Transcript 2_10 TROUT 09

Properties of Algebra
(aka all the rules that holds the
math together!)
Axioms for Rational
Numbers
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All of our axioms for rational numbers
are for ONLY addition and
multiplication!!!!
Axiom is just a property that has not
been proven but we accept and use to
do algebra and prove things
Commutative Property
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Root word is: commute
To commute means to move
The numbers move places
Commutative Property
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Addition:
a+ b = b+a
Example:
2 + 3 = 3 +2
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Multiplication
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ab= ba
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Example:
2(3) = 3(2)
Associative Property
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Root word: Associate
To associate means to group together
In math, our grouping symbols are the
()
Keep the order of the numbers the
same!!! Just change the ( )
Associative Property
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Addition
a+(b+c)=(a+b)+c
Example:
2+(3+5)=(2+3)+5
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Multiplication
a(bc) = (ab)c
Example:
2(3·5) = (2·3)5
Identity Properties
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Your identity is who you are
The same goes for numbers and
variables
3 is who 3 is and x is who x is
The idea with the identity property is
you want to get itself back
Identity Property
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Addition
a+0=a
Example:
3+0=3
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Multiplication
a (1) = a
Example:
3 (1) = 3
Inverse Properties
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The inverse in math means the
“opposite”
When we add the opposite of a
positive is a negative and vice versa
When we mult the opposite is the
reciprocal
In an inverse we want our addition to
= 0 and our mult to = 1
Inverse Property
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Addition
a + (-a) = 0
Example:
3 + (-3) = 0
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Multiplication
a(1/a) =1
Example:
3 (1/3) = 1
Distributive Property
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To distribute means to give out
You are giving the # on the outside of
the ( )’s to every # inside the ( )
The distributive property is the only
one that includes addition and mult at
the same time
Distributive Property of
Multiplication over Addition
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a (b + c + d) = ab + ac + ad
Example:
4 ( 3x + 2y – 5)
= 4 (3x) + 4(2y) + 4 (-5)
= 12x + 8y + -20
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Properties of Equality
Reflexive Property: a =a
Example: 4 =4
 Symmetric Property : If a=b, then b=a
Example: If x= 3, then 3=x
 Transitive Property: If a=b
and b=c
then a=c
Example: If x=3 and 3=y then x=y
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Homework
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