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Now, Let’s see if you learned anything!
Evaluate each expression for the given values of
the variables.
1. 6x + 9 for x = 3 27
2. x + 14 for x = 8 22
3. 4x + 3y for x = 2, y = 3 17
4. 1.6x – 2.9y for x = 19, y = 6 13
5. If n is the amount of money in a savings
account, then the expression n + 0.03n can be
used to find the amount in the account after it has
earned interest for one year. Find the total in the
account after one year if $500 is the initial amount.
$515
Question of the Day
Courtney, better knows as “Corky”, buys
buttons at a cost of 8 for $20. She in
turn resells them in her shop for $5
each. How many buttons does “Corky”
need to sell in order to make a profit of
$120?
Work with your team!
48 buttons
How do we check HW/Assignments?
Oh, Let me
5 count thy
ways!
Write down
A number
x
ALGEBRA
Has a
language of
its own!
We already know how to translate words from English
into other languages…
Puppy = Gong-A-Gee in Korean
Dog – Ge
Dog = Chien in French
Bulgarian = Koonche’
Dog = Kutha – Urdu (Pakistan)
Hebrew= Kelev
Dog = Sag in Persian
Texas = Pooch
Dog = Perro in Spanish/Italian
Viet Nam = Ja
Dog = Hunt (hoont) in German
Telugu = Kukka
Dog = Gou (go) in Chinese
Segerson = Buster
Dog = Canis in Latin
Dog = K-nine in Lattin
Dog = Inu in Japanese
Arizona = “Here boy!”
Dog = Co-baka in Russian
Turkey = köpek
Dog = Ex szorito pofa in Hungarian Romania = Cinne
Dog = Cao (cow) in Portuguese
Dog = Na-eee in India
Russian = собака
Learn to translate words into numbers,
variables, and operations.
We know, in part, the language of
mathematics!
+ = Add, plus, sum, increased by,
more than, gain of, etc.
= Subtract, minus, take-a-way,
difference, less than, decreased by, etc
X = Multiply, times, of, by, product,
= Goes into, divide by, quotient, half
of, separate into, per
Operation
Verbal Expressions
• add 3 to a number
• a number plus 3
• the sum of a number and 3
• 3 more than a number
• a number increased by 3
Algebraic
Expressions
n+3
• subtract 12 from a number
• a number minus 12
• the difference of a number
and 12
• 12 less than a number
• a number decreased by 12
• take away 12 from a number
• a number less than 12
x – 12
Operation
Verbal Expressions
Algebraic
Expressions
• 2 times a number
• 2 multiplied by a number
2m or 2 · m
• the product of 2 and a
number
• 6 divided into a number
÷
• a number divided by 6
• the quotient of a number
and 6
a ÷ 6 or
a
6
ALGEBRAIC EXPRESSION
An expression containing a
variable.
Write down
“A number”
x
Write down
“The product of a number
and 4”
4x
Write down
“The product of a number
and 4”
Not 4 x X,
4  x or 4(x)
NEVER x4
Write down
“The product of a number
and 7”
7x
Write down
“a number increased by 3”
3+X
X+3
How can we write
“seven less than a number”
C–7
If C= 10 then it would be
“seven less than 10”
write
“five less than a number”
like this:
C–5
If C= 10 then it would be
“five less than 10”
We can write
“A number increased by two
and decreased by four”
X+2-4
We can write
“The product 4 and a number
is increased by 2”
4x + 2
We can write
“half a number increased
by 2”
½x+2
x
+2
2
We can write
“The product of 4 and the
parenthetical sum of a
number and 3”
4 (x + 3)
We can write
“The product of a number
and 6 is increased by 4 and
all divided by three cubed”
6x + 4
3
3
Write
5x + 2 – 3
As a phrase!
The product of five
and number is
increased by two and
decreased by three
Write
X-3
As a phrase!
Three less than a
number
Write
3/4x(2 + 3)
As a phrase!
The product of ¾ of a
number and the sum
of two and three
Write
3a + 4b
As a phrase!
The sum of the
product of three and
number the product
of four and a different
number.
3v - 2
3
4
“The product of a number
and 3 is decreased by 2 and
all divided by four cubed”
Write
X – 3 = 34
As a phrase!
Three less than a
number results in
thirty-four
Write
5x – 2y
As a phrase!
The difference
between the product
of five and number
the product of two
and another number
Warm Up
Evaluate each expression for the given values of
the variables.
1. 9y  13 for y = 4 23
2. 6n + 2p for n = 2 and p = 3 18
3. 3x  y for x = 1 and y = 2 1
Which operation symbol goes with each word?
4. Sum +
5. Product 
6. Quotient
7. Difference


Try These……
1. The product of four and a number is decreased by ten
and increase by a different number.
2. The sum of two different numbers is decreased by two
3. The difference of two different numbers is increased
three.
Translate these expressions!
1. The product of 4 and a number
2. A number decreased by two
3. Six less than a number
4. Four more than a number
5. Three less than a number
6. A number is increased by two and decreased by three
7. The product of a number is increased by seven and
decreased by two
8. A number divided by three
9. A number divided by four is then increased by five and
decreased by 1
Problem of the Day
Find a pair of numbers that fits the description.
Their product is 221 and their sum is 30.
13, 17
Learn to write algebraic expressions.
Word Phrases
+
–
• a number plus 5
• add 5 to a number
• sum of a number and 5
• 5 more than a number
• a number increased by 5
•a number minus 11
• subtract 11 from a number
• difference of a number and 11
• 11 less than a number
• a number decreased by 11

• 3 times a number
• 3 multiplied by a number
• product of 3 and a number

• a number divided by 7
• 7 divided into a number
• quotient of a number and 7
Expression
n+5
x  11
3m
a or a  7
7
Additional Examples 1A and 1B: Translating Word
Phrases into Math Expressions
Write an algebraic expression for each word
phrase.
A. the product of 8 and a number n
the product of 8 and n
8
•
n
8n
B. a number w decreased by 9
w decreased by 9
w
–
9
w–9
Additional Examples 1C and 1D: Translating Word
Phrases into Math Expressions
Write an algebraic expression for each word
phrase.
C. 3 increased by the difference of p and 5
3 increased by the difference of p and 5
3
+
(p
–
5)
3 + (p – 5)
D. 24 decreased by the product of 6 and q
24 decreased by the product of 6 and q
24
–
(6
•
q)
24 – 6q
Try This: Examples 1A and 1B
Write an algebraic expression for each word
phrase.
A. the sum of a number h and 88
the sum of h and 88
h
+
88
h + 88
B. the quotient of a number f and 6
quotient of f and 6
f

6
f
6
Try This: Examples 1C and 1D
Write an algebraic expression for each word
phrase.
C. add 7 to 3 multiplied by m
add 7 to 3 multiplied by m
7
+
(3

m)
7 + 3m
D. the difference of 5 and the product of 2 and r
the difference of 5 and the product of 2 and r
5
–
5 – 2r
(2
•
r)
To solve a word problem, you must first interpret
the action you need to perform and then choose
the correct operation for that action.
Action
Operation
Possible Question Clues
Combine
Add
How many all together?
Combine equal groups
Multiply
How many all together?
Separate
Subtract
How many more? How many less?
Separate into equal groups Divide
How many equal groups?
Additional Example 2: Interpreting Which Operation
to Use in Word Problems
A. Jared worked for h hours at the pay rate of
$5 each hour. Write an expression to
determine how much money Jared earned.
5h
Multiply 5 by h hours.
B. How much money will he earn if he works a
total of 18 hours?
5 • 18 = 90
Evaluate the expression for
h = 18.
Jared earned $90.
Try This: Example 2
A. A taxi-cab driver charges a base fee of $2,
plus an additional $0.25 per mile. Write an
expression to determine the fare.
2 + .25m
$2 plus .25 per mile.
B. If a passenger needs to travel 12 miles,
how much money will they need to pay?
2 + .25(12) =$5 Evaluate the expression for
m = 12.
It will cost $5 to travel 12 miles.
Additional Example 3A: Writing and Evaluating
Expressions in Word Problems
Write an algebraic expression to evaluate each
word problem.
A. Ahmed bought a new sweater for $27 plus
sales tax t. If the tax was $1.76, what was the
total cost of the sweater?
$27.00 + t
Combine $27 with t.
$27.00 + $1.76 = $28.76
Evaluate for t = $1.76.
The total cost of the sweater was $28.76.
Additional Example 3B: Writing and Evaluating
Expressions in Word Problems
B. The cost to rent a banquet hall is $240. If
the cost will be shared equally among all of
the people who attend the event, how much
will it cost each person if 12, 15, 16 or 20
people attend?
$240  n
240  n
n
12
15
16
20
Separate the cost into n equal groups.
In dollars
240  n
240  12
240  15
240  16
240  40
Cost
$20
$16
$15
$12
Evaluate for n = 12,
15, 16, and 20.
Additional Example 3C: Writing and Evaluating
Expressions in Word Problems
C. An airplane was flying at an altitude of
20,000 feet when it began its descent at
9:00P.M. After ten minutes, it had descended a
feet. If the plane descended 8500 feet during
the ten minutes, what was its altitude at 9:10?
20,000 – f
Separate f feet from 20,000.
20,000 – 8500 = 11,500
Evaluate for f= 8500.
The plane’s altitude at 9:10 was 11,500 feet.
Try This: Example 3A
Write an algebraic expression and use it to
evaluate each word problem.
A. Taylor orders one pizza for dinner. The 16
pieces are to be divided equally among p
people. If she divides them equally among 4
people, how many pieces can each person get?
16  p
Separate the pieces into p equal groups.
16  4 = 4
Evaluate for p = 4.
Each person gets 4 pieces.
Try This: Example 3B
B. Gasoline costs $1.39 per n gallons. What
will the cost be for 10, 12, 14, and 15 gallons?
$1.39 • n
$1.39n
n
10
12
14
15
Combine n equal amounts of $1.39.
In dollars
$1.39 • n
$1.39 • 10
$1.39 • 12
$1.39 • 14
$1.39 • 15
Cost
$13.90
$16.68
$19.46
$20.85
Evaluate for n = 10,
12, 14, and 15.
Try This: Example 3C
C. After Kyle took his road trip, his car had
39,857 miles on the odometer. Before the trip,
his odometer read m miles less than 39,857. If
he traveled 739 miles on the trip, what was
the mileage on his car before he started the
trip?
39,857 – m
Subtract m miles from 39,857.
39,857 – 739 = 39,118 Evaluate for m = 739.
The mileage on his car before he started the trip was
39,118 miles.
What did you learn?
Write an algebraic expression for each word
phrase.
1. 5 less than a number k k – 5
x
2. a number x divided by 11
11
3. 4 times the sum of n and 5 4(n + 5)
Write an algebraic expression and used it to
solve the problem.
4. Karen buys n raffle tickets for $0.50 each. If she
buys 13 of them, how much will they cost? 0.50n; $6.50