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| 2x + 3x = (2+3)x is a consequence of what property? |
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| Numbers that have decimals which either terminate or are nonterminating with a repeating block of digits |
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3 + 5 = 8
5 + 3 = 8
3 + 5 = 5 + 3
2 • 3 = 6
3 • 2 = 6
2 • 3 = 3 • 2
These equations are a consequence of what properties?
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Definition
2 + (3 + 4) = 2 + 7 = 9
(2 + 3) + 4 = 5 + 4 = 9
2 + (3 + 4) = (2 + 3) + 4
2 • (3 • 4) = 2 • 12 = 24
(2 • 3) • 4 = 6 • 4 = 24
2 • (3 • 4) = (2 • 3) • 4
The way we add or multiply real numbers will not affect the final results. This are the properties of ____ |
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Identity Properties
0 = Additive Identity
1 = Multiplicative Identity |
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0 + a = a + 0 = a
a • 1 = 1 • a = a |
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Additive Inverse Property
Additive Inverse of a |
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a + (-a) = -a + a = 0
For every real number a, there is a real number -a, called the _____ |
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Multiplicative Inverse Property
Multiplicative Inverse, AKA reciprocal |
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a • 1⁄a = 1⁄a • a = 1 if a = 0
For every non zero real number a, there is a real number 1⁄a, called the ______, AKA _______ |
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| 0⁄a = 0 a⁄a = 1 if a =/= 0 |
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a(-b) = -(ab)
-(-a) = a
(-a)b = -(ab)
(-a)(-b) = ab
a⁄-b = -a⁄b = - a⁄b
-a⁄-b = a⁄b |
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Intersection of sets- ∩
a ∩ b = {1, 4, 6}
a = {1, 3, 4, 5, 6,}
b = {1, 2, 4, 6, |
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The set consisting of elements belonging to both a and b
a = {1, 3, 4, 5, 6,}
b = {1, 2, 4, 6, |
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Union- a set of elements belonging to sets a, b, or both
a U b = {1, 2, 3, 4, 5, 6}
a = {1, 3, 4, 5, 6,}
b = {1, 2, 4, 6, |
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Definition
a set of elements belonging to sets a, b, or both
a = {1, 3, 4, 5, 6,}
b = {1, 2, 4, 6,
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Ā
All elements in the Universal Set not appearing in Set a |
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