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Essential Question: How do you
evaluate and write variable
expressions?
Before we
start…
Look at the two items below. Tell your partner
the difference.
6 xy 6  y
What is a numerical expression?
Consists of numbers
and operations
4 10
What is a variable?
A letter used to
represent one or more
numbers.
The letter x is frequently
used.
– Often the variable used
has a connection to the
quantity it represents.
What is a variable expression?
Consists of numbers,
variables, and
operations.
The numbers are
always written in
front of the variable.
4d
5x  3 y
Variable
Expression
Meaning
Operation
5 times n
Multiplication
14 divided by y
Division
6+c
6 plus c
Addition
8–x
8 minus x
Subtraction
5(n)
14y
5·n
5n
14/y
What does evaluating an expression
mean?
To substitute a number
for each variable and
calculate the resulting
numerical expression.
The final answer is a
number!
How do you evaluate a variable
expression?
• Substitute the number for the variable.
• Perform the operation(s).
• Simplify the result, if necessary.
Evaluate the expression when x  4
a. 10  x
b. x  7
c. 2 x
32
d.
x
Evaluate the expression when n  3
a. 13n
9
b.
n
c. n  1
d. n  8
Evaluate the expression when y  2
a. 6 y
8
b.
y
c. y  4
d. 11  y
Evaluate the expression when 𝑥 = 6
𝑥+3
15 − 𝑥
2𝑥
𝑥
3
Evaluate the expression when x  10 and y  4.
a. x  y
b. xy
Evaluate the expression when x  6 and y  12.
a. xy
b. y  x
Evaluate the expression when
𝑎 = 4, 𝑏 = 2, and 𝑐 = 16.
𝑏𝑐
𝑐
𝑎
𝑎−𝑏
𝑐
𝑏
Evaluate the expression when
𝑝 = 24, 𝑠 = 5.5, and 𝑡 = 2.5.
𝑠+𝑡
𝑝
𝑡
𝑝𝑠
𝑠−𝑡
How can we use expressions?
• You can solve real world problems using a
verbal model to write a variable expression.
• A verbal model describes a problem using
words as labels and using math symbols to
relate the words.
How can we translate from words to
expressions?
• To translate from words to expressions we
want to look for words that indicate
mathematical operations.
Translating Verbal Phrases
Common Words and Phrases that Indicate Operations
Addition
Subtraction
Multiplication
Division
Plus
The sum of
Increased by
Total
More than
Added to
Minus
The difference of
Decreased by
Fewer than
Less than
Subtracted from
Times
The product of
Multiplied by
Of
Divided by
Divided into
The quotient of
Order is IMPORTANT when writing subtraction and
division expressions.
Write a variable expression to
represent the phrase.
The product of 72 and a number
The difference of a number and 1
Write a variable expression to
represent the phrase.
The quotient of a number and 3
13 more than a number
Write a variable expression to
represent the phrase.
6 fewer than a number
A number multiplied by 12
Baseball You plan to divide the 120 players in a
baseball league into teams with the same number of
players. Write a variable expression for the number of
teams if you know the number of players on each team.
Vegetables You plan to provide 8 carrot sticks for each
of the hikers to take as a snack. Write a variable
expression for the number of carrot sticks you will need
if you know the number of hikers.
Shirts You buy 5 shirts each having the same price.
Write a variable expression for the total amount you
spend on the shirts. How much money do you spend on
the shirts when each shirt costs $15?
Fundraiser Your school is organizing a fundraiser.
Each student is asked to sell gift baskets for $15
and candles for $1. The table shows the items sold
by 3 students.
a. Write a variable expression for the total amount
a student received by selling g gift baskets and c
candles.
b. Find the total amount received by each student.
Student Number of Gift Baskets Number of Candles
Sally
18
63
Steven
13
33
Rose
24
60
How do you evaluate and write variable
expressions?
Ticket Out the Door
Evaluate the expression on a piece of paper (put
your name on it) and place it in the box on your
way out…
4 x  5 when x  3