Transcript Associative_Property

Associative
Property
• You are tired of studying and need a break.
You
need to make a decision as to which group you
want to associate with during your break.
• The blue men
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• or your friends
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• Does the total number of people change if you
choose to go with the blue men
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• or your group of friends?
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• The number of people didn’t change but the
group you were associated with changed.
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• The Associative Property has the same idea.
• It doesn’t matter which group you add first,
1  3  10  1  3  10
14  14 • the result is the
same.
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ages/photobank/web/01543.jpg
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• You can group in any order and get the same
answer.
• How does this look in Algebra?
a  b   c  a  b  c
• Try different numbers for a, b, and c to see this is
true.
• Notice the only thing that changed is location of
the parenthesis.
Is Subtraction
Associative?
• Try these problems to see what you get:
8  3  2
5   2
8  3  2 
3
7
• Different answers.
not associative.
8  1
This means subtraction is
•
•
•
Is Multiplication
Associative?
You are buying your first car but need to finance a portion of
the cost. The monthly payment is $200 a month for 4 years.
How much will you have paid at the end of 4 years?
Solve using (payment)(# of months in a year)(# of years)
Here are the 2 grouping options for solving....
200 12 4
2400  4
9600
200  12  4 
200  48 
9600
• Notice you got the same answer.
This
means Multiplication is Associative.
• You can group multiplication in any order
and get the same result.
• Here’s what it looks like in Algebra:
xyz  x yz 
Is Division Associative?
• Try these to see what you get...
48  4   2
12   2
48  4  2 
48  2 
6
24
• Big different, huh?
Division is not associative.
Key points to
remember...
• Addition and Multiplication are associative.
• Subtraction and Division are not associative.