Transcript 1.5 ( + ) and ( - ) numbers

1.4 Properties of Real Numbers ( )
Vocabulary:
Equivalent Expression: two expressions that have the
same value for all values of the variable(s).
Deductive Reasoning: The process of reasoning logically
from given facts to a conclusion
Counterexample: An example showing that a statement
is false.
1.4 Properties of Real Numbers ( )
We must be able to identify and use the
properties of real numbers such as:
Commutative Property:
of Addition:
a+b=b+a
0f Multiplication:
a∙b=b∙a
3+5=5+3
3∙5=5∙3
Associative Property:
of Addition:
(a+b)+c = a+(b+c)
0f Multiplication: (a ∙ b)∙c = a∙(b∙ c)
(3 + 5)+4 = 3+(5+4)
(3∙5)4 = 3∙(5∙4)
Identity Property:
of Addition:
0f Multiplication:
a + 0= a
a∙1=a
3+0=3
3∙1= 3
Zero Property of Multiplication:
a∙0 =0
3∙0=0
Multiplication Property of - 1:
- 1 ∙ a= - a
- 1 ∙ 3 = -3
Identity Property:
of Addition:
0f Multiplication:
a + 0= a
a∙1=a
3+0=3
3∙1= 3
Zero Property of Multiplication:
a∙0 =0
3∙0=0
Multiplication Property of - 1:
- 1 ∙ a= - a
- 1 ∙ 3 = -3
We must be able to identify and use the
properties of real numbers such as:
Ex: Name the properties that each statement illustrates:
1) 76 + 5 = 5 + 76
2) 9 ∙ (-1 ∙ x)=9 ∙ (-x)
Answers:
1) Commutative Property of Additions
2) Multiplication Property of -1
Ex: Simplify and justify each step:
1) 8 + (9t + 4 )
Answers:
(8 + 4) + 9t
Associative Property
(12) + 9t
Addition of like terms
9t + 12
Solution.
We must also be able to see given information
and make decisions using some common sense:
Ex: For all real numbers r, s, and t, is (r ∙ s) ∙ t = t ∙ (s ∙ r)
true or false?
Answers:
True, this is the commutative property of multiplication
Ex: Your friend says that the associative property allows us
to change the order in which we complete any two
operations. Is this true? If false, provide a counterexample.
Answers:
False since Associative property only applies when both
operations are adding or multiplying and not a
combination of both.
Counterexample: (8 ∙ 11) + 9 = 8 ( 11 + 9). This is not true.
Class Work:
Pages: 26 - 28
Problems : 7 through 45
(2n + 1)