Mathematical Properties

Mathematical Properties

by

​E. Alexander

​Learning Targets

​I can apply the commutative, associative, and distributive properties appropriately in adding and subtracting rational numbers. 

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I can apply the commutative, associative, and distributive properties appropriately in multiplying and dividing rational numbers. 

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Properties of Addition and Multiplication​

​1. Commutative Property of Addition

​2. Commutative Property of Multiplication

​3. Associative Property of Addition

​4. Associative Property of Multiplication

​5. Identity Property of Addition

​6. Identity Property of Multiplication

​7. Distributive Property of Multiplication over Addition

​8. Distributive Property of Multiplication over Subtraction

​9. Zero Property of Multiplication

​Commutative Property of Addition

The order in which you ​add numbers does not change the sum

​Commutative Property of Multiplication

​The order in which you ​multiply numbers does not change the product

​Associative Property of Addition

Changing the ​grouping of numbers when adding does not change the sum

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​Associative Property of Multiplication

​Changing the ​grouping of numbers when multiplying does not change the product

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Multiple Choice

Which Property is illustrated when 

6 + (-3) = (-3) + 6

is shown?

• Commutative Property of Addition

• Commutative Property of Multiplication

• Associative Property of Addition

• Associative Property of Multiplication

Multiple Choice

Which property is shown?

-7(2 $$\cdot$$  4) = (-7 $$\cdot$$  2)4

• Associative Property of Addition

• Associative Property of Multiplication

• Commutative Property of Addition

• Commutative Property of Multiplication

Poll

I can identify commutative and associative properties

• Yes

• No

• I need more practice

• I can't tell the difference between the two yet

​Identity Property of Addition

​Any number added to zero will have the same number as the sum

​Identity Property of Multiplication

​Any number multiplied by 1 will result in the same number being the product.

Multiple Choice

3 + 1 = 4 

is an example of which property?

• Associative property of addition

• Commutative Property of addition

• Identity Property of Addition

• Its not a property

Multiple Choice

0 + (-4) = -4

is an example of which property?

• Associative Property of addition

• Commutative Property of Addition

• Identity Property of Addtion

• It is not a property

Multiple Choice

0 + ? = 6 

Which property is used?

• Associative Property of Addition

• Commutative Property of Addition

• Identity Property of Addition

• Identity Property of Multiplication

​Distributive Property of Multiplication over addition

​The Distributive Law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.

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​Distributive Property of Multiplication over subtraction

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Multiple Choice

Using the distributive property of Multiplication over Addition, how is this statement re-written?

6[4 + (-5)] = ?

• 6(4) + (-5)

• -5(6) + 6(4)

• 6(-5) - 6(4)

• 6(4) + 6(-5)

Multiple Choice

Which property is being used in the statement?

8 + (5 + 4) = (5 + 4) + 8

• Associative Property of Addition

• Associative Property of Multiplication

• Commutative Property of Addition

• Commutative Property of Multiplication

​Zero Property of Multiplication

​The product of any number and zero, is zero.

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Multiple Choice

Which property is show in the statement?

b + 0 = b

• Zero Property of Multiplication

• Identity Property of Addition

• Identity Property of Multiplication

• Associative Property of Addtion

Multiple Choice

Which property is shown in the statement?

3(a + 9) = 3(a) + 3(9)

• Zero Property of Multiplication

• Distributive Property of Multiplication over Subtraction

• Distributive Property of Multiplication over Addition

• Commutative Property of Addition