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Number Properties. Rules of the game 2-7-1. Properties. Properties are the rules of the game. If the rules are changed a different kind of math is played. These properties are for everyday math. Commutative Property. Order doesn’t matter. Commutative Property.

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Number properties

Number Properties

Rules of the game

2-7-1


Properties
Properties

  • Properties are the rules of the game.

  • If the rules are changed a different kind of math is played.

  • These properties are for everyday math.


Commutative property

Commutative Property

Order doesn’t matter


Commutative property1
Commutative Property

  • Commutative property of addition.

    • a + b = b + a

    • 7 + 8 = 8 + 7

    • (-3)+4=4+(-3)

    • The commutative property says the order doesn’t matter for addition.


Commutative property2
Commutative Property

  • Commutative property of addition.

    • a + b = b + a

    • 7 + 8 = 8 + 7

    • (-3)+4=4+(-3)

    • The commutative property says the order doesn’t matter for addition.


Associative property

Associative Property

Grouping Doesn’t Matter


Associative property1
Associative Property

  • Associative property of addition

    • (a+b)+c = a+(b+c)

    • (7+8)+2=7+(8+2)

    • 15+2 = 7 + 10

    • The associative property says the grouping doesn’t matter for addition.


Associative property2
Associative Property

  • Associative property of multiplication.

    • (axb)xc=ax(bxc)

    • (7x8)x2=8x(7x2)

    • 56x2=8x14

    • The associative property says the grouping doesn’t matter for multiplication.


Identity

Identity

No change


Identity1
Identity

An identity for a particular operation doesn’t change the identity of the number when the operation is done.


Identity2
Identity

  • Additive Identity is 0

    • a+0=a

    • 7 + 0 =7

    • Zero plus a number is that number.


Identity3
Identity

  • Multiplicative Identity is 1

    • 1xa=a

    • 8x1=8

    • One times a number is that number.


Inverse

Inverse

Opposite


Inverse1
Inverse

  • Additive inverse - opposite

  • Another number that added to the original number is equal to the additive identity. 0

  • Multiplicative inverse

  • Another number that multiplied by the original number is equal to the Multiplicative identity. 1


Distributive property

Distributive Property

Connecting Addition to Multiplication


Distributive property1
Distributive Property

  • Distributive property

    • a(b+c)=ab+ac

    • example

    • example

    • Multiplying a sum by some number is the same as multiplying each term by that same number.


Identify the properties
Identify the Properties

3x(4x)=3(4)xx=12x2

commutative and associative properties of multiplication.


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