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Why a negative times a negative makes sense

Use the repeated addition model of multiplication to give an understanding of multiplying negative numbers. Created by Sal Khan.

Want to join the conversation?

• i still don't get it but Im trying
• It's alright just keep watching the video and listen carefully I hope this helps :)
• strange way to think about it... -2*-3=6
i have a large amount of warriors, each warrior can take out 2 scouts. an enemy has a camp and i send out three of my scouts -3, then they come back each having taken out two scouts -2. how many scouts did they take out total. -3*-2=6 does this make sense or did i not understand this well enough. word problems are rough haha
• 4years ago wow
• I believe it would help to think of 0 not as nothing but as an equilibrium or balanced amount, having the same on both sides. For example I spent a fair amount of time thinking about this and I came up with this holes and hills analogy.

A hill is positive, meaning a grassy hill and hole is negative, a hole I dug in the ground. Let say I have 10 hills and 10 holes to start so I'm balanced and I'm at 0 equilibrium.

1. If I then start and I make three more groups of three hills (3 x 3) I will get 9 extra hills. So I have +9 hills overall.

2. If I make three holes and make three groups of them (-3 x 3) I will get -9 or 9 more holes in the ground so I will have -9 or 9 more holes than hills.

3. If I take away 3 groups of 3 holes (-3 x -3) I will be removing a total of 9 holes therefore leaving me with, in regards to my example, 1 hole and 10 hills or 9 hills equilibrium so +9.

This example is the same as you might think about balance scales it's the same principle. It works the same with money and I believe it applies in possibly all areas. In money the money you no longer have to pay back in debt payment becomes yours and is therefore kept by you as a positive amount. In wood working if you no longer have to build and give 3 items to three people you can keep those items yourself and you'll be up 9 items. Ect... Ect....

What do you think?
• Upvote if you are just watching this for energy points ๐
• Who is the ancient philosopher? By the way you are a really good artist.
• I don't think that it a specific ancient philosopher. He is just trying to put it into perspective

And I agree he is a very good drawer
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• if i were a ancient philosopher...!

Bah, i'd leave it up to the gods and future generations to figure out.
• Oh no! Quick! Figure it out on your own!
• my head is exploding and nothing makes any sense
:)
• Yeah, me too I'm really confused and I don't understand...
• This is a way I think of a negative times a negative.

I visualize the number line as a scale with a pivot on the 0. I think that the "0" always has to be at the center of the two sides (negative/positive infinity) in order for them to be balanced. If I see -3*-4 it means "start from zero" and take out 4 groups of negative 3s from the number line (make them disappear). At this point the center between the positive and negative infinity would be skewed to the left by 12, otherwise the two sides wouldn't be balanced.

This is the best sense I can make of it!
• I just view it as a 0 and removing a negative is the same as adding a positive. Like how making it 2 degrees warmer is the same as making it 2 degrees less cold. If that makes sense.
• why dose it take so long to say one anwser
• Gโโโโโโโโโโโโโโโโโโโโโโโโโโ
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