SOLUTION: please explain the difference between Distrributive, Associative and communitative properties. When i am doing my homework, and asked to do a question involving one of the properi

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Question 119917: please explain the difference between Distrributive, Associative and communitative properties. When i am doing my homework, and asked to do a question involving one of the properites, i cannot figure out which is the correct one. If there is some formula for remembering the correct solutions, please let me know.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I don't know of any "formula" for remembering these definitions but a thorough understanding of them is essential if you want to apply them correctly.
"Distributive Property" has to do with multiplying each number inside the parenthese by the number that is outside of the parentheses.
Example:
3%284%2B2%29+=+3%2A4%2B3%2A2= 12%2B6+=+18 Notice that the 3 outside the parentheses multiplies each term (number) inside the parenthese.
Another example:
5%286-4%29+=+5%2A6-5%2A4 = 30-20+=+10
Pay particular attention when the number outside the parentheses is negative.
The result of multiplying a number by a negative number is a change in the sign.
Example:
-3%287%2B3%29+=+%28-3%29%287%29%2B%28-3%29%283%29=-21%2B%28-9%29+=+-30
"Associative Property" has to do with grouping (associating).
This property tells you that the way in which numbers are grouped (associated) when added or multiplied does not change the sum or product.
Examples:
"Associative property of addition"
%283%2B4%29%2B5+=+3%2B%284%2B5%29 = 7%2B5+=+3%2B9 = 12
Notice that it doesn't matter whether you add the 3 and the 4 first then the 5 or add the 4 and the 5 first then the 3, you will get the same result.
"Associative property of multiplication"
%283%2A4%29%2A5+=+3%2A%284%2A5%29 =12%2A5+=+3%2A20 = 60
Here you'll see that it doesn't matter whether you multiply the 3*4 first then the 5 or multiply the 4*5 first then the 3, you get the same result.
"The Commutative Property" To "commute" means to change location or position.
The commutative (notice the spelling, it's not "communative") Property tells you that the order in which numbers are add or multiplied does not change the sum or product.
Examples:
Comutative property of addition:
5%2B8+=+8%2B5 = 13
5%2B6%2B7+=+6%2B5%2B7=7%2B6%2B5+=+18
Commutative property of multiplication:
3%2A4+=+4%2A3 = 12
5%2A6%2A7+=+7%2A6%2A5 = 210
I hope this helps!