Name:________________
Unit 9 Study Guide
Parent Signature:
Order of Operations, Algebraic Expressions and Number Properties
_____________________
I can evaluate exponents.
(Base)34 (exponent) Say: “Three to the 4th power.”
The Base is the Big number.
An exponent is a little number high and to the right of a
regular or base number.
34 = 3x3x3x3 (This is expanded form.)
34= 81 (This is the value.)
You Try It!
Evaluate 36 = ___________________
Write 78 in expanded form. _________________________
In ( )9, what is the Base?___________Exponent?________
Evaluate 24=____________
Evaluate ( )3=___________
I can evaluate numerical expressions using the order of operations.
The order of operations:
PEMDAS: Please Excuse My Dear Aunt Sally
23 + 7(9 ÷ 3 – 1)
23 + 7(3 – 1)
23 + 7(2)
8 + 7(2)
Side by side multiply
8 + 14
22
You Try It!
(0.2)2 + 1.4 - .14
2
Fraction bar = divide
I can translate verbal phrases into algebraic expressions.
Algebraic expressions contain numbers, operation symbols AND variables.
Variables: Lowercase letters that represent numbers.
A number increased by 4
n +4
You Try It! (Make sure to use parentheses when necessary)
Some number decreased by 14
m – 14
The quotient of a number and 7 _____________________
The sum of 12 and some number increased by 3_________
The quotient of 27 and a number
27 ÷ n or n

The difference of a number and 12, multiplied by 7
A number less THAN 12
12 – p
(Do you need parentheses to show subtraction first?)
The product of 7 and x, increased by 9
7x + 9
The difference of a number and 6, divided by 3
(n-6)÷3 ________________________________________________
A number greater than 54 __________________________
REMEMBER: WRITE IT AS YOU SEE IT, LEFT TO
Some number less than 4 times 6 ____________________
RIGHT…UNLESS THE WORD “THAN” IS IN THE PHRASE,
THEN YOU REVERSE IT.
I can substitute numbers for variables to evaluate expressions.
Evaluate 16 + b – 7 if b = 5
Step 1: Substitute b with 5
16 + 5 - 7
Step 2: Evaluate using the order of operations
16 + 5 – 7
21 – 7
14
The rate for renting a car is $25.00 per day plus an
additional $0.25 per mile. The algebraic expression,
25d + 0.25m, can be used to calculate the price. If Jose
rents a car for one day and travels 80 miles, how much will
he owe? Write and solve an expression. 25 + 0.25(80)
25 + 20
$45
You Try It!
Evaluate the following expressions when a = 6 and b = 4.
a+8
a–b
ab + 9
12b - a2
5a
3
Use the same algebraic expression from the example:
25d + 0.25m
If Savannah rents a car for 3 days and travels 358 miles,
how much will she owe the rental company? Write and
solve an algebraic expression to solve.
I can identify and apply the Commutative Property of Addition and Multiplication.
Commutative Property: Remember “commute” means to
move, or go from one place to another. The numbers in
the Commutative Property “move.” (The #s flip flop.)
Commutative Property of Addition: The order in which you
add numbers doesn’t change the sum.
a + b = b + a 7 + 6 = 6 + 7 (3 + 9) + 7 = 7 + (3 + 9)
You Try It!
m x b = __x m
__ x 9 = 9 x 12
17 + 7 = 7 + __
Commutative Property of Multiplication: The order in
(5 + 3) + 8 = (__ + 5) + 8
which you multiply numbers doesn’t change the product.
ab = ba
6 x 11 = 11 x 6
(7 x 8) x 2 = 2 x (7 x 8)
4 + (6 + 1) = 4 + (1 + __)
I can identify and apply the Identity Property of Multiplication and Addition.
Identity Property: Think “IDENTITY”! A person’s
You Try It!
IDENTITY, who they are, doesn’t change. With addition,
Identity Property for Addition: When you add ___ to a
think of what you can add to a number that will NOT
number, it does not _______. It keeps its _________!
change that number’s IDENTITY. With multiplication,
think of what you can multiply a number by and that
Identity Property for Multiplication: When you multiply
number keep its’ IDENTITY.
any number by ____, it does not change. It keeps its
Identity Property of Addition: When you add 0 to any
_______!
number, the number doesn’t change. (Keep’s its IDENTITY)
4+0=4
485 + 0 = 485 1 x = 0.56 x 1 = 0.56
x + ___= x
5 x __ = 5
y(1) = ____
45 + ___=45
I can identify and apply the Associative Property of Multiplication and Addition
Associative Property: The numbers do NOT “commute”
(move)…they stay in the same order on each side of the
equal sign. The parentheses DO move…the numbers
“associate” or “hang out” with a different number.
Ex: (5 + 3) + 7 = 5 + (3 + 7) The different grouping
8 + 7 = 5 + 10
does NOT change the
answer.
15
= 15
Ex: 7 x (5 x 6) = (7 x 5) x 6
7 x 30
= 35 x 6
210
210
I can identify and apply the Distributive Property.
You Try It!
Place the parentheses where they should go to show the
Associative Property.
5 + (6 + 7) = 5 + 6 + 7
“DISTRIBUTE” ive Property – Distribute the term outside of
the parentheses to every term inside the parentheses.
3(4 + 7) Distribute the 3 to each term in the parentheses
3(4) + 3(7) Simplify using the order of operations.
12 + 21
33
You Try It!
Use the Distributive Property to simplify the expressions.
6(n – 4) Distribute the 6 to each term in the parentheses.
6n – 6(4) Simplify using the order of operations.
6n – 24 This is as “simplified” as it gets on this one!
(3 x 4) x 9 = 3 x 4 x 9
6(7 + 4)
3(x – 4)
x(x + 7)
(7 - 4)4
I can simplify algebraic expressions by combining like terms.
Term: a number (7, 8, 4, etc.)
a variable (x, y, b, etc.)
a combination of number/variable (7x, 8b, 3x, etc.)
or, (7 x 6)
Simplify.
6b + 4b + 7 + 2b
12b + 7
You Try It!
Simplify.
12x – 9x + 3
f + f + f + 2f -7
4c – 2c + 5v - 10