Name: PERIOD · 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

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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: ________________________________________________________________________________


Associate – _____________________________________________________________________________

Associative Property of Addition

Words: ________________________________________________________________________________


Associative Property of Multiplication

Words: ________________________________________________________________________________


Identical – _____________________________________________________________________________

Identity Property of Addition

Words: ________________________________________________________________________


Identity Property of Multiplication

Words: ________________________________________________________________________________


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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: ________________________________________________________________________________

___________________________________________________________________________________


Distributive Property of Multiplication over Subtraction

Words: ________________________________________________________________________________

___________________________________________________________________________________


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: ________






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: ________






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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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

25

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

Documents

Name: PERIOD · 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