MTH 11203 Algebra PROPERTIES OF THE REAL NUMBER SYSTEM CHAPTER 1 SECTION 10.

MTH 11203Algebra

PROPERTIES OF THE REAL NUMBER SYSTEM

CHAPTER 1 SECTION 10

If a and b represent any real numbers thena + b = b + a

Commutative property involves a change in order

The order that you add does not matter same results

Exp 5 + 2 = 2+ 5 7 = 7

Exp -3 + (-5) = -5 + (-3) -8 = -8

Commutative property will not work for subtraction

Commutative Property of Addition

If a and b represent any real numbers thena b = b a

The order that you multiply does not matter same results

Exp (5)(6) = (6)(5) 30 = 30

Exp (r)(g) = (g)(r) rg = rg

Commutative property will not work for division

Commutative property changes the order

Commutative Property of Multiplication

If a and b represent any real numbers then(a + b) + c = a + (b + c)

The associative property involves a change in grouping

Exp (2 + 3) + 4 = 2 + (3 + 4) Exp 6 + (w + 1) = (6 + w) + 1

5 + 4 = 2 + 7 7 + w = 7 + w 9 = 9

Exp (3 + 4) + x = 3 + (4 + x) 7 + x = 7 + x

Associative property will not work for subtraction

Associative Property of Addition

If a and b represent any real numbers then(a b) c = a (b c)

Exp (2 6) 4 = 2 (6 4) 12 4 = 2 24 48 = 48

Exp (3 7) x = 3 (7 x) 21 x = 21 x 21x = 21x

Associative property will not work for divisionThe associative property changes grouping

Associative Property of Multiplication

If a and b represent any real numbers thena(b + c) = ab + ac

Exp 3(2 + 4) = (3)(2) + (3)(4) (3)(6) = 6 + 12 18 = 18

Exp 6(x ndash 9) = (6)(x) ndash (6)(9)6x ndash (6)(9) = 6x ndash 546x ndash 54 = 6x ndash 54

Expand a (b + c + d + e + f + hellip + n) = ab + ac + ad + ae + af + hellip + an

Distributive Property

Identity Property of AdditionIf a and b represent any real numbers thena + 0 = a and 0 + a = a Zero is the identity element of addition

Exps 3 + 0 = 3 6 + 0 = 6 50 + 0 = 50

Identity Property of MultiplicationIf a and b represent any real numbers thena 1 = a and 1 a = a One is the identity element of Multiplication

Exp 3 1 = 3 6 1 = 6 50 1 = 50

Identity Property

Inverse Property of AdditionIf a and b represent any real numbers thena + (-a) = 0 and -a + a = 0 Additive inverses are any two numbers whose sum is 0 or opposites

Exp 3 + (-3) = 0 6 + (-6) = 0 50 + (-50) = 0

Inverse Property of MultiplicationIf a and b represent any real numbers thena = 1 and a = 1 a ne 0

Multiplicative inverses are any two numbers whose product is 1 or reciprocal

Exp 3 = 1 6 = 1 50 = 1

Inverse Property

29 pg 84) p (q r) = (p q) rAssociative Property of Multiplication

24 pg 84) 3 + y = y + 3Commutative Property of Addition

31 pg 84) 4(d + 3) = 4d + 12Distributive Property

28 pg 84) -4x + 4x = 0Inverse Property of Addition

33 pg 85) 3z 1 = 3zIdentity Property of Multiplication

Name the property

Exp 4(x ndash 7) = 4x + (4)(-7)4(x ndash 7) = 4x ndash 28Distributive Property

Exp 5y + (-5y) = 0Inverse Property of Addition

Name the property

Exp (3 6) 9 =(3 6) 9 = 3 (6 9)Associative Property of Multiplication

Exp 7(x ndash 4) = 7(x ndash 4) = 7x ndash 28 Distributive Property

33 pg 85) 6b + 0 = 6b + 0 = 6bIdentity Property of Addition

Complete the equation and name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

If a and b represent any real numbers thena + b = b + a

Commutative property involves a change in order

Exp 5 + 2 = 2+ 5 7 = 7

Exp -3 + (-5) = -5 + (-3) -8 = -8

Commutative property will not work for subtraction

Commutative Property of Addition

Exp (5)(6) = (6)(5) 30 = 30

Exp (2 + 3) + 4 = 2 + (3 + 4) Exp 6 + (w + 1) = (6 + w) + 1

5 + 4 = 2 + 7 7 + w = 7 + w 9 = 9

Exp (3 + 4) + x = 3 + (4 + x) 7 + x = 7 + x

Exp (2 6) 4 = 2 (6 4) 12 4 = 2 24 48 = 48

Exp (3 7) x = 3 (7 x) 21 x = 21 x 21x = 21x

Exp 3(2 + 4) = (3)(2) + (3)(4) (3)(6) = 6 + 12 18 = 18

Exps 3 + 0 = 3 6 + 0 = 6 50 + 0 = 50

Exp 3 1 = 3 6 1 = 6 50 1 = 50

Identity Property

Exp 3 + (-3) = 0 6 + (-6) = 0 50 + (-50) = 0

Exp 3 = 1 6 = 1 50 = 1

Inverse Property

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

Exp (5)(6) = (6)(5) 30 = 30

Exp (2 + 3) + 4 = 2 + (3 + 4) Exp 6 + (w + 1) = (6 + w) + 1

5 + 4 = 2 + 7 7 + w = 7 + w 9 = 9

Exp (3 + 4) + x = 3 + (4 + x) 7 + x = 7 + x

Exp (2 6) 4 = 2 (6 4) 12 4 = 2 24 48 = 48

Exp (3 7) x = 3 (7 x) 21 x = 21 x 21x = 21x

Exp 3(2 + 4) = (3)(2) + (3)(4) (3)(6) = 6 + 12 18 = 18

Exps 3 + 0 = 3 6 + 0 = 6 50 + 0 = 50

Exp 3 1 = 3 6 1 = 6 50 1 = 50

Identity Property

Exp 3 + (-3) = 0 6 + (-6) = 0 50 + (-50) = 0

Exp 3 = 1 6 = 1 50 = 1

Inverse Property

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

Exp (2 + 3) + 4 = 2 + (3 + 4) Exp 6 + (w + 1) = (6 + w) + 1

5 + 4 = 2 + 7 7 + w = 7 + w 9 = 9

Exp (3 + 4) + x = 3 + (4 + x) 7 + x = 7 + x

Exp (2 6) 4 = 2 (6 4) 12 4 = 2 24 48 = 48

Exp (3 7) x = 3 (7 x) 21 x = 21 x 21x = 21x

Exp 3(2 + 4) = (3)(2) + (3)(4) (3)(6) = 6 + 12 18 = 18

Exps 3 + 0 = 3 6 + 0 = 6 50 + 0 = 50

Exp 3 1 = 3 6 1 = 6 50 1 = 50

Identity Property

Exp 3 + (-3) = 0 6 + (-6) = 0 50 + (-50) = 0

Exp 3 = 1 6 = 1 50 = 1

Inverse Property

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

Exp (2 6) 4 = 2 (6 4) 12 4 = 2 24 48 = 48

Exp (3 7) x = 3 (7 x) 21 x = 21 x 21x = 21x

Exp 3(2 + 4) = (3)(2) + (3)(4) (3)(6) = 6 + 12 18 = 18

Exps 3 + 0 = 3 6 + 0 = 6 50 + 0 = 50

Exp 3 1 = 3 6 1 = 6 50 1 = 50

Identity Property

Exp 3 + (-3) = 0 6 + (-6) = 0 50 + (-50) = 0

Exp 3 = 1 6 = 1 50 = 1

Inverse Property

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

Exp 3(2 + 4) = (3)(2) + (3)(4) (3)(6) = 6 + 12 18 = 18

Exps 3 + 0 = 3 6 + 0 = 6 50 + 0 = 50

Exp 3 1 = 3 6 1 = 6 50 1 = 50

Identity Property

Exp 3 + (-3) = 0 6 + (-6) = 0 50 + (-50) = 0

Exp 3 = 1 6 = 1 50 = 1

Inverse Property

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

Exps 3 + 0 = 3 6 + 0 = 6 50 + 0 = 50

Exp 3 1 = 3 6 1 = 6 50 1 = 50

Identity Property

Exp 3 + (-3) = 0 6 + (-6) = 0 50 + (-50) = 0

Exp 3 = 1 6 = 1 50 = 1

Inverse Property

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

Exp 3 + (-3) = 0 6 + (-6) = 0 50 + (-50) = 0

Exp 3 = 1 6 = 1 50 = 1

Inverse Property

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

Name the property

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

HOMEWORK 110

ndash 8523 25 27 37 39 41 43 53

MTH 11203 Algebra PROPERTIES OF THE REAL NUMBER SYSTEM CHAPTER 1 SECTION 10.

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