Multiplication as Scaling: Why a Negative Times a Negative Is Positive // Math Minute [#56]

I would not generally describe myself as a builder, but today I am proud to release a special multiplication visualizer that I built in Desmos. You can play around with it yourself at this link: bit.ly/Scaling....
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Although we usually learn multiplication initially as some form of repeated addition, this intuition fails us in two ways: it doesn't help at all when it comes to irrational numbers, which by definition can't be separated into useful equal parts. But more importantly it tends to misinform us when it comes to why negative numbers multiplied by other negative numbers return positive results. Teachers have various workarounds to this, but my preference is to simply go with what multiplication actually is: scaling. When we think of multiplication this way, it reveals to us that the number line itself is expanding and contracting with different scalars, and even more important, that the number line is reversing when we multiply by negatives.
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[@allworld1357]

This visualization is really helpful. I love the fact that you showed the "flipping of the number line" effect.

[@lazerlegae3516]

Your scalling method makes perfect sense. Thank you

[@kamome7098]

Good video. And it shows why multiplying a negative with a positive results in negative

[@matthewenglish4721]

This is an amazing visualization!

[@polymathematic]

glad you like it!

[@jeannedobgenski5159]

Incredible. Great explanation!

[@ThanHtayAung-q1d]

Amazing video. I must subscribe this channel. 🎉🎉🎉

[@Francesca-nq4if]

Genius

[@seanmurphy7727]

Great visualization! Do you think we do a disservice it kids if we teach multiplication as repeated addition?

[@polymathematic]

This is a great question. I wouldn't say disservice. But I would say that, like counting on fingers, it's a concept we use for a time, but then need to move beyond. If I have a 3rd grader who thinks multiplication *is* repeated addition, so be it. If I have a 10th grader who thinks that? That's more of a problem.

[@LDRep]

what actual in life example that taking advantage from this math? -- x -- = +

[@polymathematic]

computing how much you still owe on your mortgage

[@LDRep]

@@polymathematic wow you are right.. i crosscheck it with chatgpt.. and tells certain economics situations have negative interest rate.. so amount i owe reduced