Math 5: Multiplication as Scaling

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.

5th GradeMath
Elementary and Middle School5th Grade
LanguageEnglish Language

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]