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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.