Post on 21-Oct-2014
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Algebra Algebra PropertiesProperties
Notes 1 - 4Notes 1 - 4
Rules, Rules, Rules……Rules, Rules, Rules……
IdentityIdentity
and and
Equality Equality PropertiesProperties
AdditionAddition
The additive identity propertyThe additive identity property
a + 0 = 0 + a = aa + 0 = 0 + a = a
(adding 0 to anything (adding 0 to anything
doesn’t change what it is!)doesn’t change what it is!)
MultiplicationMultiplication
Multiplication identity propertyMultiplication identity property
a(1) = 1(a) = aa(1) = 1(a) = a
(multiplying something by 1 doesn’t (multiplying something by 1 doesn’t change what it is!)change what it is!)
BIG FAT ZERO!BIG FAT ZERO!
Multiplicative Property of Zero
a • 0 = 0 • a = 0
(0 times any number equals 0!)
“Duh” property
INVERSEINVERSE
Multiplicative Inverse Property:
Two numbers whose product is 1 are called multiplicative inverses or reciprocals
(like 1/5 and 5, or 2/3 and 3/2: you just flip the fraction!)
Properties of Equality Properties of Equality (=)(=)
Reflexive Property The reflexive property of equality says that any number equals itself. For any number a, a = a.
Symmetric Property The symmetric property of equality says that if one quantity equals a second quantity, then the second quantity also equals the first. For any numbers a and b, if
a = b, then b = a.
MORE Properties of MORE Properties of Equality….Equality….
Transitive PropertyFor any numbers a, b, and c, if a = b
and b = c, then a = c.
SubstitutionIf a =b, then a may be replaced by b
in any expression.
Your Turn…..Your Turn…..Name the
multiplicative inverse of each number or variable:
1. 32. 2/73. 4/x4. 2 ½5. m
Pretty good….now try Pretty good….now try these:these:
Name the property or properties illustrated:
6. x • 1 = x7. 15/3 + 4 = 5 + 48. 2/3 • 3/2 = 19. 11 • 0 = 010. 2 + 3 = 2 + 311. If 12 + 3 = 15 then 15 = 12 + 312. 0 + m = m
Bet you can’t get Bet you can’t get this one!this one!
Which property is illustrated?Which property is illustrated?
If x + 5 = 9 and 9 = y, then x + 5 = yIf x + 5 = 9 and 9 = y, then x + 5 = y
Hmmmm…..Hmmmm…..
What would the multiplicative inverse ofWhat would the multiplicative inverse of
____55__ __
r – 7 look like?r – 7 look like?
Coming Soon….Coming Soon….To a classroom near you……To a classroom near you……
More Properties!!More Properties!!(It will be a real scream!)(It will be a real scream!)