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Math 5: Multiplication as Scaling 202 Views
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Description:
When you multiply two fractions, you end up with just a fraction of the previous fractions, and in fact, a smaller fraction than either of those other two fractions. But that's only a fraction of what this video is about.
Transcript
- 00:03
[Dino and Coop singing]
- 00:13
When we're multiplying fractions, it's helpful to have an idea of what the answer looks like
- 00:17
before we actually find it. [Confused boy looking at a blackboard]
- 00:19
It saves us from awkwardly introducing ourselves to the wrong fraction a bunch of times…so
- 00:24
embarrassing.
Full Transcript
- 00:25
And guess what?
- 00:26
There's a technique to do just that.
- 00:28
It's called…scaling.
- 00:29
And don't worry; unlike in cooking, it doesn't involve removing the scales from a dead fish.
- 00:34
Say what you will about math, but at least you don't need to touch any dead fish to do it. [Man runs away from smelly fish to vomit]
- 00:40
So, this whole "scaling" process is easiest to understand with an example.
- 00:44
Say we want to multiply four fifths by one third.
- 00:46
It turns out it's possible to visualize the product without actually doing any multiplying.
- 00:51
And nope, we don't even need to be a psychic. [Psychic women with crystal ball that has math problems on it]
- 00:54
Believe it or not, mathematicians have tools that are even more powerful than crystal balls
- 00:58
and big, chunky jewelry.
- 01:00
We start by thinking of four fifths times one third…
- 01:03
…as four fifths of one third, since they really mean the same thing.
- 01:08
Now it's time to think visually.
- 01:10
We can imagine a visual representation of one third…
- 01:13
…and then imagine what fourth fifths of that third would look like.
- 01:16
And we don't need to get our imaginary rulers out so that we can get an exact, imaginary
- 01:21
measurement. [Person with a ruler tries to measure the imaginary fraction and the ruler disappears]
- 01:22
Just by looking at it, you can tell that four fifths of a third will be a bit less than
- 01:27
a third.
- 01:28
So thanks to scaling we have a pretty good idea about the scale of our final answer.
- 01:32
And we didn't even need to touch a dead fish.
- 01:34
We'd call that a win. [Woman looks disgusted by a dead fish]
- 01:36
One interesting thing to notice is
- 01:37
the product is less than either of the fractions we were multiplying.
- 01:41
This isn't some kind of fluke.
- 01:42
It turns out that if we're multiplying two fractions that are each less than one… [Woman holds up a flute]
- 01:46
…the product will be less than either of those fractions.
- 01:49
In other words, less than one times less than one gets you even less. [Coop points to the blackboard]
- 01:55
Which, kinda makes sense.
- 01:56
When we multiply fractions that are less than one…
- 01:59
…we're always taking something that's less than one…
- 02:02
…and then taking a smaller part of that part…
- 02:04
…so we always end up with something even smaller than what we started with.
- 02:08
Unfortunately there's no way to use this knowledge to multiply homework by homework to get less
- 02:13
homework.
- 02:14
Sorry…we were disappointed, too. [School kid gets surrounded by lots of textbooks]
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