Integers
Rules for integers:
1. 2.
3.
4.
5.
6.
7.
8.
9.
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Real Numbers
R (Real)
Q (Rational)
Z (Integers)
I (Irrational)
W (Whole)
N (Natural)
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Sets
Set = a collection of objects
the objects are elements of the set
If B is a set, the notation a ∈ B means that a is an element in the set B
and the notation c ∉ B means that c is not an element in the set B.
Some sets can be listed with braces : for instance A = {1,2,3,4} (the set A has 4 elements which are 1,2,3,4)
Some sets can be written using set builder notation: D = { x | x > 10} which is read D is the set of all x's such that x is greater than 10 Set Union, Intersection, or Empty:
Union: Given H and G then H ∪ G means the set that contains the elements of H and G
Intersection: H ∩ G means the set that contains just the elements H & G have in common
Empty: ∅ means there are no elements in the set
EX: H = {1,2,3,4,5} G = {4,5,6,7,8} M = {9,10,11}
H ∩ G = {4,5} H G = {1,2,3,4,5,6,7,8}
M ∩ G = ∅
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Intervals ­ Interval Notation
Open Intervals are indicated by open circles on a number line and by ( ) in interval notation ­ these mean that the number isn't included in the answer.
Closed Intervals are indicated by closed circles on a number line and by [ ] in interval notation ­ these mean that the number is included in the answer.
Notation
Set Description Graph
(a, b) [a,b]
[a,b)
(a, b]
(a, ∞)
[a, ∞)
(­∞, b)
(­∞, b]
(­∞, +∞)
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3 Big Properties:
1. Distributive:
2. Commutative:
3. Associative:
Order of Operations
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Fractions ­ Our Friends!
To add or subtract fractions you must have a common ____________________
Ex.
To add or subtract Mixed fractions you should first ____________________________ then ________________________________________________________
Ex.
To multiple fractions you _________________________________
Ex
To divide fractions you ___________________________________________
or ___________________________________________
or ___________________________________________
EX.
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Sample Problems:
1. State the property: 3x ­ 5y + 12x = 3x + 12x ­ 5y
2. solve. (¼ -½)¾ ÷ 3
3. A = {1,3,7,8} B = {2,4,5,6,7,8} C = {1,2,3}
A∪C
A∩C
4. Write in set builder notation and then graph [-2, 8)
5. Write in set builder notation and then graph [2, ∞)
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