We need like tike terms to add or subtract. We don't need like terms to multiply or divide. Why
I need some ideas because i have to write a few paragraphs and dont know where to start.
Well, for addition have you ever heard the phrase "You can't add apples and oranges?" The basic idea is that you have terms like $\displaystyle 2mn + 3m^2n$. Now, the $\displaystyle mn$ and $\displaystyle m^2n$ form a kind of "category" (or perhaps "unit" is a better term?). What we need to know when we add these terms is how many categories of $\displaystyle mn$ and $\displaystyle m^2n$ we have. So we can't combine them in this case because they are not the same.
I can't seem to find a way to explain multiplication that well, so I'll leave it to someone else.
-Dan
When I read this yestreday afternoon, I thought it was easy to explain. But when I reached the multiplication/division part, I stopped. Couldn't explain that part well, without me saying corny, not-funny, blabberings.
Heck, let me do it again. With the blabberings.
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Addition/subtraction:
We cannot add or subtract unlike terms that's why we need like terms to add or subtract.
Say we have 3 dogs and 3 cats.
(Naturally we cannot add those, in whatever manner, mathematically or not!)
Ummm, say we have 3 apples and 3 oranges.
(3 apples) +(3 oranges) = (3 apples +3 oranges)
It cannot be = (6 apples and oranges).
6 appples and oranges could mean (1 apple and 5 oranges) or (5 apples and 1 orange) or (2 1/2 apples and 3 1/2 oranges) or ........
5y -32x = ?
5y -32x = 5y -32x -----------answer.
Not = -27(y-x) -----------not on our Earth. In Pluto, maybe.
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Mutiplication/Division:
(3 dogs) *(3 cats) = ?
More chaos than addition, I presume/assume/think.
(3 apples)*(3 oranges) = ?
(3 apples)*(3 oranges) = 9 apples*oranges -----answer.
Say what?
Yeah. That's Math. Ain't Math fun!
5y divided by 32x is what?
It is 5y /32x = (5/32)(y/x).
Why?
That's Math, that's why.
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That is why when they say, "collect like terms" in Math, you can do that in addition or subtraction only.
Comment:
Looks like addition/subtraction are choosy, while multiplication/division are happy-go-lucky or "anything, whatever, yeah", as long as there is no division by zero.
Sorry, girls.
Looks like addition/subtraction are females and multiplication/division are males. Young females and young males. Old females are more "anything goes" than old males.
I'm not sure if this helps, but multiplication wise:
3 x 2 is another way of saying 3 lots of 2 (or 2 lots of 3's) which can be simplified by saying there are 3 2 (3 Two's)...
So apple x orange = apple lots of orange, which can be simplified as apple orange...?
Not an educational answer at all, but it's certainly how I thought when I first saw that question