Pre-Algebra
Terms
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- Properties
- Statements that are true for every number.
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Communitive Property
of Addition -
For Any Numbers A and B:
A+B = B+A
Example: 3+4 = 4+3 -
Communitive Property
of Multiplication -
For Any Numbers A and B:
AxB = BxA
Example: 5x6 = 6x5 -
Associative Property
of Addition -
For Any Numbers A,B,and C:
(A+B)+C = A+(B+C)
Example: (2+3)+4 = 2+(3+4) - Associative Property of Multiplication
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For Any Numbers A,B and C:
(AxB) x C = A x(BxC)
Example: (2x4)x6 = 2x(4x6) - Additive Identity
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For Any Number A:
A+0=0+A=A
Example: 5+0=0+5=5 - Multiplicative Identity
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For Any Number A:
Ax1=1xA=A
Example: 8x1=1x8=8 - Multiplicative Property
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For Any Number A:
Ax0=0xA=0
3x0=0x3=0 - Equation
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Mathematical Sentence with an Equal(=) Sign
Example: 7+5=12 - Open Sentence
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Equation That Has Variables,
Not True or False Until Proven.
Example: x + 7 =19
Solve for x: x = 12 - Solution
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The Value That Makes a Statement True.
Example: 12-M=8
Solve: 2,4,7 M=4 - Properties of Equalities
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The Symmetric Property
and
The Transitive Property
are Properties of Equality - Symmetric Property
-
For any numbers A and B:
If A=B, then B=A
Example:
5=x+2 which equals x+2=5 - Transitive Property
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For Any Numbers A, B and C:
If A=B and B=C, then A=C
Example:
2+3=5 and 5=1+4, then 2+3=1+4 -
Variable: Place holder for any value symbol.
Algebraic Expression: Combo of numbers, variables and operations. -
Rule # 1:
For All Numbers A and B, if A=B,then A may be replaced by B.