## jigglypuff314 one year ago 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)

1. 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?)

2. 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.

3. 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

4. misssunshinexxoxo

Exactly. When looking at a question and trying to solve, they forget to bring it over.

5. jigglypuff314

a question? the question is as simple as that they are given 25(x - 3) and they still get 25x - 3

6. jigglypuff314

7. misssunshinexxoxo

Honestly, I stick to the formulas of the properties. Always carry it over.

8. misssunshinexxoxo

Lol :)

9. 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

10. 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...

11. Loser66

*not the same,

12. 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.

13. 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.

14. jigglypuff314

15. hartnn

Try explaining with symbols $$\large ☻(☺+♥) = ☻☺+☻♥ \\ \text {this is distributing}$$ and then just replace the symbols with the numbers in the question!

16. 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!

17. UsukiDoll

^ awww that's cute and a neat way to show the distributive property done correctly.