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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 3

Lesson 8: Relating multiplication and division# Division word problem: school building

Sal uses a picture and understanding of multiplication to solve a division word problem. Created by Sal Khan.

## Want to join the conversation?

- Can you divide anything by zero?(15 votes)
- No, we do not divide by zero.

Consider: suppose there were 9 cookies and you want to share them equally among 3 people, you*divide*them up so that each person get 3 cookies - right?

Now, suppose you want to divide the 9 cookies among zero people.

Can you see that dividing 9 cookies among zero people does not make sense?

How can it be done?

That is why dividing by 0 is not allowed - it makes no sense.

Mathematicians say that dividing by zero is "undefined".

As you keep studying math, you will learn more concepts that will help you understand why this is so.

These videos might interest you - though the math is more difficult than what you are doing right now:

https://www.khanacademy.org/math/algebra/introduction-to-algebra/division-by-zero/v/why-dividing-by-zero-is-undefined(12 votes)

- How meany numbers are there in the world??(3 votes)
- Numbers have no end as you can always add another number after one number. If you think 10000000 is it, it could also be 100000000(0 votes)

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run(2 votes) - What does Sal mean when he said question mark is equal to 9?(2 votes)
- He illustrated the example using ? to represent the unknown number. When he reached the end of the problem, he found the unknown number was equal to 9 so ?=9.(1 vote)

- But is each story the same? The bottom floor could be taller, at maybe 12 feet, making each other floor smaller. In addition, the top floor could be a storage room, and therefore be smaller.(1 vote)
- It could be, but even if the top floor was not as tall as the others the answer would still be correct. You are asked to find the average floor height, not the actual floor height.(1 vote)

- What do they mean by 7 stories?(1 vote)
- They mean how many floors, like how houses have two or three floors.(1 vote)

- How many windows do they have?(1 vote)
- It is good to be curios! Here is your answer!

Okay, so on three of the sides, the windows are seven by five, and seven times five is thirty-five.

Because there are three sides, you want to multiply 35 by three, and that is 105!

Now, the front is missing a window.

So 35 - 1 is 34.

105 plus 34 is 139.

So, this new KA building should have 139 windows. But, if there are windows on the doors, there are either 140 or 141, depending on if they have 1 or 2 doors.(1 vote)

- From the problem statement, is it certain all the floors are the same height?(1 vote)
- It is assumed they will be for the purposes of teaching averages, but in practice a building's floors can have different heights. Don't let that stop you from asking questions though!(0 votes)

- does Sal need the part: the parking lot fits 90 cars or not because he did cross it out??(0 votes)
- It is not needed because it is not related to the height of the building or the height of each story. For this reason it is crossed out.(2 votes)

## Video transcript

- The new headquarters of Khan Academy is at 314 Math Avenue. It has 200 windows and has seven stories. The parking lot can fit 90 cars. The building itself is 63 feet tall. How tall is each story? So, I encourage you to pause this video and try this on your own. So let's try to answer it. They're asking us how tall is each story? So, what information do we need? Well, we definitely
don't need the address. We don't care how many windows it has. Now, the number of
stories seems interesting, especially because they tell us the total number of feet or the total height of the building. For example, they tell us that the building is 63 feet tall. So, this height right over here, the building's height is 63 feet tall and they tell us that
it has seven stories. Seven stories. So, one, two, three, four, five, six and seven. So it has seven stories. So if we divide 63 by seven, we should figure out
how tall each story is. So let's do that. We're going to divide 63 feet divided by, divided by seven stories and this is going to tell us how tall each story is. So that's going to be
equal to question mark. Now, 63 divided by seven be equal to question mark. This is another way of saying that seven times question mark is going to be equal to 63. Let me write that down. So this is another way of saying that 63 is equal to, is equal to seven, seven times, times question mark. Times question mark. So, if we can figure out what do we have to multiply seven by to get to 63, then we know what 63 divided by seven is. And to do that, I'm just going to skip count by seven. So, let's start with seven. So seven times one is seven. Seven, so let me just write this. Seven times one is seven. Seven times two is 14. Seven times three is 21. Seven times four is 28. Notice I'm just adding by seven each time. Seven times five is 35. Seven times six is 42. Seven times seven is 49. Seven times eight is 56. Just adding seven. Seven times nine is 63. So we see, seven times nine is 63. So the question mark
must be equal to nine. Question mark must be equal to nine. So we can write that 63 divided by seven, 63, 63 divided by seven, let me do the same colors that I just used, 63 divided by seven is equal to nine. Divided by seven is equal to nine. And let's, let's think about that. We're saying that if we take 63 feet and divide it into seven equal stories, that each story is going
to be nine feet on average. Does that make sense? So, does it make sense that each of these, each of these stories are
going to be nine feet? Well, we have seven of them, so it should be, just the first story should be nine feet. By the time we get to the second story, we should be at 18 feet. I'm adding by nine now. Third story, the top of the third story should be 27 feet. Top of the fourth story
is going to be 36 feet. Top of the fifth story
is going to be 45 feet. Top of the sixth story
is going to be 54 feet. And then the top of the seventh story, which is also the top of the building, is going to be 63 feet. So, if each floor is nine feet high, you just have to keep adding nine every time you add a floor and you see if you do that, if you have seven floors you're going to get to 63 feet. So it completely makes sense, each story is nine feet tall.