Question

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)

Answer 1

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?)

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

Lol :)

Answer 8

yes, I know that too
but I what to know
(perhaps from someone who has made this mistake)
why they made such a mistake

Answer 9

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...

Answer 10

*not the same,

Answer 11

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.

Answer 12

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.

Answer 13

Thanks for your answers @Loser66 @UsukiDoll
this was really insightful ^_^

Answer 14

Try explaining with symbols
\(\large ☻(☺+♥) = ☻☺+☻♥ \\ \text {this is distributing}\)

and then just replace the symbols with the numbers in the question!

Answer 15

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!

Answer 16

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