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Transcript of Do Now LT: I can identify the real set of numbers that has special subsets related in particular...
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Do Now
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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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
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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Vocabulary pg 11
• Opposite
• Additive inverse
• Reciprocal
• Multiplicative inverse
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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Real Numbers
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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REAL NUMBERS (REAL NUMBERS (RR))
Definition:Definition:
REAL NUMBERS (REAL NUMBERS (RR))
- Set of all rational and - Set of all rational and
irrational numbers.irrational numbers.
Definition:Definition:
REAL NUMBERS (REAL NUMBERS (RR))
- Set of all rational and - Set of all rational and
irrational numbers.irrational numbers.
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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SUBSETS of SUBSETS of RR
Definition:Definition:
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}
Definition:Definition:
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.
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SUBSETS of SUBSETS of RR
Definition:Definition:
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 ,…}
Definition:Definition:
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
has special subsets related in particular ways.
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SUBSETS of SUBSETS of RR
Definition:Definition:
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, …}
Definition:Definition:
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, …}
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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SUBSETS of SUBSETS of RR
Definition:Definition:
NATURAL NUMBERS (NATURAL NUMBERS (NN))
- counting numbers- counting numbers
- positive integers- positive integers
- {1, 2, 3, 4, ….}- {1, 2, 3, 4, ….}
Definition:Definition:
NATURAL NUMBERS (NATURAL NUMBERS (NN))
- counting numbers- counting numbers
- positive integers- positive integers
- {1, 2, 3, 4, ….}- {1, 2, 3, 4, ….}
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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SUBSETS of SUBSETS of RR
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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Real Numbers
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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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
Definition: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 = 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
has special subsets related in particular ways.
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PROPERTIES of PROPERTIES of RRDefinition:Definition:
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)
Definition:Definition:
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)
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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PROPERTIES of PROPERTIES of RRDefinition:Definition:
DISTRIBUTIVE PROPERTY of DISTRIBUTIVE PROPERTY of MULTIPLICATION OVER ADDITIONMULTIPLICATION OVER ADDITION
Given real numbers a, b and c,Given real numbers a, b and c,
a (b + c) = ab + aca (b + c) = ab + ac
Definition:Definition:
DISTRIBUTIVE PROPERTY of DISTRIBUTIVE PROPERTY of MULTIPLICATION OVER ADDITIONMULTIPLICATION OVER ADDITION
Given real numbers a, b and c,Given real numbers a, b and c,
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
has special subsets related in particular ways.
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PROPERTIES of PROPERTIES of RRDefinition:Definition:
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
Definition:Definition:
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
has special subsets related in particular ways.
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PROPERTIES of PROPERTIES of RR
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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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
LT: I can identify the real set of numbers that has special subsets related in particular ways.
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Order the numbers on a number line
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HomeworkPg 15-17
#11-39 odds and 50,57,61,63
Challenge (CH) – 68
LT: I can identify the real set of numbers that has special subsets related in particular ways.