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Commutative, Associative, Distributive, Identity, and Zero Properties

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Presentation on theme: "Commutative, Associative, Distributive, Identity, and Zero Properties"— Presentation transcript:

1 Commutative, Associative, Distributive, Identity, and Zero Properties
𝐴∗𝐵=𝐵∗𝐴 𝐴+𝐵=𝐵+𝐴 𝐴+ 𝐵+𝐶 = 𝐴+𝐵 +𝐶 Math Properties 𝐴∗1=𝐴 𝐴∗0=0 Commutative, Associative, Distributive, Identity, and Zero Properties 𝐴 𝐵+𝐶 =𝐴𝐵+𝐴𝐶 𝐴+0=𝐴

2 What are properties? Math Properties are rules in math. Properties are always true for every number. **Once you go beyond the set of Real numbers the properties may no longer hold.

3 Commute To commute means to travel from one place to another.
For example, you commute to school in the morning.

4 Commutative Property Just like you commute from home to school, a number may commute from one spot to another. A + B = B + A (The numbers change places.) This is called the commutative property of addition. Ex) = 3 + 2 Both and equal 5.

5 The commutative property may be used with addition and multiplication.
A * B = B * A Ex) 3 * 5 = 5 * 3 Both 3 * 5 and 5 * 3 equal 15. This is called the commutative property of multiplication.

6 Associate An associate is a friend or someone you work with.
For example, the head cheerleader is an associate of the school mascot.

7 Suddenly the cheerleader associates with someone else.
Now imagine the football team played a late game and the cheerleader and mascot forgot to study for the math test. Suddenly the cheerleader associates with someone else.

8 Associative Property A + (B + C) (A + B) + C A + + C B
The associative property is when a number associates with a different number. A + (B + C) (A + B) + C A C B

9 Associative Property (A + B) + C = A + (B + C) is called the associative property of addition. Ex) (2 + 3) + 4 = 2 + (3 + 4) The order in which you add does not change your answer. A * (B * C) = (A * B) * C is called the associative property of multiplication.

10 Identity Your identity is who you are.
Changing your clothes or getting a new haircut does not change your identity. Your identity remains the same.

11 Identity Property of Addition
A number also has an identity The identity of a number is the value of the number The additive identity is the number that when added to another number does not change the identity of the original number 3 + __ = 3 (What goes in the blank?)

12 Identity Property of Multiplication
We also have a multiplicative identity 3 * __ = 3 (What goes in this blank?) We can multiply any number by one and the answer will be the original number. 1

13 Identity Properties A + 0 = A A * 1 = A Identity Property of Addition
Identity Property of Multiplication A + 0 = A A * 1 = A

14 Zero Property The zero property sounds just like what it is, a property about zero. A * 0 = 0 The zero property tells us that any number multiplied by zero equals zero.

15 Summary Property Name Rule Commutative Property of Addition
A + B = B + A Commutative Property of Multiplication A * B = B * A Associative Property of Addition A + (B + C) = (A + B) + C Associative Property of Multiplication A * (B * C) = (A * B) * C Identity Property of Addition A + 0 = A Identity Property of Multiplication A * 1 = A Zero Property A * 0 = 0


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