Operations and Algebraic Thinking 189-200
Course: Operations and Algebraic Thinking 189-200 > Unit 3Lesson 3: Relating multiplication and division
- Relating division to multiplication
- Relate division to multiplication
- Relate multiplication and division equations
- Fact families
- Multiplication word problem: parking lot
- Division word problem: school building
- Relate division to multiplication word problems
Division word problem: school building
Sal uses a picture and understanding of multiplication to solve a division word problem. Created by Sal Khan.
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- 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:
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- 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.