It is not an idle question: I'm unsure at what level to answer this question Add a comment. Active Oldest Votes. Arturo Magidin Arturo Magidin k 49 49 gold badges silver badges bronze badges. Bill Dubuque Bill Dubuque k 36 36 gold badges silver badges bronze badges. Upcoming Events. Featured on Meta. January 5, at am. Jagjit Jack says:. May 10, at am. May 23, at am. Another Soln This is not a proof, however a demonstration for a curious kid why negative times negative is positive.
Nullius in Verba says:. Then as soon as you continue the progression to k negative, the result is obvious. July 12, at am. Leona says:. June 9, at am. Search for:. Brent's blogging goal. Blog at WordPress. Follow Following. The Math Less Traveled Join other followers. Sign me up. Already have a WordPress. Log in now.
The most intuitive way I know for demonstrating this idea is:. So a filled up hole has the same value as flat ground — zero. With this heaps and holes idea as a learning system the maths works beautifully and intuitively. How many groups? This is the grouping type of division. Each would get 3 holes. This is the sharing type of division. But there are lots of zeros!! So if we convert two zeros we create another two holes and heaps. Now we have 5 heaps and 2 holes. So now we can take away -2 tho holes we just created leaving… 5 heaps.
Well, I am no mathematician but I cannot find errors in the original proof. Most of the other are life problems constructions not math. What about a positive number multiplied by a negative number? What does it even mean? What about -1 bricks? 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. Walking Randomly Because it's more fun than getting there in a straight line.
September 28th, Categories: general math Tags:. Practice: Multiplying negative numbers. Dividing positive and negative numbers. Practice: Dividing negative numbers. Why a negative times a negative is a positive. Why a negative times a negative makes sense.
Multiplying negative numbers review.
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