Name______________________________ Date_______________

Integrated Algebra ANotes/Homework Packet 12

Lesson HomeworkNumber Properties HW#1

Rational/Irrational Numbers HW#2Union/Intersection & Venn Diagrams HW#3

Absolute Value HW#4Review

Test

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Number PropertiesIdentity Properties: _______________________________________________________________

Additive Identity: a + 0 = _______ Ex:

Multiplicative Identity: a x 1 = _______ Ex:

Inverse Properties: _______________________________________________________________

Additive Inverse: a + (-a) = _______ Ex:

Multiplicative Inverse: a x ( ) = _______ Ex:

Commutative Property: ___________________________________________________________________________________________________________________________________________

Commutative Property of Addition:

Commutative Property of Multiplication:

Associative Property: _____________________________________________________________________________________________________________________________________________

Associative Property of Addition:

Associative Property of Multiplication:

Distributive Property: ______________________________________________________________________________________________________________________________________________

Addition:

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Subtraction:Let’s answer the following questions:

1. What is the additive inverse of the following numbers?

a. -2.75 ___________ b. 5 __________ c. __________ d. –2 __________

2. What is the multiplicative inverse of the following numbers?

a. ____________ b. __________ c. 8 ___________ d. 1 __________

For #s 3-10, to a property in Column I, match an example from Column II.

Column I Column II

3. Associative Property of Multiplication _____ a. 3 + 4 = 4 + 3

4. Associative Property of Addition _____ b. 3 1 = 3

5. Commutative Property of Addition _____ c. 0 4 = 0

6. Commutative Property of Multiplication _____ d. 3 + 0 = 3

7. Identity Element of Multiplication _____ e. 3 4 = 4 3

8. Identity Element of Addition _____ f. 3(4 + 5) = 3 4 + 3 5

9. Distributive Property _____ g. 3(4 5) = (3 4)5

10. Multiplication Property of Zero _____ h. (3 + 4) + 5 = 3 + (4 + 5)

11. Which equation is an illustration of the additive identity property?(1) 6 1 = 6 (2) 4 + 0 = 4 (3) 10 - 10 = 0 (4) 4

= 1

12. Which equation illustrates the distributive property for real numbers?(1) + = + (3) (1 x 7) x 6 = 1 x (7 x 6)

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(2) + 0 = (4) -3(5 + 7) = (-3)(5) + (-3)(7)

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Name _________________________ Date ____________HW#1

1. What is the additive inverse of 6?______ 2. What is the additive inverse of -3?______

3. What is the multiplicative inverse of ?______

4. What is the additive inverse of 4?______

5. Which expression must be added to 3x - 7 to equal 0?

(1) 0 (2) 3x + 7 (3) -3x - 7 (4) -3x + 7

6. Which number property is illustrated by the equation 4 1 = 4?

(1) identity property for addition (3) identity property for multiplication(2) inverse property of multiplication (4) inverse property of addition

7. Which is an illustration of the commutative property?(1) 3 (4 5) = (3 4) 5 (3) 3 (4 5) = (3 4) (3 5)(2) (3 4) 5 = 5 (3 4) (4) 3 1 = 3

In #s 8-9, below: a) Replace each question mark with a number that makes the sentence true, and

b) Name the property illustrated in each sentence that is formed when the replacement is made.

8. 3 (?) = 1 9. 8 + (2 + 9) = (8 + ?) + 9

a) a)

b) b)

10. Which equation is an illustration of the distributive property of multiplication over subtraction?

a) 5 - 8 = 8 - 5 c) 6 (a + b) = 6a + 6bb) 7 (25 - 14) = 7 (25) - 7 (14) d) 3 = 1

MORE ON NEXT PAGE

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15. Write the following phrase/sentence as an algebraic expression:

a. the sum of a number and 4, divided by 7 _______________________

b. 10 times a number increased by 6 is 112. _______________________

c. Five less than a number exceeds that number by 10. _______________________

16. Christine took a survey of 15 people to find out how many pages were in the last book

they read. Her data consisted of the following numbers:

397, 90, 165, 100, 205, 270, 85, 150, 310, 450, 45, 190, 250, 101, and 97

(a) Construct a frequency table for the given data.Interval(pages) Tally Frequency

0-99    100-199     200-299300-399     400-499     

(b) Construct a frequency histogram using the table completed in part a.

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Number SystemA diagram and chart showing Real Numbers and the subsets are displayed below:

WORD NOTES EXAMPLESCounting (or Natural) Numbers

These are the numbers you learn when you first learn how to count.

Whole Numbers Like Counting Numbers, but also includes zero.

Integers Includes negative and positive Whole Numbers.

Rational Numbers A number that can be made into a fraction. A decimal is a rational number if it terminates (ends) or repeats.

Irrational Numbers A number that cannot be made into a fraction. A decimal is an irrational number if it never ends and never repeats.

Vocab in OUR own words:

Rational - _____________________________________________________________________________

Irrational - _____________________________________________________________________________

Tell whether the number is rational or irrational and WHY:

1) 3.333 ___________________ because: _______________________________________

2) ___________________ because: _______________________________________

3) ___________________ because: _______________________________________

4) ___________________ because: _______________________________________

5) 7.253871695487… ________________ because: ____________________________________

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Irrational #s

REAL NUMBERS

Counting #s

Whole #s

Integers

Rational #s

6) ___________________ because: _______________________________________

7) 1.222222… _________________ because: ______________________________________

Review: Solve for x, to the nearest tenth, in each of the diagrams below.

1. 2.

8

11cm

43

x

12m

17mx

x10ft

72

Name_______________________________ Date__________________HW #2

Tell whether the number is rational or irrational and WHY:

1) ___________________ because: _______________________________________

2) 8.11 ___________________ because: _______________________________________

3) 0 ___________________ because: _______________________________________

4) ___________________ because: _______________________________________

5) 5.23232323… ________________ because: _______________________________________

6) ___________________ because: _______________________________________

7) 1.3548731296… _________________ because:___________________________________

Review: Solve for x, to the nearest tenth, in each of the diagrams below.

1. 2.

3. 4.

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62x

10 yd 45

x10 cm

12ft x

15ft

11yds

8ydsx

Intersection & Union

A set is a collection of numbers. We can put sets together to create new sets.

Intersection of two sets - ________________________________________________________

_______________________________________________________________________________________

Example: A = {1, 2, 3, 4, 5} B = {2, 4, 6, 8, 10}

is { } because they are the numbers that show up in both sets.

Union of two sets - ______________________________________________________________

_______________________________________________________________________________________

Example: A = {1, 2, 3, 4} B = {2, 4, 6}

is { } because it combines all of the numbers without repeating any they have in common.

Disjoint Sets – if two sets do not intersect; the have no common values

Example: A = {1, 3, 5, 7, 9} B = {2, 4, 6, 8, 10}

= Ø means “empty set”

Practice: A = {1, 2, 3} B = {3, 4, 5, 6} C = {1, 3, 4, 6} D = {7, 8, 9}

1. = ________________ 2. =_______________ 3. =____________

4. =________________ 5. =_______________ 6. =_____________

7. =_______________ 8. =_________________ 9. =_____________

Venn Diagrams

Intersection and Union can be shown graphically by using Venn Diagrams. These are a set of overlapping circles that shows the relationships between sets.

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Example: A = {1, 2, 3, 4, 5} B = {2, 4, 6, 8, 10}

We don’t always have to organize numbers. We can organize other things such as people, colors, etc.

Set Elements

Faces on U.S. bills{Washington, Lincoln, Hamilton, Jackson, Grant, Franklin}

Faces on U.S. coins{Lincoln, FDR, Kennedy, Jefferson, Washington}

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A B

A and B

A B

5

31

42

108

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Faces on U.S. bills

Faces on U.S. coins

= _______________

= _______________

Name______________________________ Date_________________HW #3

A = {11, 12, 13} B = {5, 6} C = {1, 2, 3, 4, 5, 6} D = {0, 6, 10}

1. = __________________ 2. =__________________ 3. =__________________

4. =____________________ 5. =__________________ 6. =__________________

7. =____________________ 8. =____________________ 9. =_________________

Fill in the Venn diagram with the information in the given table.

Set ElementsAlex's favorite TV channels {2, 4, 5, 6, 7, 8}

Sam's favorite TV channels {4, 6, 7, 9, 10, 14}

Put the elements into the appropriate section of the Venn diagram according to what you know about the items:

{stop sign, cherry, banana, fire truck, bread, popcorn, tomato}

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Alex’s favorite TV channels

Sam’s favorite TV channels

Food Red

Absolute Value

Vocabulary:

Absolute Value: ___________________________________________________________________Symbol:

Activity: Write down results from the classroom Activity

Student Name Position on Line Distance from Zero

Absolute Value

No matter where the person stands on the line, their distance is always ______________ so their absolute value is always _______________.

Examples:

1. = 2. = 3. = 4. =

5. = 6. - = 7. = 8. =

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Now we could perform operations with absolute value but we must watch out for tricks!

1. = 2. = 3. =

4. = 5. = 6. =

7. = 8. = 9. =

Review: Solve the following equations for x and CHECK your answers.1. 2.

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Name__________________________________ Date_________________HW #4

1. = 2. = 3. =

4. = 5. = 6. =

7. = 8. = 9. =

Review: Solve the following equations for x and CHECK your answers.

1. 5x + 9 + 5x = 60 + 7x 2. 5x + 3(x + 4) = 28

3. Jay goes to the store to buy dish detergent. He wants to get the best buy. The 32-ounce box sells for $2.19 and the large economy box of 54 ounces sells for $4.25. Which one should Jay buy to get the most for his money?

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