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July 7th, 2014, 01:32 AM  #1 
Senior Member Joined: Oct 2012 Posts: 460 Thanks: 0  Easy clear example for x(y)
Hello! If I want to explain to a small kid, why is 3(2) = 3+2, what woould be the best example form real life explaining that simply and clearly? many thanks for all the ideas!!! 
July 11th, 2014, 01:20 PM  #2 
Senior Member Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 
It is better just to memorize in early age. Something like this: ( â‰¡ + (an enemy of my enemy is my friend) (+ â‰¡  (an enemy of my friend is my enemy) +( â‰¡  (a friend of my enemy is my enemy) +(+ â‰¡ + (a friend of my friend is my friend) Later, you can explain adding money that he/she has in a wallet and has as a debt. 
July 11th, 2014, 01:42 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,685 Thanks: 2666 Math Focus: Mainly analysis and algebra  Suppose I have some sweets, but my mum tells me to share them with my friend. So I decide to give him two sweets, which would leave me with three. But just as I'm about to hand them over, his mum tells him that his dinner is ready and he has to go home. Bonus for me! I don't have to give him the sweets. So I don't have the minus two, I can subtract the action of taking two sweets away from myself and find that I now have five sweets, rather than the three I was expecting.

July 11th, 2014, 05:25 PM  #4 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88 
When we first learn about numbers, they represent "a number of things". For example, 2 is the number of one orange, and another orange. So what in the world could 2 oranges possibly mean? When we introduce SIGNS to numbers, a number now has TWO pieces of information: a sign, and an amount. The amount means the same thing it always did. So what does the SIGN mean? It's a direction. For example, if "positive" means TO me ( I get two oranges), then negative means AWAY from me (I lose two oranges). There are still "two oranges" (the amount), but they have different directions. So, what does "minus" mean, in the absence of an "amount" attached? It means: "change direction" (or, as they say in the military: "About face"). If you "about face" twice (subtract a negative), your direction remains unchanged, which is what the ABSENCE of a minus sign means. Since we don't really need a SIGN to indicate "not changing the sign", we write: $a + b$ instead of $+a + (+b)$, which would be silly. 

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