Operations With Real Operations With Real Numbers Numbers SOL 7.3SOL 7.3

by by Lisa BeebeLisa Beebe

Chincoteague Combined SchoolChincoteague Combined School

Commutative PropertyCommutative PropertyAssociative PropertyAssociative PropertyDistributive PropertyDistributive PropertyIdentity PropertiesIdentity PropertiesInverse PropertiesInverse Properties

Multiplicative Property of Zero Multiplicative Property of Zero

Commutative PropertyCommutative Property(ORDER)(ORDER)

• The order in which numbers are added The order in which numbers are added or multiplied does not change the or multiplied does not change the answer. answer.

• Examples:Examples:

3 + 5 = 5 + 3 3 + 5 = 5 + 3

Both sides equal 8.Both sides equal 8.

2 2 · 7 = 7 · 2· 7 = 7 · 2

Both sides equal 14.Both sides equal 14.

Commutative PropertyCommutative Property

Associative PropertyAssociative Property(GROUPING)(GROUPING)

• The way in which three numbers are The way in which three numbers are grouped with parentheses in addition or grouped with parentheses in addition or multiplication does not change the answermultiplication does not change the answer

• Examples:Examples:(1 + 2) + 3 = 1 + (2 + 3)(1 + 2) + 3 = 1 + (2 + 3)Both sides equal 6.Both sides equal 6.

(2 · 3) · 5 = 2 · (3 · 5)(2 · 3) · 5 = 2 · (3 · 5)Both sides equal 30.Both sides equal 30.

Associative PropertyAssociative Property

Distributive PropertyDistributive Property(Distribute)(Distribute)

• States that the product of a number States that the product of a number and the sum (or differences) of two and the sum (or differences) of two other numbers equals the sum (or other numbers equals the sum (or difference) of the products of the difference) of the products of the number and each other numbernumber and each other number

• For any three numbers a, b, and c – it For any three numbers a, b, and c – it is true that a(b + c) = ab + acis true that a(b + c) = ab + ac

Distributive PropertyDistributive Property

Identity Property of AdditionIdentity Property of Addition

• A number plus zero is always A number plus zero is always itself.itself.

• Example:Example:11 + 0 = 1111 + 0 = 11

Identity Property of Identity Property of MultiplicationMultiplication

• A number multiplied by 1 is always A number multiplied by 1 is always itselfitself

• Example:Example:17 · 1 = 1717 · 1 = 17

Additive Inverse PropertyAdditive Inverse Property

• States that the sum of a number and States that the sum of a number and its additive inverse always equals its additive inverse always equals zero. zero.

• What you need to add to a number to What you need to add to a number to get the identityget the identity

• Example: 5 + -5 = 0 Example: 5 + -5 = 0

Multiplicative Inverse Multiplicative Inverse PropertyProperty

• States that the product of a number States that the product of a number and its multiplicative inverse (or and its multiplicative inverse (or reciprocal) always equals onereciprocal) always equals one

• What you need to multiply to a What you need to multiply to a number to get the identitynumber to get the identity

• Example:Example:4 × ¼ = 14 × ¼ = 1

Multiplicative Property of Multiplicative Property of ZeroZero

• States that the product of any States that the product of any real number and zero is always real number and zero is always zero. zero.

• Example: 5 × 0 = 0 Example: 5 × 0 = 0

Identify the following property:Identify the following property: a + b = b + a a + b = b + a

Commutative Pro

perty ..

Associa

tive Pro

perty

Commutative Pro

perty ..

Additive

Identity

Property

25% 25%25%25%A.A. Commutative Commutative Property of Property of MultiplicatonMultiplicaton

B.B. Associative Associative PropertyProperty

C.C. Commutative Commutative Property of additionProperty of addition

D.D. Additive Identity Additive Identity Property Property

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Which property is shown in the Which property is shown in the equation 26 + 0 = 26?equation 26 + 0 = 26?

Inverse

property

of addi...

Inverse

property

of mult..

.

Identity pro

perty of a

dd...

Multi

plicative pro

perty o...

25% 25%25%25%A.A. Inverse property Inverse property of additionof addition

B.B. Inverse property Inverse property of multiplicationof multiplication

C.C. Identity property Identity property of additionof addition

D.D. Multiplicative Multiplicative property of zeroproperty of zero

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Identity the following property: Identity the following property:

5 · (x · y) = (5 · x) · y 5 · (x · y) = (5 · x) · y

Dist

ributive

Property

Associa

tive pro

perty of ..

.

Associa

tive Pro

perty of ..

.

Commutative pro

perty ..

25% 25%25%25%A.A. Distributive PropertyDistributive Property

B.B. Associative property Associative property of multiplicationof multiplication

C.C. Associative Property Associative Property of additionof addition

D.D. Commutative Commutative property of property of multiplicationmultiplication

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Identify the following property: Identify the following property: 5 · (x · y) = 5 · (y · x)5 · (x · y) = 5 · (y · x)

Associa

tive Pro

perty of ..

.

Associa

tive Pro

perty of..

.

Dist

ributive

Property

Commutative Pro

perty ..

25% 25%25%25%A.A. Associative Associative Property of Property of Multiplication Multiplication

B.B. Associative Associative Property of AdditionProperty of Addition

C.C. Distributive Distributive PropertyProperty

D.D. Commutative Commutative Property of Property of multiplicationmultiplication

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Which equation uses the Which equation uses the distributive property?distributive property?

-3(4 + 7) =

-3(4) +

-3(7)

-3(4 + 7) =

-3(11)

-3(4 + 7) =

-3(4) +

7

-3(4 + 7) =

4(-3) +

4(7)

25% 25%25%25%A.A. -3(4 + 7) = --3(4 + 7) = -3(4) + -3(7)3(4) + -3(7)

B.B. -3(4 + 7) = --3(4 + 7) = -3(11)3(11)

C.C. -3(4 + 7) = --3(4 + 7) = -3(4) + 73(4) + 7

D.D. -3(4 + 7) = 4(--3(4 + 7) = 4(-3) + 4(7)3) + 4(7)

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Which equation shows the Which equation shows the multiplicative property of zero?multiplicative property of zero?

-35.9(1) =

-35.9

-35.9(0) =

0

-35.9(359/1

0) = 1

-35.9(35.9) =

1

25% 25%25%25%A.A. -35.9(1) = -35.9-35.9(1) = -35.9

B.B. -35.9(0) = 0-35.9(0) = 0

C.C. -35.9(359/10) = -35.9(359/10) = 11

D.D. -35.9(35.9) = 1-35.9(35.9) = 1

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Which property is shown in the Which property is shown in the equation 7 × 0 = 0?equation 7 × 0 = 0?

Additive

identity pro

perty

Multi

plicative Id

entity ...

Multi

plicative in

verse

p...

Multi

plicative pro

perty o...

25% 25%25%25%A.A. Additive identity Additive identity propertyproperty

B.B. Multiplicative Multiplicative Identity propertyIdentity property

C.C. Multiplicative Multiplicative inverse propertyinverse property

D.D. Multiplicative Multiplicative property of zeroproperty of zero

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What is the identity for What is the identity for addition?addition?

0 -1 1 1/0

25% 25%25%25%A.A. 00

B.B. -1-1

C.C. 11

D.D. 1/01/0

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What is the identity for What is the identity for multiplication?multiplication?

0 -1 1 1/0

25% 25%25%25%A.A. 00

B.B. -1-1

C.C. 11

D.D. 1/01/0

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Which of the following is the Which of the following is the additive inverse of 4?additive inverse of 4?

¼ 0 -4 2

25% 25%25%25%A.A. ¼¼

B.B. 00

C.C. -4-4

D.D. 22

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Identify the property used.Identify the property used.(1 + 3) × (4 + 1) = (1 + 3) × (1 + (1 + 3) × (4 + 1) = (1 + 3) × (1 + 4)4)

Associa

tive pro

perty of ..

.

Associa

tive pro

perty of ..

.

Commutative pro

perty ..

Commutative pro

perty o...

25% 25%25%25%A.A. Associative property Associative property of multiplicationof multiplication

B.B. Associative property Associative property of additionof addition

C.C. Commutative Commutative property of property of multiplicationmultiplication

D.D. Commutative Commutative property of additionproperty of addition

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Jessica has found that Jessica has found that ¼ × 4/1 = 1. She has ¼ × 4/1 = 1. She has discovered an example of discovered an example of _____________._____________.

the m

ultiplicati

ve identity

the additi

ve id

entity

a multiplic

ative in

verse

an additive inve

rse

25% 25%25%25%A.A. the the

multiplicative multiplicative identityidentity

B.B. the additive the additive identityidentity

C.C. a multiplicative a multiplicative inverseinverse

D.D. an additive an additive inverseinverse

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What is the reciprocal, or What is the reciprocal, or multiplicative inverse , of -3?multiplicative inverse , of -3?

-3 3 1/3

-1/3

25% 25%25%25%A.A. -3-3

B.B. 33

C.C. 1/31/3

D.D. -1/3-1/3

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The expression x + (-x) = 0 The expression x + (-x) = 0 demonstrates which property?demonstrates which property?

Multi

plicative in

verse

Dist

ributive

property

Additive

inve

rse

Multi

plicative pro

perty o...

25% 25%25%25%A.A. Multiplicative Multiplicative inverseinverse

B.B. Distributive Distributive propertyproperty

C.C. Additive inverseAdditive inverse

D.D. Multiplicative Multiplicative property of zeroproperty of zero

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If the distributive property is If the distributive property is applied to 5(7 + 3), which is applied to 5(7 + 3), which is the result?the result?

5(7)(3)

5 + 7 + 3

5(7) + 3

5(7) + 5(3)

25% 25%25%25%

A.A. 5(7)(3)5(7)(3)

B.B. 5 + 7 + 35 + 7 + 3

C.C. 5(7) + 35(7) + 3

D.D. 5(7) + 5(3)5(7) + 5(3)

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