1. Variables & Algebraic Expressions
A symbol, usually a letter, that represents one or more numbers.
Algebraic Expression
A mathematical phrase that includes one or more variables.
Numerical Expression
A mathematical phrase involving numbers and operation symbols, but no variables.
Equation
A mathematical sentence that has an equal sign.
If a plumber earns $60 per hour, in order to calculate how much money he made for a particular job, you would multiply the number of hours he worked by $60.
hours
worked
pay
(in dollars) 1 60 2
120 3
180 4
240 5
300 6
360
You could model this relationship with an algebraic expression using h as a variable to represent the number of hours worked.

2. Verbal Phrases Involving Addition
The algebraic expression a + b can be used to represent several different verbal phrases.
a plus b
a added to b
a is increased by b
the sum of a and b
b is added to a
b more than a
The word exceeds means “is more than”. So, the number that exceeds 5 by 2 can be written as “2 more than 5” or

3. Verbal Phrases Involving Subtraction
The algebraic expression a - b can be used to represent several different verbal phrases.
a minus b
a decreased by b
b less than a
b subtracted from a
a diminished by b
a reduced by b
the difference between a and b

4. Verbal Phrases Involving Multiplication
The algebraic expressions a X b, a . b, (a)(b), and ab can be used to represent several different verbal phrases.
a times b
the product of a and b
b multiplied by a
The preferred form to indicate multiplication in algebra is ab.
In algebraic expressions, parenthesis may be used but are not needed.
The multiplication symbol X is avoided in algebra because it can be confused with the variable x.

5. Verbal Phrases Involving Division
The algebraic expressions
and
can be used to represent several different verbal phrases.
a divided by b
the quotient of a and b
and
means one-forth of a as well as a divided by 4.
Commas are very important in some verbal phrases..
The product of x and y, decreased by 2.
The product of x and y decreased by 2.

6. Translating Words to Algebra
3 more than a number
5 less than a number
a number decreased by 7
the product of 6 and a number
These are examples of Algebraic Expressions.
twice a number decreased by 4
25, diminished by 4 times a number
the sum of a number and 2, divided by 9

7. Got It? 1)
What is an algebraic expression for 18 more than a number n? 2)
What is an algebraic expression for each word phrase? a)
6 times a number n b)
The quotient of 18 and a number n 3)
What is an algebraic expression for each word phrase? a)
8 less than the product of a number x and 4 b)
Twice the sum of a number x and 8 c)
The quotient of 5 and the sum of 12 and a number x 4)
What word phrase can you use to represent the algebraic expression? d) a) b) c)
The sum of a number x and 8.1
The sum of 10 times a number x and 9
The quotient of a number n and 3
Five times a number x less 1

8. Homework
Page 7: even #’s only

9. Modeling Relationships with Equations
A mathematical sentence that uses an equal sign.
Open Sentence
An equation that contains one or more variables.
Brianna paid 17 dollars for batteries and film for her camera. If the batteries cost x dollars, express the cost of the film in terms of x.
That was easy
Relate:
Film equals $17 minus the cost of the batteries.
Define:
x = cost of batteries
f = cost of film
Write:

10. More Modeling Relationships with Equations
CD’s
Cost
(in dollars) 1 15 2 30 3 45 4 60
Define the variable and write an equation to model the relationship in the table.
Number of Workers
Radios Built 1 11 2 22 3 33 4 44
Define:
Define:
n = number of CD’s
c = cost of CD’s
w = number of workers
r = number of radios
Asi de Facil
Write:
Write:

11. Even More Modeling Relationships with Equations
Define the variable and write an equation to model the relationship in the table.
Sales
Earnings
(in dollars) 3 21 6 42 9 63 12 84
Number of Hours
Total
Pay 5
$37.50 10
$75.00 15
$112.50 20
$150.00
First divide to determine the earnings for one sale.
First divide to determine the pay for one hour.
Define:
Define:
n = number of sales
e = earnings
Asi de Facil
n = number of hours
p = total pay
Write:
Write:

12. Writing a Rule to Describe a Pattern
A state park charges an entrance fee of $ 20, plus $18 for each night of camping. a)
If n is the number of nights that you spend camping, write an expression that gives the total cost, c, of camping for n nights. b)
What is the total cost of camping for 3 nights?
total cost of camping
price per night
# of nights
entrance fee
(constant)
That was easy

13. Homework
Page 8: 25, 26, 32, 33, 34

14. Now I’ll try doing 3 times 2 first.
Order of Operations
Let’s look at an example of a computation with more than one operation.
I’ll try doing 11 – 3 first.
Now I’ll try doing 3 times 2 first.
That was easy
Please Excuse My Dear Aunt Sally
Please Excuse My Dear Aunt Sally
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

15. Examples
Simplify the following. For all fractions, express the exact value and the rational approximation rounded to the nearest hundredth.

16. Examples
Simplify the following. For all fractions, express the exact value and the rational approximation rounded to the nearest hundredth.

17. Examples
Simplify the following. For all fractions, express the exact value and the rational approximation rounded to the nearest hundredth.

18. Evaluating Algebraic Expressions
To evaluate an algebraic expression, replace the variables with the given values, and then follow the proper order of operations.
Don’t forget about my dear Aunt Sally.
Evaluate
when
Rewrite the expression with empty parenthesis where the variables are
Replace the variables with the given values
Follow the proper order of operations

19. More Evaluating Algebraic Expressions
Evaluate
Evaluate
when
when
when

20. Using a Calculator to Evaluate Algebraic Expressions
The given values can be stored in the calculator.
when
Press
(-) 4
STO [
ALPHA A
ENTER
Evaluate 10
STO [
ALPHA N
ENTER
when 3
STO [
ALPHA D
ENTER
2A/5+(N-1)D
ENTER 10
STO [
ALPHA A
ENTER
2A/5+(N-1)D
(-) 6
STO [
ALPHA N
ENTER
ENTER
(-) 5
STO [
ALPHA D
ENTER

21. Homework
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