Download Section 1.3 Properties

Section 1.3 Properties
Properties of Equality
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Reflexive Property: a=a
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Symmetric Property: If 3=x, then x=3
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Transitive Property: If x=y and y=4 then x=4
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Addition Property: If x=3, then x+4=3+4
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Multiplication Property: If x=7, then 2x=14
Closure Property
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a+b and ab are unique real numbers.
The sum of 3 and 5 is only 8
The product of 3 and 5 is only 15
Commutative Property
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“Order changes”
a+b=b+a
ab=ba
3+4=4+3
xyz=yxz
Order can NOT change for subtraction or
division
Associative Property
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Order stays the same. Parentheses move.
(a + b) + c = a + (b +c)
(ab)c=a(bc)
Identity Properties
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Identity property of addition
(additive identity): a + 0 = a
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4+0=4
Identity property of multiplication
(Multiplicative Identity): a•1=a
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5•1=5
Inverse Properties
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Property of Opposites: a + (-a) = 0
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7 + (-7) = 0
Property of Reciprocals:
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1
8 1
8
1
a 1
a
Distributive Property
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a(b + c) = ab + ac
“To give out”
Name the property illustrated.
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Using the Properties to Simplify & Solve
Equations
1
1
x  4   x    x  ( x  4)
4
4
Commutative of +
1
  x  x   4 Associative of +
4
1
Property of Opposites
 0  4 
4
1
  4 Additive Identity
4
1
Property of Reciprocals
1
1
1
(1  3t )   1  (3t )
3
3
3
1
1 
  1    3 t
3
3 
1
 1  1 t
3
1
 t
3
Distributive Property of +
wrt multiplication
Associative of multiplication
Property of Reciprocals
Multiplicative Identity