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Number Properties Rules of the game 2-7-1

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**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.

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Commutative Property Order doesn’t matter

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**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.

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**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.

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**Grouping Doesn’t Matter**

Associative Property Grouping Doesn’t Matter

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**Associative Property Associative property of addition**

(a+b)+c = a+(b+c) (7+8)+2=7+(8+2) 15+2 = The associative property says the grouping doesn’t matter for addition.

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**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.

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Identity No change

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

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**Identity Additive Identity is 0 a+0=a 7 + 0 =7**

Zero plus a number is that number.

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**Identity Multiplicative Identity is 1 1xa=a 8x1=8**

One times a number is that number.

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Inverse Opposite

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**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

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**Distributive Property**

Connecting Addition to Multiplication

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**Distributive Property**

a(b+c)=ab+ac example Multiplying a sum by some number is the same as multiplying each term by that same number.

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**Identify the Properties**

3x(4x)=3(4)xx=12x2 commutative and associative properties of multiplication.

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Properties of Real Numbers CommutativeAssociativeDistributive Identity + × Inverse + ×

Properties of Real Numbers CommutativeAssociativeDistributive Identity + × Inverse + ×

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