition, so we have $\frac{1}{2}s+\frac{1}{3}e$.
- "divided into ten teams" means we divide the sum by 10, so the expression is $\frac{\frac{1}{2}s+\frac{1}{3}e}{10}$ (or we can also write it as $\frac{1}{10}(\frac{1}{2}s + \frac{1}{3}e)$ or after getting a common denominator for the numerator: $\frac{3s + 2e}{60}$ but the most direct translation from the verbal description is $\frac{\frac{1}{2}s+\frac{1}{3}e}{10}$).

# Answer: $\frac{\frac{1}{2}s+\frac{1}{3}e}{10}$ (where $s$ is the number of seventh graders and $e$ is the number of eighth graders, or equivalent algebraic expression)

### Problem 5: Thirty percent of the green house flowers are added to 25 ferns for the school garden.
# Explanation:
## Step1: Define variable
Let $f$ be the number of green - house flowers.
## Step2: Translate each part
- "Thirty percent of the green house flowers": $0.3f$ (since 30% is 0.3 and "of" means multiply).
- "are added to 25 ferns": the addition sign " + " is used, so we add 25 to $0.3f$.

## Step3: Form the expression
The algebraic expression is $0.3f + 25$ (where $f$ is the number of green - house flowers).

# Answer: $0.3f+25$ (where $f$ represents the number of green - house flowers)

### Problem 6: 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 $x$ be the number of egg orders and $y$ be the number of waffle orders.
## Step2: Translate each part
- "Three times the number of egg orders": $3x$ (since "three times" means multiply by 3).
- "Four less than three times the number of egg orders": $3x-4$ (since "less than" means subtract, so we subtract 4 from $3x$).
- "Two times the number of waffle orders": $2y$ (since "two times" means multiply by 2).
- "Six more than two times the number of waffle orders": $2y + 6$ (since "more than" means add, so we add 6 to $2y$).
- "and" means we combine these two expressions with addition (since we are talking about the combination of these two quantities). So the expression is $(3x - 4)+(2y+6)$ which simplifies to $3x+2y + 2$ (but the non - simplified form $(3x - 4)+(2y + 6)$ is also a correct translation from the verbal description).

# Answer: $(3x - 4)+(2y + 6)$ (or simplified $3x+2y + 2$, where $x$ is the number of egg orders and $y$ is the number of waffle orders)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \(100 - 5n\)

Step1: Analyze each term

Step2: Combine the clues

Step1: Analyze each term

Step2: Combine the clues

Step1: Analyze the numerator and denominator

Step2: Combine the clues

Answer:

Problem 2: \(0.25r + 0.6s\)