Download Variables, Expressions & Properties

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Objective
Evaluate expressions and identify
properties
Vocabulary
Variable
A symbol, usually a letter, used to represent a
number
x
a
y
Vocabulary
Algebraic expression
An expression that contains a variable, a
number, and at least one operation symbol
4n
x-3
Vocabulary
Numerical expression
An expression that contains numbers and at
least one operation
3+4
7–6
6+4-3
Vocabulary
evaluate
To find the numerical value of the expression
Vocabulary
powers
Numbers written using exponents
43
82
Vocabulary
equation
A mathematical sentence that contains an equal
sign (=)
3+4=7
X-4=8
Vocabulary
Open sentence
An equation that contains a variable
2x - 4 = 12
Vocabulary
property
An open sentence that is true for any numbers
Vocabulary
counterexample
A statement or example that shows a conjecture
is false
Vocabulary
Order of operations
A set of rules to evaluate expressions
Order of Operations Rules
P 1. Do all operations within grouping symbols first.
( )
[ ]
{ }
E 2. Evaluate all powers before other operations.
exponents
32
square roots  16
MD3. Multiply and divide in order from left to right.


x
3(4)
AS 4. Add and subtract in order from left to right.
+
-
Please Excuse My Dear Aunt Sally
Example 1 Evaluate a Numerical Expression
Example 2 Evaluate Algebraic Expressions
Example 3 Evaluate Algebraic Expressions
Evaluate

3 + 9 - 2  (8  2)
3 + 9 - 2  4
Write problem
Follow the rules of Order of Operations
P
E
MD
AS
Work inside parenthesis first
Bring down 3 + 9 - 2 
Divide 8 by 2
1/4
Evaluate

3 + 9 - 2  4
Follow the rules of Order of Operations
P
E
MD
AS
3 + 9 - 8
Multiply before adding and subtracting
Bring down
3 + 9 -
Multiply 2  4
1/4
Evaluate
3 + 9 - 8
12 - 8
4

Follow the rules of Order of Operations
P
E
MD
AS
Add and subtract from left to right
Add 3 + 9
Bring down
- 8
Subtract 12 - 8
Answer: 4
1/4
Evaluate

Answer: 2
1/3
Evaluate the expression
3r + 2s - 4
Write problem
3(6) + 2(3) - 4
Replace r with 6
Replace s with 3
Bring down - 4
2/3
Evaluate the expression
3(6) + 2(3) - 4
Follow the rules of Order of Operations
P
E
MD
AS
Multiply before adding and subtracting
18 + 6 - 4
Multiply 3(6)
Bring down +
Multiply 2(3)
Bring down - 4
2/3
Evaluate the expression
18 + 6 - 4
24 - 4
20
Follow the rules of Order of Operations
P
E
MD
AS
Add and subtract from left to right
Add 18 + 6
Bring down - 4
Subtract 24 - 4
Answer: 20
2/3
Evaluate the expression
Answer: 24
2/3
Evaluate the expression
Write problem
Replace q with 5
Replace r with 6
Bring down - 3
3/3
Evaluate the expression
Follow the rules of Order of Operations
P
E
MD
AS
30 .
18 - 3
Remember: The fraction bar is a
grouping symbol
Work in the numerator first
Multiply 6(5)
Now work in the denominator
Multiply 3(6)
Bring down - 3
3/3
Evaluate the expression
30 .
18 - 3
30
15
.
2
Follow the rules of Order of Operations
P
E
MD
AS
Finish working in the denominator
Bring down
30 .
Subtract 18 - 3
Now use the fraction bar as division
Divide 30 by 15
Answer: 2
3/3
Evaluate the expression
Answer: 2
3/3
Assignment
Lesson 1:2
Variables, Expressions &
Properties
14 - 40 All
Name the property shown by
Multiplying by 1 does not change the number.
Answer: This is the Multiplicative Identity.
4/4
Name the property shown by the statement
Answer: Commutative Property of Multiplication
4/4