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.
|Elementary and Middle School||5th Grade|
And guess what?
There's a technique to do just that.
And don't worry; unlike in cooking, it doesn't involve removing the scales from a dead fish.
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]
So, this whole "scaling" process is easiest to understand with an example.
Say we want to multiply four fifths by one third.
It turns out it's possible to visualize the product without actually doing any multiplying.
And nope, we don't even need to be a psychic. [Psychic women with crystal ball that has math problems on it]
Believe it or not, mathematicians have tools that are even more powerful than crystal balls
and big, chunky jewelry.
We start by thinking of four fifths times one third…
…as four fifths of one third, since they really mean the same thing.
Now it's time to think visually.
We can imagine a visual representation of one third…
…and then imagine what fourth fifths of that third would look like.
And we don't need to get our imaginary rulers out so that we can get an exact, imaginary
measurement. [Person with a ruler tries to measure the imaginary fraction and the ruler disappears]
Just by looking at it, you can tell that four fifths of a third will be a bit less than
So thanks to scaling we have a pretty good idea about the scale of our final answer.
And we didn't even need to touch a dead fish.
We'd call that a win. [Woman looks disgusted by a dead fish]
One interesting thing to notice is
the product is less than either of the fractions we were multiplying.
This isn't some kind of fluke.
It turns out that if we're multiplying two fractions that are each less than one… [Woman holds up a flute]
…the product will be less than either of those fractions.
In other words, less than one times less than one gets you even less. [Coop points to the blackboard]
Which, kinda makes sense.
When we multiply fractions that are less than one…
…we're always taking something that's less than one…
…and then taking a smaller part of that part…
…so we always end up with something even smaller than what we started with.
Unfortunately there's no way to use this knowledge to multiply homework by homework to get less
Sorry…we were disappointed, too. [School kid gets surrounded by lots of textbooks]