If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# 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 :)
• 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?
• This is a good way to think of it!
(1 vote)
• 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
• 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!
• Pain is just a mindset
• 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
• So what I dont understand is
• my head is exploding and nothing makes any sense
:)
• Khan explained it really well, yet the "philosopher" seemed to be judging his work by the way he looks at it.