Name__________________________________________________________ Period ________
Math 7 Chapter 5
Study Guide
PART 1: Order of Operations
Complete the following information about the order of operations:
1) What does “PEMDAS” or “Please Excuse My Dear Aunt Sally” mean? Please tell what each
letter/word stands for.
Parentheses Exponents Multiply and Divide Add and Subtract
2) What is special about the order in which you add and subtract and multiply and divide?
You do them in order from left to right
PART 2: Evaluating Algebraic Expressions
Evaluate each expression if r = 5, s = 2, t = 7, and u = 1.
Show all work, and all steps. You must rewrite the problem and each step along the way.
3) 10 – s + t
4) 2r – 4
10-2+7
8+7
15
2∙5-4
10-4
6
5) 13 – s + 10
t
13 -2+10
7
11+10
7
21
3
=7
6)
42 - 2∙3 + (2 + r)
42 - 2∙3 + (2 + 5)
42 - 2∙3 + 7
16 - 6 + 7
10 + 7
17
PART 3: Writing Algebraic Expressions
Write an algebraic expression for each situation and use it to solve the given situation.
7.) For Luke to have a birthday party at Sky Zone it cost $100 plus
$9 per friend. Write an algebraic expression that represents
the cost of inviting any number of friends. Then use it to find
the cost of inviting 9 friends to his party.
7.) _f=number of friends__
(define the variable)
_____9f+100________
(algebraic expression)
____$181_________
(solution)
8.) You are going to the store to buy chips and pop. The pop is
$1.50 per bottle and the chips cost $2.00 for each bag. Write
an algebraic expression to represent the total cost of buying
any number of chips and any number of pop bottles.
Use it to find the cost of buying 6 bags of chips and 4 bottles
of pop. 1.50 ∙ 4 + 2.00 ∙ 6
6.00 + 12.00
$18.00
8.)_p=pop bottles_c= chips_
(define the variable)
_____1.50p+2.00c_____
(algebraic expression)
___$18.00________
(solution)
9.) The cost of tickets to the movies is $7 per student. Write and
9.) _s=number of students_
algebraic expression that can be used to find the cost of any
(define the variable)
number of students. Use your expression to find the cost of 20
students.
___7s_____________
7∙20=140
(algebraic expression)
___$140_________
(solution)
PART 4: Identifying Properties
A. Name the property illustrated in each example.
10.) 2 + 3 = 3 + 2
11.) a + 0 = a
Commutative Property of Addition
Additive Identity
12.) (12∙2)∙4=12∙(2 ∙4)
Associative Property of Multiplication
13.) a ∙ b = b ∙ a
Commutative Property of Multiplication
14.) 6 ∙ 1 = 6
Multiplicative Identity
15.) a + b = b + a
Commutative Property of Addition
16.) (a+b)+c = a+(b+c)
Associative Property of Addition
17.) 3(2 + 4) = 3 ∙ 2 + 3 ∙ 4
Distributive Property
B. Rewrite each expression to illustrate the given property.
17.) Rewrite to illustrate the associative property of addition
2 + (12 + 4) = (2 + 12) + 4
18.) Rewrite to illustrate the commutative property of multiplication
6∙a=a∙6
19.)Rewrite to illustrate the associative property of multiplication
(12 ∙ 4) ∙ a = 12 ∙ (4 ∙ a)
20.)Rewrite to illustrate the commutative property of addition
2x + 3 = 3 + 2x
C. Answer each question and provide an example
21.) Does the commutative property apply to division? If false, provide a counterexample to
illustrate. If true provide an example to illustrate.
False 15 divided by 3 = 5 but 3 divided by 15= 1/5
22.) Does the associative property apply to subtraction? If false, provide a counterexample to
illustrate. If true provide an example to illustrate.
False (5-2)-1=2 but 5-(2-1)=4
PART 5: Simplifying Algebraic Expressions
A. Answer the following questions about algebraic expressions.
23.) Like terms are terms that have the same ___variable______________.
24.) If a term has no co-efficient such as x, the “invisible” co-efficient is a ___1_____.
25.) We can only add or subtract terms that are __like____ terms.
B. Simplify.
25.) 5x + 7x
12x
27.)
28.)
29.)
9x + 4y – 4x + 5y + 2
5x + 9y + 2
2y + 4y + 9
6y + 9
10x + 4y + 3 – 2x + 3y + 4
8x + 7y + 7
PART 6: Distributive Property
Use the Distributive Property to rewrite each expression.
30.) 2(5 + 3)
2∙5+2∙3
10 + 6
16
31.) 6(a - 6)
6∙a-6∙6
6a - 36
32.)
2(2x + 5)
2 ∙ 2x + 2 ∙ 5
4x + 10
Simplify the following algebraic expressions. Use the Distributive Property when appropriate.
33.) 3(g + 9) + 6g
3 ∙ g + 3 ∙ 9 + 6g
3g + 27 + 6g
9g +27
34.) x + 3(7x - 2)
x + 2 ∙ 7x + 3 ∙ -2
x + 14x + - 6
15x + -6 0r 15x-6
35.) 6(y - 2) + 12
6 ∙ y + 6 ∙ -2 + 12
6y + -12 + 12
6y
PART 7: Factoring Linear Expressions
Find the GCF (greatest common factor) of each pair of monomials.
36.) 12, 18
6
37.) 8xy, 16y
8y
38.) 12x, 21xy
3x
Factor each expression. If the expression cannot be factored, write cannot be factored.
39.)
35x + 15
40.) 20 - 16y
41.)
5 is factor of both terms
4 is factor of both terms
35x divided by 5 is 5x
20 divided by 4 is 5
15 divided by 5 is 3 so,
16y divided by 4 is 4y so,
5(7x+3)
4(5-4y)
42.) 23q - 10
no common factors
45)
14p + 20
2 is factor of both terms
14p divided by 2 is 7p
20 divided by 2 is 10 so,
2(7p + 10)
43.) 12 + 15h
44.) 3x + 16
3 is factor of both terms
12 divided by 3 is 4
no common factors
15h divided by 5 is 3h so,
3(4 + 3h)
12x + 9x
3x is a factor of both terms
12x divided by 3x is 4
9x divided by 3x is 3 so,
3x(4 + 3)