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Name: _________________________ PERIOD _________
Chapter 2 – Solving Equations
7.N.12 – Add, subtract, multiply, and divide integers
8.N.2 – Evaluate expressions with integral exponents
8.M.1 – Solve equations/proportions to convert to equivalent measurements Measurement within
metric and customary measurement systems Note: Also allow Fahrenheit to Celsius and vice versa.
8.A.8 – Multiply a binomial by a monomial or a binomial (integer coefficients)
Disclaimer: This packet is your notes for all of chapter 2. It is expected you
will take good notes and work the examples in class with your teacher in
pencil. It is expected that you bring your packet to class every day and do not
lose it! Should you be absent, it is expected that you get the notes and
examples you missed. This packet will be collected and graded out of 50
points the class after the chapter 2 test.
Notes
Examples
Neatness
Total
_____/20
_____/20
_____/10
_____/50
Comments:
Day
Topic
Assignment
1 2.1 Number Properties Assign 2.1: TB Page 66 #20-31 all, 36, 44-46 all, 52,
65
2 2.2 Distributive Property
Assign 2.2:TB Page 74 #12-18 even, 28-36 all, 38, 40,
46-49 all, 61, 62
3 2.3 Simplifying Variable Expressions Assign 2.3: TB Page 81 #10-30 all (just evaluate), 33-
35 all, 38, 52, 53
4 2.4 Variables and Equations Assign 2.4: TB Page 87 #8-19 all, 32, 35, 36, 53, 54
5 2.5 Solving Equations involving addition
and subtraction
Assign 2.5: TB Page 93 #11-25 all, 28-40 even, 64, 65
6 2.6 Solving Equations involving
multiplication and division
Assign 2.6: TB Page 99 #8-23 all (check with your
calculator), 28-33 all (check with your calculator), 39,
57, 58
2
Day
Topic
Assignment
7 2.7 Equations with Decimals Assign 2.7 TB Page 105 #24-34 even (check with your
calculator), 29, 35, 39-44 all, 56 (for 56b round the
hours to the nearest whole number and days to the
nearest tenth of a day).
8/9 Review
Study
10 Chapter 2 Test
None
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Guided Notes 2.1 – Properties and Operations Date: ________
A property in mathematics is a statement that something that is true for all values. Today we will look at
three properties of numbers: the commutative property, the associative property, and the identity property.
Commute – ____________________________________________________________________________
Commutative Property of Addition
Words: ________________________________________________________________________________
Numerical Example: ________________________ Algebraic Example: _________________________
Commutative Property of Multiplication
Words: ________________________________________________________________________________
Numerical Example: ________________________ Algebraic Example: _________________________
Associate – _____________________________________________________________________________
Associative Property of Addition
Words: ________________________________________________________________________________
Numerical Example: ________________________ Algebraic Example: _________________________
Associative Property of Multiplication
Words: ________________________________________________________________________________
Numerical Example: ________________________ Algebraic Example: _________________________
Identical – _____________________________________________________________________________
Identity Property of Addition
Words: ________________________________________________________________________
Numerical Example: ________________________ Algebraic Example: _________________________
Identity Property of Multiplication
Words: ________________________________________________________________________________
Numerical Example: ________________________ Algebraic Example: _________________________
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What we will use these properties for is to make evaluating expressions easier. Using properties does not
undermine the order of operations, it supplements them.
Example 1: Evaluate the expression using mental math.
a) 4 19 25
b) 17 32 23 c) 6.8 9.7 2.2
d) 3.06 0 5.37 4.94
e) 10 8 10 4 f) 15 9 1 4 5
Example 2: Evaluate the expression when 10, 4, and 2a b c .
a) 2 2a bc
b) 223 5c c) 23bc
d) 2 6a b
e) 29 9 25a b f) 3 5 6b a c
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Example 3: Simplify the expression.
a) 7 96s
b) 33 14j c) 21 3t
d) 32 6r
e) 5.36 6.47p f) 2 3x
Example 5: During the summer, you work 5 hours a day as a lifeguard at a beach and earn $9 each
hour. Use properties of multiplication to find how much money you earn during a 6-day work week.
Example 6: A lunch box is 30 centimeters long,
14 centimeters wide, and 12 centimeters high. The formula for the
volume of a box is V lwh . Find the volume of the lunch box, in
cubic centimeters.
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Guided Notes 2.2 – The distributive Property Date: ________
Distribute– ____________________________________________________________________________
Distributive Property of Multiplication over Addition
Words: ________________________________________________________________________________
___________________________________________________________________________________
Numerical Example: ________________________ Algebraic Example: _________________________
Distributive Property of Multiplication over Subtraction
Words: ________________________________________________________________________________
___________________________________________________________________________________
Numerical Example: ________________________ Algebraic Example: _________________________
Example 1: Use the distributive Property to evaluate the expression.
a) 15 7 20
b) 10 6.4 8.9
c) 5 12 7
d) 4 9 8
e) 29 14 3
Example 2: Evaluate the expression using the distributive property and mental math.
a) 312 4
b) 487 6
c) 17.98 3
d) 7 82
e) 5 190
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Example 3: You and a friend go to a restaurant. You each order a salad, a cup of soup, and a drink.
Each salad costs $5.99, each cup of soup costs $3.90, and each drink costs $1.15. Use the distributive
property to find the total cost of the meal.
Example 4: Use the distributive property to write an equivalent variable expression.
a) 2 6x
b) 2 6x c) 8 9x
d) 11x
e) 4x f) 3 x
g) 4 6x
g) 9 4x
i) 5 7x
j) 3 2 4x
k) 11 5 2x l) 6 2 3x
m) 10 4 5x
n) 6 3 7x o) 7 8 12x
p) 4x x y
q) 3 7y y
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Example 5: Find the area of the triangle or rectangle.
a)
b)
c)
d)
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Example 6: There are several rectangular parcels of land for sale in a neighborhood. The Gonzalez
family wants to purchase Lot A and half of the neighboring lot.
a) Use the distributive property to find the area, in square yards, of Lot A.
b) Use the distributive property to find the area, in square yards, of half of Lot B.
c) Find the total area of the land the Gonzalez family wishes to purchase.
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Guided Notes 2.3 – Simplifying Variable Expressions Date: ________
Consider the mathematical expression: 5 4 7 2x x
The ___________ of an expression that are always separated by either addition or by subtraction.
In the above example the terms are: ____________________________
The __________________of a term with a variable is the number part of the term.
In the above example the coefficients of the variable x are : ____________________________
Keep in mind that a variable with no coefficient really means a coefficient of 1. We seldom write the
number one as a coefficient though.
A ______________________ term is a number without a variable
In the above example the constant terms are: ____________________________
Keep in mind that an expression with no constant term really means a constant of 0. We seldom write
the number zero as a constant though.
______________ terms are terms with identical variable parts.
In the above example the like terms are: ___________________________________
Example 1: For the given expression, identify the like terms, coefficients, and constant terms.
Simplify the expression.
a) 4 5 9 17d d
b) 6 14 26 3 15 3f f f f
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Example 2: Simplify the expression.
a) 2 3 6 15 26a a b) 4 5 7 3 13c c
c) 24 6 8 4 52u u
d) 8 6 11 5 20 3h h
e) 10 7 4 9 21 8b b
f) 28 6 7 2 8 3n n n
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Example 3: Write and simplify an expression for the perimeter of the triangle or rectangle.
a)
b)
c)
d)
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Guided Notes 2.4 – Variables and Equations Date: ________
Example 1: Translate each verbal phrase into an equation
a) The sum of a number (n) and 25 is 14. ____________________
b) 5 points less than your grade (g) is a 78% . ____________________
c) 7.5 centimeters more than the plant’s height (h) is 145 cm. ____________________
d) Adam’s age (a) divided by 3 is 5. ____________________
e) The dog’s weight (w) decreased by 2 pounds is 50 pounds. ____________________
f) $39 is three times the cost (c) of an item. ____________________
Example 2: Translate these equations into words.
a) 6 8x __________________________________________________________________________
b) 4 9k ___________________________________________________________________________
c) 6 12x ___________________________________________________________________________
d) 39
t ____________________________________________________________________________
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Example 3: Decide if the given number is a solution to the equation (answer yes or no). This is
called a check.
a) 6 8x ?
14x
b) 4 9k ?
5k
c) 10 13t ?
3t
d) 6 12x ?
6x
e) 4 16k ?
4k
f) 39
t
?27t
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Guided Notes 2.5 – Solving One-step Equations (addition and subtraction) Date: ________
To solve an equation means to find the only value of the variable that makes the equation ______________.
To solve an equation you use the __________________________________. You must always do the same
inverse operation to both sides of the equation.
Keep in mind you want the ______________________ all alone on one side of the equation.
Example 1: Solve the equation and check your solution.
a) 16 4z
Check:
b) 0 17m Check:
c) 3 5j
Check:
d) 13 21h Check:
e) 9 20g
Check:
f) 7 26d Check:
g) 24 12t
Check:
h) 28 3p Check:
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Example 2: Use a let statement to define your variable. Write an equation to model the situation
and then solve the equation.
a) Your friend is 3 years older than you. You are 15 years old. How old is your friend?
b) You pay $1.70 for a box of oatmeal after using a coupon for $.80 off. Find the regular price of the
oatmeal.
c) There are 160 players in a soccer league. This is 23 more than last year. Find the number of players that
were in the soccer league last year.
Example 3: Simplify the equation and solve. Check your solution.
a) 10 6 22k
Check:
b) 9 15 3b Check:
c) 6 10 0y
Check:
d) 18 13 20w Check:
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Example 4: Set up and solve an equation to find the value of x.
a) Perimeter = 70 in.
b) Perimeter = 41 cm
c) Perimeter = 72 mm
d) Perimeter = 29
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Guided Notes 2.6 – Solving One-step Equations (multiplication and division) Date: ________
To solve an equation means to find the only value of the variable that makes the equation ______________.
To solve an equation you use the __________________________________. You must always do the same
inverse operation to both sides of the equation.
Keep in mind you want the ______________________ all alone on one side of the equation.
Example 1: Solve the equation and check your solution.
a) 15 600c
Check:
b) 6 84y
Check:
c) 418 19a
Check:
d) 152 8t
Check:
e) 119
d
Check:
f) 1512
w
Check:
19
g) 182
z
Check:
h) 208
f
Check:
i) 7r
Check:
j) 8 4 24x x Check:
Example 2: Use a let statement to define your variable. Write an equation to model the situation
and then solve the equation.
a) Sixty-four people show up for a volleyball tournament. How many 4-person teams can be formed.
b) The area of the fenced-in yard is 117 square feet.
The length of the yard is 13 feet. Find the width of the
yard.
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Example 3: The figure shown below is composed of a triangle and a rectangle.
a) Write and simplify an expression in terms of x for the area of
the figure.
b) What is the value of x if the area of the figure is 108 square
inches?
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Guided Notes 2.7 – Solving One-step Equations with Decimals Date: ________
To solve an equation means to find the only value of the variable that makes the equation ______________.
To solve an equation you use the __________________________________. You must always do the same
inverse operation to both sides of the equation.
Keep in mind you want the ______________________ all alone on one side of the equation.
Example 1: Solve the equation and check your solution.
a) 21.3 19.79r
Check:
b) 13.49 8.56 a
Check:
c) 20.57 3.78m
Check:
d) 17.06 29.08v Check:
e) 14.88 34.76d
Check:
f) 31.45 12.56p
Check:
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Example 2: Solve the equation and check your solution.
a) 30.75 73.8b
Check:
b) 70.448 25.16 f
Check:
c) 42.12 7.8t
Check:
d) 13.256
k
Check:
e) 24.367.9
w
Check:
f) 7.3520.18
c
Check:
For3-4, use a let statement to define your variable. Write an equation to model the situation. Solve the
equation.
Example 3: You deposit a check for $236.79 into your savings account. Your account has a
balance of $319.23 after the deposit. Find the balance of your savings account before the deposit.
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Example 4: At an amusement park, you spend $7.40 on lunch and $6.20 on admission. Admission,
lunch, and playing arcade games cost $19. How much did you spend on arcade games?
Example 5: Set up and solve an equation to find the value of x.
a) Perimeter = 50.35 m
b) Perimeter = 24.31 ft.
c) Area = 49.65 2cm
d) Area = 223.25 2ft
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Chapter 2 Test Review Date:__________
Multiple Choice Questions: For 1-6, circle the best answer to the question. Although it
is multiple choice, when you see the saw graphic SHOW ALL WORK. Calculators are
not allowed on this section.
1) Which equation illustrates the commutative property of addition?
A) a b c a c b
B) a b c a b c
C) 0a a
D) a bc ab c
2) Which expression represents the area (in square units) of the rectangle shown?
A) 5 8y
B) 10 16y
C) 55 3y
D) 55 33y
3) In which expression is 5 a constant term?
A) 3 – 5a
B) 5 16 a
C) 5 10 a
D) 5 5 a a
4) Which equation represents the sentence "The quotient of z and 9 is 7."?
A) 79
z
B) 97
z
C) 7
9z
D) 9
7z
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5) What is the solution of 10 6? p
A) 16
B) 6
C) 4
D) 6
6) What is the solution of 3.4 22.1 ?w
A) –75.14
B) –6.5
C) 6.5
D) 75.14
Short Response Questions: For 7-30, when you see the saw graphic, SHOW ALL
WORK in the space provided. No credit will be given for just an answer. Calculators
are allowed on this section.
For 7-10 write an equation that represents the given sentence.
7) A number increased by 6 is 15
__________________________
8) A number minus 4 is 8. __________________________
9) The product of 8 and a number is 17
__________________________
10) 11 is the quotient of a number and 3. __________________________
For 11-14, simplify the expression.
11) 5 14 2t t
12) 4 3 4x x 13) 13 8 10k k 14) 6 8 4x x
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For 15-16, write and simplify an expression for the perimeter of the rectangle or triangle.
15)
16)
For 17-20, use the distributive property to simplify the expression.
17) 4 7z
18) 5 4 2y 19) 4 2 5 7u u 20) 9 2 6 2a a
For 21-22, write and simplify an expression to find the area of the rectangle or triangle.
21)
22)
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For 23-30, solve the one-step equation and check by hand.
23) 7 2r
Check
24) 15 11 t
Check
25) 4 24 d Check
26) 153
h
Check
27) 8.5 3.2 a
Check
28) 5.2 1.6 c
Check
29) 5.47
k
Check
30) 6 4.8 g Check
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Extended Response Questions: For 31-32, when you see the saw graphic, SHOW ALL
WORK in the space provided. Calculators are allowed on this section.
For 31-33, find the value of x for the given geometric shape with perimeter P by writing and solving
and equation.
31) P = 59 in.
32) P = 432 ft