Do Now LT: I can identify the real set of numbers that has special subsets related in particular...

Do Now

LT: I can identify the real set of numbers that has special subsets related in particular ways.

CHAPTER 1.2 CHAPTER 1.2 PROPERTIES OF REAL PROPERTIES OF REAL

NUMBERS (NUMBERS (RR))

CHAPTER 1.2 CHAPTER 1.2 PROPERTIES OF REAL PROPERTIES OF REAL

NUMBERS (NUMBERS (RR))Learning Target: I can identify the real set of numbers that has special subsets related in particular ways.

• I will identify operations and relations among numbers• I will learn about sets of numbers


Vocabulary pg 11

• Opposite

• Additive inverse

• Reciprocal

• Multiplicative inverse


Real Numbers


REAL NUMBERS (REAL NUMBERS (RR))

Definition:Definition:


- Set of all rational and - Set of all rational and

irrational numbers.irrational numbers.



- Set of all rational and - Set of all rational and

irrational numbers.irrational numbers.


SUBSETS of SUBSETS of RR


RATIONAL NUMBERS (RATIONAL NUMBERS (QQ))

- numbers that can be expressed as - numbers that can be expressed as a quotient a quotient a/ba/b, where , where aa and and bb are are integers.integers.

- terminating or repeating decimals- terminating or repeating decimals

- Ex: {1/2, 55/230, -205/39}- Ex: {1/2, 55/230, -205/39}


RATIONAL NUMBERS (RATIONAL NUMBERS (QQ))

- numbers that can be expressed as - numbers that can be expressed as a quotient a quotient a/ba/b, where , where aa and and bb are are integers.integers.

- terminating or repeating decimals- terminating or repeating decimals

- Ex: {1/2, 55/230, -205/39}- Ex: {1/2, 55/230, -205/39}LT: I can identify the real set of numbers that

has special subsets related in particular ways.



INTEGERS (INTEGERS (ZZ))

- numbers that consist of - numbers that consist of positive integers, negative positive integers, negative integers, and zero,integers, and zero,

- {…, -2, -1, 0, 1, 2 ,…}- {…, -2, -1, 0, 1, 2 ,…}


INTEGERS (INTEGERS (ZZ))

- numbers that consist of - numbers that consist of positive integers, negative positive integers, negative integers, and zero,integers, and zero,

- {…, -2, -1, 0, 1, 2 ,…}- {…, -2, -1, 0, 1, 2 ,…}LT: I can identify the real set of numbers that




WHOLE NUMBERS (WHOLE NUMBERS (WW))

- nonnegative integers- nonnegative integers

- { 0 } - { 0 } {1, 2, 3, 4, ….} {1, 2, 3, 4, ….}

- {0, 1, 2, 3, 4, …}- {0, 1, 2, 3, 4, …}


WHOLE NUMBERS (WHOLE NUMBERS (WW))

- nonnegative integers- nonnegative integers

- { 0 } - { 0 } {1, 2, 3, 4, ….} {1, 2, 3, 4, ….}

- {0, 1, 2, 3, 4, …}- {0, 1, 2, 3, 4, …}




NATURAL NUMBERS (NATURAL NUMBERS (NN))

- counting numbers- counting numbers

- positive integers- positive integers

- {1, 2, 3, 4, ….}- {1, 2, 3, 4, ….}


NATURAL NUMBERS (NATURAL NUMBERS (NN))

- counting numbers- counting numbers

- positive integers- positive integers

- {1, 2, 3, 4, ….}- {1, 2, 3, 4, ….}


Real Numbers


PROPERTIES of PROPERTIES of RRDefinition:Definition:

COMMUTATIVE PROPERTYCOMMUTATIVE PROPERTY

Given real numbers a and b,Given real numbers a and b,

Addition: Addition: a + b = b + aa + b = b + a

Multiplication: Multiplication: ab = baab = ba


COMMUTATIVE PROPERTYCOMMUTATIVE PROPERTY

Given real numbers a and b,Given real numbers a and b,

Addition: Addition: a + b = b + aa + b = b + a

Multiplication: Multiplication: ab = baab = baExample:Example:

Addition: Addition: 2.3 + 1.2 = 1.2 + 2.32.3 + 1.2 = 1.2 + 2.3

Multiplication: Multiplication: (2)(3.5) = (3.5)(2)(2)(3.5) = (3.5)(2)

Example:Example:

Addition: Addition: 2.3 + 1.2 = 1.2 + 2.32.3 + 1.2 = 1.2 + 2.3

Multiplication: Multiplication: (2)(3.5) = (3.5)(2)(2)(3.5) = (3.5)(2)LT: I can identify the real set of numbers that



ASSOCIATIVE PROPERTYASSOCIATIVE PROPERTY

Given real numbers a, b and c,Given real numbers a, b and c,

Addition: Addition: (a + b) + c = a + (b + c)(a + b) + c = a + (b + c)

Multiplication: Multiplication: (ab)c = a(bc)(ab)c = a(bc)


ASSOCIATIVE PROPERTYASSOCIATIVE PROPERTY


Addition: Addition: (a + b) + c = a + (b + c)(a + b) + c = a + (b + c)

Multiplication: Multiplication: (ab)c = a(bc)(ab)c = a(bc)



DISTRIBUTIVE PROPERTY of DISTRIBUTIVE PROPERTY of MULTIPLICATION OVER ADDITIONMULTIPLICATION OVER ADDITION


a (b + c) = ab + aca (b + c) = ab + ac


DISTRIBUTIVE PROPERTY of DISTRIBUTIVE PROPERTY of MULTIPLICATION OVER ADDITIONMULTIPLICATION OVER ADDITION


a (b + c) = ab + aca (b + c) = ab + ac

Example 5:Example 5:4.3 (0.11 + 3.02) = (4.3)(0.11) + (4.3)(3.02)4.3 (0.11 + 3.02) = (4.3)(0.11) + (4.3)(3.02)

Example 6:Example 6:

2x (3x – b) = (2x)(3x) + (2x)(-b)2x (3x – b) = (2x)(3x) + (2x)(-b)

Example 5:Example 5:4.3 (0.11 + 3.02) = (4.3)(0.11) + (4.3)(3.02)4.3 (0.11 + 3.02) = (4.3)(0.11) + (4.3)(3.02)

Example 6:Example 6:

2x (3x – b) = (2x)(3x) + (2x)(-b)2x (3x – b) = (2x)(3x) + (2x)(-b)LT: I can identify the real set of numbers that



IDENTITY PROPERTYIDENTITY PROPERTY

Given a real number a,Given a real number a,

Addition: Addition: 00 + a = a + a = a

Multiplication: Multiplication: 11 (a) = a (a) = a


IDENTITY PROPERTYIDENTITY PROPERTY

Given a real number a,Given a real number a,

Addition: Addition: 00 + a = a + a = a

Multiplication: Multiplication: 11 (a) = a (a) = a

Example:Example:

Addition: Addition: 0 + (-1.342) = -1.342 0 + (-1.342) = -1.342

Multiplication: Multiplication: (1)(0.1234) = 0.1234(1)(0.1234) = 0.1234

Example:Example:

Addition: Addition: 0 + (-1.342) = -1.342 0 + (-1.342) = -1.342

Multiplication: Multiplication: (1)(0.1234) = 0.1234(1)(0.1234) = 0.1234LT: I can identify the real set of numbers that


PROPERTIES of PROPERTIES of RR


EXERCISESEXERCISESTell which of the properties of real numbers justifies each of the following statements.

1. (2)(3) + (2)(5) = 2 (3 + 5)2. (10 + 5) + 3 = 10 + (5 + 3)3. (2)(10) + (3)(10) = (2 + 3)(10)4. (10)(4)(10) = (4)(10)(10)5. 10 + (4 + 10) = 10 + (10 + 4)6. 10[(4)(10)] = [(4)(10)]107. [(4)(10)]10 = 4[(10)(10)]8. 3 + 0.33 is a real number


Order the numbers on a number line


HomeworkPg 15-17

#11-39 odds and 50,57,61,63

Challenge (CH) – 68


Do Now LT: I can identify the real set of numbers that has special subsets related in particular...

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