Identity Properties, Study notes of Mathematics

Statements that are true for any number of variables. Identity Properties. 1) Additive Identity. What do you add to get the same?

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Properties
Statements that are true
for any number of
variables.
Identity Properties
1) Additive Identity
What do you add to get the same?
a + 0 = a
2) Multiplicative Identity
What do you mult. to get the
same?
a • 1 = a
Inverse Properties
1) Additive Inverse (Opposite)
a + (-a) = 0
2) Multiplicative Inverse
(Reciprocal)
a
1
a1
Properties of Equality
1) Reflexive: a= a
5 = 5
2) Symmetric: If a= bthen b= a.
If 4 = 2 + 2 then 2 + 2 = 4.
3) Transitive:If a= band b= c, then a= c.
If 4 = 2 + 2 and 2 + 2 = 3 + 1 then 4 = 3 + 1.
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Properties

Statements that are true for any number of variables.

Identity Properties

1) Additive Identity

What do you add to get the same?

a + 0 = a

2) Multiplicative Identity

What do you mult. to get the

same?

a • 1 = a

Inverse Properties

1) Additive Inverse (Opposite)

a + (-a) = 0

2) Multiplicative Inverse

(Reciprocal)

a 

a

Properties of Equality

1) Reflexive: a = a **5 = 5

  1. Symmetric: If** a = b then b = a. **If 4 = 2 + 2 then 2 + 2 = 4.
  2. Transitive:If** a = b and b = c , then a = c. If 4 = 2 + 2 and 2 + 2 = 3 + 1 then 4 = 3 + 1.

Multiplicative Property of Zero

a • 0 = 0

(If you multiply by 0, the answer is 0.)

Commutative Property

Commutative means that the

order does not make any

difference.

a + b = b + a a • b = b • a Examples 4 + 5 = 5 + 4 2 • 3 = 3 • 2

The commutative property does

not work for subtraction or

division.

Associative Property

Associative means that the grouping

does not make any difference.

(a + b) + c = a + (b + c) (ab) c = a (bc) Examples (1 + 2) + 3 = 1 + (2 + 3) (2 • 3) • 4 = 2 • (3 • 4)

The associative property does not work

for subtraction or division.

  • Commutative property of addition a + b = b + a
  • Commutative property of Multiplication ab = ba
  • Associative property of addition a + ( b + c ) = ( a + b ) + c
  • Associative property of multiplication a(bc) = (ab)c
  • Distributive property a(b + c) = ab + ac

6. 1  m = m

Multiplicative Identity

7. k + 7 = k + 7

Reflexive

8. x + 0 = x

Additive Identity

9. 11 ^

Multiplicative Inverse

Name the property

a. 6 + (2 + 7) = (6 + 2) + 7 b. 15  10 = 10  15 c. 4  1 = 4 d. 4(6 + 8) = 4(6) + 4(8) e. a + 0 = a f. 1  (3  4)=(1  3)  4 g. yz = zy h. 5 + 4 = 4 + 5 i. 62 = 9(4) j. 5 + 4 = 5 + 4 k. 2.5 = 1.5 + 1 and 1.5+1 = 2.