jigglypuff314
  • jigglypuff314
I have a question regarding the distributive property... where a(b+c) = a*b + a*c but I have seen many many many people make the mistake of > a(b+c) = a*b + c or if not that, then when there are negatives involved... supposed to be --> -a(b - c) = (-a)*b + (-a)*(-c) but instead --> -a(b - c) = -a*b - a*c (or some variation)
Mathematics
katieb
  • katieb
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jigglypuff314
  • jigglypuff314
I want to understand: - Why this is such a common mistake? The concept is clear (to me at least) so I can't seem to find why others make that mistake.. - How to teach it in a way to get the point across and stop people from making that mistake? (What is your method of teaching this concept that seems to work?)
misssunshinexxoxo
  • misssunshinexxoxo
Sometimes could be the arrangement of how they perceive it. We truly know it's a(b+c) = a*b + a*c or -a(b - c) = (-a)*b + (-a)*(-c). Sometimes in mathematical problems could be differentiated to reflect a question. These are the foreground of the distribution property.
jigglypuff314
  • jigglypuff314
I was thinking it might be as simple as that they do the a*b part and simply don't remember that they have to bring the "a" over to the "c" as well

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misssunshinexxoxo
  • misssunshinexxoxo
Exactly. When looking at a question and trying to solve, they forget to bring it over.
jigglypuff314
  • jigglypuff314
a question? the question is as simple as that they are given 25(x - 3) and they still get 25x - 3
jigglypuff314
  • jigglypuff314
misssunshinexxoxo
  • misssunshinexxoxo
Honestly, I stick to the formulas of the properties. Always carry it over.
misssunshinexxoxo
  • misssunshinexxoxo
Lol :)
jigglypuff314
  • jigglypuff314
yes, I know that too but I what to know (perhaps from someone who has made this mistake) why they made such a mistake
Loser66
  • Loser66
To me, the best way to "awake" person who has that mistake is to give him/her an example like Suppose you and me together give out the same amount of money to buy a lottery ticket. I put $1 dollar and you put $2 . So, our fund is (1 +2) where 1 is my money and 2 is your money. Fortunately, we win with the price is $1,000,000* our fund. Now, we calculate how to divide the price. I do: $1,000,000 *(1 +2) = $1,000,000*1 +2, the first number is my price and the second one is yours. Hence, I get $1,000,000 and you get $2. Do you accept that result?? hehehe...
Loser66
  • Loser66
*not the same,
UsukiDoll
  • UsukiDoll
I bet it's due to distributing too fast (or working on a problem too fast) and end up making a mistake by accident. Test anxiety can cause people to become nervous and just write...solve... so take this problem for example (as you wrote earlier) 25(x - 3) using the distributive property we are supposed to multiply 25 throughout the parenthesis 25(x-3) 25(x)+(-3)(25) 25x-75 Maybe if we say that we are supposed to distribute the 25 thoughout (x-3) as in multiply 25 times x multiply 25 times -3 that concept will stick.
UsukiDoll
  • UsukiDoll
Last semester, I've read my Math books with a bad case of astigmatism so I saw double sentences and the tiny fonts for the exponent were really hard to see.
jigglypuff314
  • jigglypuff314
Thanks for your answers @Loser66 @UsukiDoll this was really insightful ^_^
hartnn
  • hartnn
Try explaining with symbols \(\large ☻(☺+♥) = ☻☺+☻♥ \\ \text {this is distributing}\) and then just replace the symbols with the numbers in the question!
hartnn
  • hartnn
chances of error here are less because when you choose a symbol to replace, you will, without any mistake, replace all the symbols with the proper number!
UsukiDoll
  • UsukiDoll
^ awww that's cute and a neat way to show the distributive property done correctly.

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