Math 5: Dividing Fractions to Determine Business Growth or Loss

“But when will I ever use math in real life?” you ask. Here. Literally right here. You’re welcome.

5th GradeMath
Elementary and Middle School5th Grade
LanguageEnglish Language

Transcript

00:27

Well…yeah, actually.

00:28

This kind of math's really important in business. [Students walks across classroom yelling and holding math workings]

00:30

After all, yelling angrily will only get you so far.

00:33

To see how this works, let's take a look at a couple of examples.

00:35

Kim's an accountant at a toy company, but just because there are toys all over the place

00:39

doesn't mean that her work's all fun and games. [Kim is knocked over by an RC car]

00:41

Right now, she's in a bit of a pickle.

00:43

She's looking over the files for their sled division, and appropriately enough, profits [Kim's body is replaced by a pickle]

00:48

are going downhill.

00:49

She knows that over the last two years, profits have decreased by a total of four fifths.

00:54

But she can't find the records that tell her how much profits fell each year.

00:58

If she knows that each year's profits decreased by an equal value relative to where profits [Kim thinking about the problem]

01:04

were two years ago, by how much did profits decrease each year?

01:08

She could spend the next few days rifling through the company's basement, trying to [Kim looking through filing cabinets]

01:12

find the missing information...

01:13

Or she could just do some math.

01:15

We vote math.

01:16

Less chance of running into mice and dust bunnies. [Kim's face turns green]

01:19

Since the profits decreased by the same amount relative to where profits were the first

01:23

year, we can take the total drop, of four fifths…

01:26

…and divide it by two, for each of the two years that passed.

01:29

Luckily we know a thing or two about dividing fractions, so we multiply four fifths by the

01:33

reciprocal of two, one half…

01:36

…which gives us four tenths.

01:39

And once we divide the common factor of two out of the numerator and the denominator… [Fraction workings on a whiteboard]

01:44

…we're left with our final answer: two fifths.

01:47

It might have taken a few steps, but it was a lot quicker than a few hours in the basement.

01:51

And a lot less dusty, too. [Kim sneezes and a big dust cloud appears]

01:52

It turns out Kim has some more incomplete data to wrestle with.

01:56

Over the last three years, the jack-in-the-box division saw their profits go up seven eighths.

02:01

Again, though, there are some gaps in her data. [Arrows point to gaps in the graph]

02:04

If she knows that each year's profits increased by an equal value relative to where profits

02:09

were three years ago, by how much did profits increase each year?

02:13

Unfortunately, she's unlikely to find the answer in a jack-in-the-box. [Kim winds the handle on the box]

02:17

Well, unless the answer is: "a creepy clown face." [A clown jumps out the box and scares Kim]

02:21

Time for more fraction division.

02:24

Since the profits increased by the same amount relative to where profits were that first

02:29

year, we can take the total increase, of seven eighths…

02:31

…and divide it by three, for each of the three years that passed.

02:35

So we multiply seven eighths by the reciprocal of three, one third…

02:38

…which gives us seven twenty-fourths.

02:41

With no common factors, we're done! [The missing data is written on the chart]

02:43

And bonus: no one got a crippling fear of clowns that hide in boxes. [Kim chucks the Jack-in-the-box away and it explodes]