SOLUTION: I have to do a project about the associative property. I need example problems but I don't quite understand it well enough. I already have some simple problems but my teacher wants

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Question 156679: I have to do a project about the associative property. I need example problems but I don't quite understand it well enough. I already have some simple problems but my teacher wants challenge problems too. Can you give me an example of a challenge problem for the associative property of addition and another for the associative property of multiplication so I can see how to make one. Thank you very much.
Troy

Answer by Electrified_Levi(103) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, Hope I can help
.
I have to do a project about the associative property. I need example problems but I don't quite understand it well enough. I already have some simple problems but my teacher wants challenge problems too. Can you give me an example of a challenge problem for the associative property of addition and another for the associative property of multiplication so I can see how to make one. Thank you very much.
Troy
.
I think of associative property as " how you arrange the parentheses, associative = "arrange"(parentheses),(both associative, and arrange start with "a" )
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Here are some examples of associative property
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Example: +%285+%2B+3%29+%2B+7+=+5+%2B+%283+%2B+7%29+ = +%288%29+%2B+7+=+5+%2B+%2810%29+ = +15+=+15+
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Example: +%286+-+4%29+%2B+3+=+6+%2B+%28-4%2B3%29+ = +%282%29+%2B+3+=+6+%2B+%28-1%29+ = +5+=+6+-1+ = +5+=+5+ ( +6-4+ is the same thing as saying +6+%2B+%28-4%29+)
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Example: +%28x+%2B+8x%29+%2B+10x+=+x+%2B+%288x+%2B+10x%29+ = +%289x%29+%2B+10x+=+x+%2B+%2818x%29+ = +19x+=+19x+
.
Now lets use multiplication in the associative property
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Example: +%282+%2A+6%29+%2A+7+=+2+%2A+%286+%2A+7%29+ = +%2812%29+%2A+7+=+2+%2A+%2842%29+ = +84+=+84+
.
Example: +%28x+%2A+4%29+%2A+y+=+x+%2A+%284+%2A+y%29+ = +%284x%29+%2A+y+=+x+%2A+%284y%29+ = +4xy+=+4xy+
.
Example: +%28x%5E2+%2A+5%29+%2A+y%5E3+=+x%5E2+%2A+%285+%2A+y%5E3%29+ = +%285x%5E2%29+%2A+y%5E3+=+x%5E2+%2A+%285y%5E3%29+ = +5x%5E2y%5E3+=+5x%5E2y%5E3+
.
Here is a challenging one for multiplication
.
+%28a%5E12+%2A+%2812b%29%5E3%29%2A+%288c%29%5E4+=+a%5E12+%2A+%28+%2812b%29%5E16+%2A+%288c%29%5E10%29+ =
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+%28a%5E12+%2A+1728b%5E3%29%2A+4096c%5E4+=+a%5E12+%2A+%28+1728b%5E3+%2A+4096c%5E4%29+ =
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+%281728a%5E12b%5E3%29%2A+4096c%5E4+=+a%5E12+%2A+%28+7077888b%5E3c%5E4%29+ =
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+7077888a%5E12b%5E3c%5E4+=+7077888a%5E12b%5E3c%5E4+
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If you are trying to use just numbers, here is another multiplication using associative property
.
+%28%28%286%29%284%29%29%5E2+%2A+%28%283%29%2812%29%29%5E3%29+%2A+%28%285%29%284%29%29%5E4+=+%28%286%29%284%29%29%5E2+%2A+%28%28%283%29%2812%29%29%5E3+%2A+%28%285%29%284%29%29%5E4%29+ =
.
+%28%2824%29%5E2+%2A+%2836%29%5E3%29+%2A+%2820%29%5E4+=+%2824%29%5E2+%2A+%28%2836%29%5E3+%2A+%2820%29%5E4%29+ =
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+%28576+%2A+46656%29+%2A+160000+=+576+%2A+%2846656+%2A+160000%29+ =
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+%2826873856%29+%2A+160000+=+576+%2A+%287464960000%29+ =
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+4299816960000+=+4299816960000+
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You can always use smaller numbers, if that was too hard
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A challenging problem using addition and associative problems is
.
+%28%28%288%29%287%29%29%5E2+%2B+%28%285%29%283%29%29%5E3%29+%2B+%28%284%29%289%29%29%5E3+=+%28%288%29%287%29%29%5E2+%2B+%28%28%285%29%283%29%29%5E3+%2B+%28%284%29%289%29%29%5E3%29+ =
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+%28%2856%29%5E2+%2B+%2815%29%5E3%29+%2B+%2836%29%5E3+=+%2856%29%5E2+%2B+%28%2815%29%5E3+%2B+%2836%29%5E3%29+ =
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+%283136+%2B+3375%29+%2B+46656+=+3136+%2B+%283375+%2B+46656%29+
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+%286511%29+%2B+46656+=+3136+%2B+%2850031%29+ =
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+53167+=+53167+
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You can also do more than three numbers
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+%281%2B2%29%2B3%2B4%2B5%2B6%2B7%2B8+=+1%2B%282%2B3%29%2B4%2B5%2B6%2B7%2B8+=+1%2B2%2B3%2B4%2B5%2B%286%2B7%29%2B8+ =
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+%283%29%2B3%2B4%2B5%2B6%2B7%2B8+=+1%2B%285%29%2B4%2B5%2B6%2B7%2B8+=+1%2B2%2B3%2B4%2B5%2B%2813%29%2B8+ =
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+%283%29%2B33+=+%285%29+%2B+31+=+%2813%29%2B23+ =
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+36+=+36+=+36+
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You can also do more than two numbers in side the parentheses
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Lets use multiplication
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+%282%2A3%2A5%29%2A7%2A11%2A13%2A15%2A20+=+2%2A3%2A5%2A%287%2A11%2A13%29%2A15%2A20+=+2%2A3%2A5%2A7%2A%2811%2A13%2A15%29%2A20+ =
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+%2830%29%2A7%2A11%2A13%2A15%2A20+=+2%2A3%2A5%2A%281001%29%2A15%2A20+=+2%2A3%2A5%2A7%2A%282145%29%2A20+ =
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+%2830%29%2A+300300+=+%281001%29%2A9000+=+%282145%29%2A+4200+
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+9009000=+9009000=+9009000
.
Hope I helped, Levi