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Lesson 1-3
KEY TERMS___________________________________________________________
Evaluate
Term
Coefficient
Constant Term
Like Terms
How much do you earn each week by walking the dogs?
How much do you earn each week working in the studio?
How much will you earn in 10 weeks?
Today we are going to evaluate and simplify algebraic expressions.
ESSENTIAL UNDERSTANDING – We can represent some mathematical phrases and
real world quantities using algebraic expressions.
EXAMPLE 1 – Modeling Words With an Algebraic Expressions
Which algebraic expression models the word phrase one less than the product of six
and w?
A.
1 6  w
B.
w1  6
C.
6  w 1
D.
1 6  w
Got It?
Which algebraic expression models the word phrase two times the sum of a and b?
F.
a b
H. 2( a  b)
C.
2a  b
D.
a  2b
Lesson 1-3
To model a situation with an algebraic expression, do the following:
- Identify the actions that suggest operations
- Define one or more variables to represent the unknown(s)
- Represent the actions using the variables and the operations.
EXAMPLE 2 – Modeling a Situation
You are on a bicycling trip. You travel 52 miles the first day. Since then, your average
rate has been 12 miles per hour. What algebraic expression models the distance you
traveled so far?
Got It? You had $150, but you are spending $2 each day. What algebraic expression
models this situation?
To evaluate an algebraic expression, substitute a number for each variable in the
expression. Then simplify using the order of operations.
EXAMPLE 3 – Evaluating Algebraic Expressions
What is the value of the expression for the given values of the variables?
A. 2r  5( s  6)  1 for r = 3 and s = –9
B. c 
3
d
1
for c  and d = 1
8
4
EXAMPLE 4 – Writing and Evaluating an Expression
Ticket prices for admission to a museum are $8 for adults, $5 for children, and $6 for
seniors.
A. What algebraic expression models the total number of dollars collected in ticket
sales?
B. If 20 adult tickets, 16 children’s tickets, and 10 senior tickets are sold one morning,
how much money is collected in all?
Lesson 1-3
An expression that is a number, a variable, or the product of a number and one or more
variables is a term. A coefficient is the numerical factor of a term. A constant term is
a term with no variables. You can add terms to form longer expressions. The
expression below has three terms.
-4ax + 7w – 6
Like terms have the same variables raised to the same power.
3x 2  5 x 2  9 y 3 z  2 yz  4 y 3 z
You can simplify an algebraic expression that has like terms. You combine like terms
using the properties of real numbers. An expression and its simplified form are
equivalent. Their values are equal for all values of their variables.
Definition of Subtraction
Definition of Division
Distributive Property for Subtraction
Multiplication by 0
Multiplication by – 1
Opposite of a Sum
Opposite of a Difference
Opposite of a Product
Opposite of an Opposite
Lesson 1-3
EXAMPLE 5 – Simplifying Algebraic Expressions
What is the simplified form of each expression?