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!)