ShmoopTube

00:03

[Coop and Dino singing]

00:14

The members of our family are some of the most important people in our life.

00:17

Yes, even when they force us to go to bed way too early, when there's still so much [Father telling daughter to go to bed and switches off TV]

00:20

good TV to watch.

00:22

And believe it or not, some numbers have families of their own!

00:25

They're called fact families. [Framed photo's of numbers]

00:27

And since numbers don't sleep, they never have to go to bed.

00:30

…of course, they also don't have eyes, so they can't really watch TV… [Numbers 3 and 8 attempting to watch TV]

00:33

Anyway, a fact family is a set of three numbers, which are either related through addition

00:38

and subtraction, or multiplication and division.

00:40

For example, two, three, and six are a fact family, because two times three is equal to

00:45

six…

00:46

…as is three times two.

00:48

It's also true that six divided by two is three… [Dino pointing to the chalkboard at a fact family example]

00:50

…and six divided by three is two.

00:53

There are even fact families with fractions.

00:56

If we divide two by three, we get two thirds.

00:59

These family ties grow tighter when we see that three times two thirds is two… [Coop pointing to a fact family of fractions]

01:03

…and two divided by two thirds is three.

01:06

You might not see a lot of equations in your family photo albums, but for two, three, and

01:09

two thirds, these equations are clear reminders that they're all part of one happy family.

01:15

We might wonder why it is that all these calculations happen to work. [Girl thinking about fact families]

01:18

Well, when in doubt, draw it out.

01:20

And no, this doesn't just work because it rhymes.

01:22

First, let's look at what we mean when we divide two by three.

01:25

Take two identical bars… [Two identical bars side by side]

01:27

…and divide each of them into three bars of equal size.

01:30

If we shade in two from each bar, and count them up…

01:33

…we get a total of four parts out of six…

01:35

…which is just a fancy way of saying two thirds.

01:37

Not quite "afternoon tea with the Queen" fancy, but we're not sure if that's the kind of fancy [Girl drinking tea with the queen]

01:42

we'd even want to experience.

01:43

We can do similar stuff for the other equations.

01:46

If we want to show that three times two thirds is two, we start with three identical bars.

01:51

Then we divide them each into three…

01:53

…and shade in two of the three parts of each bar. [Three identical bars with 2 out of 3 sections for each bar shaded yellow]

01:56

If we rearrange the colored parts, we see that they make up two wholes.

02:00

Similarly, to check that two divided by two thirds is three, we start with two identical

02:05

bars…

02:06

…and divide each of them into three bars of equal size.

02:08

Now we count how many pairs of those smaller bars we can find, and the answer is – surprise

02:12

surprise – three.

02:14

So the moral of the story? [Family of numbers hugging]

02:15

You can always depend on your family to be there for you.

02:18

Until you want to stay up late to watch TV.

02:20

Then those suckers will stab you in the back faster than you can say, "emancipation." [Father shouting at girl and girl runs off to bed]

Full Transcript