math properties commutative, associative, distributive, identity, and zero properties
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Math Properties
Commutative, Associative, Distributive, Identity, and Zero
Properties
𝐴+𝐵=𝐵
+𝐴
𝐴 (𝐵+𝐶 )=𝐴𝐵+𝐴𝐶
𝐴+(𝐵+𝐶 )=(𝐴+𝐵 )+𝐶
𝐴+0=𝐴
𝐴∗𝐵=𝐵∗ 𝐴
𝐴∗1=𝐴 𝐴∗0=0
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.
Commute
• To commute means to travel from one place to another.
• For example, you commute to school in the morning.
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) 2 + 3 = 3 + 2• Both 2 + 3 and 3 + 2 equal 5.
The commutative property may be used with addition as seen previously and also with 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.
Associate
• An associate is a friend or someone you work with.
• For example, the head cheerleader is an associate of the school mascot.
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.
Associative Property
The associative property is when a number associates with a different number.
A + (B + C)
(A + B) + CA + + CB
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.
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.
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?)0
Zero• The additive identity is zero.
• We can add zero to any number and the answer is the original
number.
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
Identity Properties
Identity Property of Addition
A + 0 = A
Identity Property of Multiplication
A * 1 = A
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.
SummaryProperty 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
Distribute
• Distribute means to deliver or pass out• If we distribute food to three boxes, we put
food in each of the three boxes
Distributive Property
• A(B + C) = A*B + A*C• The A is the food and the boxes are B and C.• We pass out A to each of B and C.• In this case that means that we multiply A by
both B and C separately and then add the resulting products.
Ex) 4(X + 3)
4
X 34X 12
=4X + 12
Now you try these examples.
1) 5(X + 3) =
2) 7(X + 4) =
3) 2(Z -3) =
5X + 15
7X + 28
2Z - 6
SummaryProperty 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
Distributive Property A(B + C) = A*B + A*C
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