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 2∙5-4

8+7 10-4

15 6

5)  13 – s + 10 6) 42 - 2∙3 + (2 + r)

t

13 -2+10 42 - 2∙3 + (2 + 5)

7 42 - 2∙3 + 7

16 - 6 + 7

11+10 10 + 7

7 17

21 = 7

3

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 7.) _f=number of friends__

$9 per friend. Write an algebraic expression that represents (define the variable)

the cost of inviting any number of friends. Then use it to find _____9f+100______

the cost of inviting 9 friends to his party. (algebraic expression)

____$181______

(solution)

8.)  You are going to the store to buy chips and pop. The pop is 8.)_p=pop bottles_c= chips_

$1.50 per bottle and the chips cost $2.00 for each bag. Write (define the variable)

an algebraic expression to represent the total cost of buying

any number of chips and any number of pop bottles. _____1.50p+2.00c_____

Use it to find the cost of buying 6 bags of chips and 4 bottles (algebraic expression)

of pop. 1.50 ∙ 4 + 2.00 ∙ 6

6.00 + 12.00

$18.00 ___$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) 13.) a ∙ b = b ∙ a

Associative Property of Multiplication Commutative Property of Multiplication

14.) 6 ∙ 1 = 6 15.) a + b = b + a

Multiplicative Identity Commutative Property of Addition

16.) (a+b)+c = a+(b+c) 17.) 3(2 + 4) = 3 ∙ 2 + 3 ∙ 4

Associative Property of Addition 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 27.) 2y + 4y + 9 12x 6y + 9

28.) 9x + 4y – 4x + 5y + 2 29.) 10x + 4y + 3 – 2x + 3y + 4 5x + 9y + 2 8x + 7y + 7

PART 6: Distributive Property

Use the Distributive Property to rewrite each expression.

30.) 2(5 + 3) 31.) 6(a - 6) 32.) 2(2x + 5)

2 ∙ 5 + 2 ∙ 3 6 ∙ a - 6 ∙ 6 2 ∙ 2x + 2 ∙ 5

10 + 6 6a - 36 4x + 10

16

Simplify the following algebraic expressions. Use the Distributive Property when appropriate.

33.) 3(g + 9) + 6g 34.) x + 3(7x - 2) 35.) 6(y - 2) + 12

3 ∙ g + 3 ∙ 9 + 6g x + 2 ∙ 7x + 3 ∙ -2 6 ∙ y + 6 ∙ -2 + 12

3g + 27 + 6g x + 14x + - 6 6y + -12 + 12

9g +27 15x + -6 0r 15x-6 6y

PART 7: Factoring Linear Expressions

Find the GCF (greatest common factor) of each pair of monomials.

36.) 12, 18 37.) 8xy, 16y 38.) 12x, 21xy

6 8y 3x

Factor each expression. If the expression cannot be factored, write cannot be factored.

39.) 35x + 15 40.) 20 - 16y 41.) 14p + 20

5 is factor of both terms 4 is factor of both terms 2 is factor of both terms

35x divided by 5 is 5x 20 divided by 4 is 5 14p divided by 2 is 7p

15 divided by 5 is 3 so, 16y divided by 4 is 4y so, 20 divided by 2 is 10 so,

5(7x+3) 4(5-4y) 2(7p + 10)

42.) 23q - 10 43.) 12 + 15h 44.) 3x + 16

3 is factor of both terms

no common factors 12 divided by 3 is 4 no common factors

15h divided by 5 is 3h so,

3(4 + 3h)

45) 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)