Why minus x minus is plus

Can one have a negative brick? We can visualize a negative brick as little hole or gremlin in our brick box that eats up a brick when added leaving no hole or gremlin and no brick. And that difference is very important to understand.

Even though the construction of the hole is different the effect on future bricks added to the box is the same. This lets us we say the result is equal despite the different structure. We need a different approach to try to understand this. We know from the above that multiplying by -1 makes a brick-eating-hole exactly the size of brick being passed to it. In a sense multiplying by minus 1 creates the inverse of a brick: a brick-eating-hole.

Hopefully most people can see how with ease how multiplying by -4 is the same as multiplying by 4 and then by So we have. In English in our metaphor it means take a brick-eating-hole -1 and make 4 of them, then take the inverse of that which is 4 bricks. Or something like that! Actually the maths teacher response in the comments does a much better job of explaining things.

Think opposites or inverseses , not negatives. Negative and positive signs represent the direction. Multiplication is the simplest way of addition. Therefore two negative numbers when multiplied gives positive number.

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Leave a comment Trackback. Reply Quote 1. Reply Quote 2. Reply Quote 3. A modification of the vector explanation should probably hold… All numbers can be represented using Euler notation. Reply Quote 4. Reply Quote 5. Mike Croucher. Reply Quote 6. Thanks for all the comments people… valter — I like that way of looking at it and will try it out on our target when I next see her. Tom Rod. Reply Quote 7. David Jones. Reply Quote 8.

Reply Quote 9. Reply Quote Of course, multiplication corresponds to scaling , or stretching: for example, if we start at a point on the number line and multiply by 3, we will end up at a point three times as far from zero as we started. And what about multiplying by a negative number? It corresponds to a scale in the other direction : for example, if we start at a point on the number line and multiply by -3, we end up at a point on the other side of zero, and three times as far.

That is, multiplying by a negative number means that we flip from one side of zero to the other. So, of course if we start from the left of zero a negative number and multiply by a negative, we end up on the right of zero a positive number!

Also, I meant to put nice pictures in this post, but for now if I wait to make nice pictures it will never happen. I think the next question to your explanation would be: why is multiplication with -1 a reflection on the number line? Pingback: Negative times negative « The Number Warrior. When a factor decreases by 1, the product decreases by the amount of the other factor.

Here all the products will decrease by 3. Now we can apply the same pattern, only to the other factor. The product will now decrease by -3, or increase by 3. I like this because it is a pattern that is both easy to see and obviously true.

I had never seen your reasoning before, and I like it too. Shades of raising something to a -ve power here. David: all good points. If you have a positive and a negative, there is one dash left over, and the answer is negative. Of the original seven Millennium Prize Problems set by the Clay Mathematics Institute in , six have yet to be solved as of July, Skip to content Popular. Community Bot 1. It is not an idle question: I'm unsure at what level to answer this question Add a comment.

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