Agenda• Call Roll• Introduce• Class policies & procedures

– Syllabus, textbook form,

• Student Handbook• Info sheets• Notes

• Icebreaker• Assign HW

The Essential 55 by Ron Clark

• Rule 1: When responding to any adult, you should answer by saying “Yes ma’am” or “No sir.”

Notes 1.1

Addition and Subtraction

Reals

Rationals(fractions, decimals)

Integers(…, -1, -2, 0, 1, 2, …)

Whole(0, 1, 2, …)

Natural(1, 2, …)

Irrationals(no fractions)

pi, e

The Real Number System

Rational vs. IrrationalRational numbers CAN be expressed as a fraction.

Irrational numbers CANNOT be expressed as a fraction.

1

2-2.5

2 -2.569234567…

-9.212121…

Decimals that end or repeat

9

The number line

-5 -4 -3 -2 -1 0 1 2 3 4 5

1

2 2 -2.5

1) 3.12112111211112…

2) 8.974974974…

3) 4.325

Irrational

Rational or Irrational?

Rational

Rational

Irrational174)

You Try …Rational or Irrational?

5)

6)

7) .47646464..

8)

9) 2.573407656631….

49

59

37

32 Irrational

Rational

Rational

Irrational

Rational

Signs are alike, ADD10) -5 + (-9) =

Addition

11) 6 + 20 =

-14

26

Signs are different, SUBTRACT

12) 23 + (-11) =

keep the sign of the larger number

Subtraction

13) -12 + 7 =

12

-5

14) 5 – (- 4)

15) 8 – (- 9)

16) 23.7 – 5.9

17) -12 + (-16)

= 5 + 4 = 9

= 8 + 9 = 17

=17.8

= -28

You Try …

Adding and Subtracting Fractions

5

4

1

718)

19)

20)

6

5

8

3

10

23

5

6

If signs are the same, POSITIVE.

1) 5 (10) =

Multiplication

2) -6 ( -9) =

50

54

If signs are different, NEGATIVE

3) 6(-7) =

Multiplication

4) -4(5) =

-42

-20

Multiplying FractionsMultiply across

1

2

3

7

1

2

2

5

5)

6)

7)

24

15

3

6

•Addition: a + b = b + a

•Multiplication: a • b = b • a

•Addition: a + (b + c) = (a + b) + c

•Multiplication: a • (b • c) = (a • b) • c

Commutative Properties

Associative Properties

5.) Use the commutative property of addition to write an expression equivalent to 3x + 4y

6.) Use the associative property of multiplication. to write an expression equivalent to 3x(7y • 9z)

•Addition: a + 0 = a

•Multiplication: a • 1 = a

Identity Properties

0 is the additive identity

1 is the multiplicative identity

3

x

y =8

24

x

y

The identity property allows us to take an expression and multiply it by 1.

8

8

This is 1.

These two expressions are equivalent.

7.) Write an expression equivalent to by simplifying.

6

2

xy

x

6

2

xy

x

3y

2 3

2

x y

x

2

2

3

1

x

x

y

Reciprocal2

3

3

2

8 1

8

2

3

3

2 = 1

= 1

8

1

1

8

DivisionIf signs are alike, POSITIVE.

10 5 =

24

6

8)

9)

2

4

If signs are different, NEGATIVE

Division

-10 5 =

10

40

10)

11)

-2

1

4

Dividing FractionsMultiply by the reciprocal

1

4

3

512)

13)

14)

9

4

3

2

15

7

5

12

Zero

7

0

0

7

Homework• Get syllabus signed

• Get book covered!!!!!

• Get notebook together

• Homework:

7-9/ 15-54 mult. of 3, 55-58 all