Multiplication fun
Basic Multiplication Introduction to multiplication
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- Let's learn to multiply.
- M U L T I P L Y.
- And the best way I think to do anything is just to actually do some examples,
- and then talk through the examples,
- and try to figure out what they mean.
- In my first example I have two times three.
- By now you probably know what two plus three is.
- Two plus three.
- That's equal to five.
- And if you need a bit of a review you could think of
- if I had two-- I don't know-- two magenta--
- this color-- cherries.
- And I wanted to add to it three blueberries.
- How many total pieces of fruit do I now have?
- And you'd say, oh, one, two, three, four, five.
- Or likewise, if I had our number line,
- and you probably don't need this review, but it never hurts.
- Never hurts to reinforce the concept.
- And it this is zero, one, two, three, four, five.
- If you're sitting two to the right of zero
- and in general when we go positive we go to the right.
- And if you were to add three to it,
- you would move three spaces to the right.
- So if I said, if I just moved over three to the right,
- where do I end up?
- One, two, three.
- I end up at five.
- So either way, you understand that two plus three is equal to five.
- So what is two times three?
- An easy way to think about multiplication or "timesing" something
- is it's just a simple way of doing addition over and over again.
- So that you means is, and it's a little tricky.
- You're not going to add two to three.
- You're going to add--
- and there's actually two ways to think about it.
- You're going to add two to itself three times.
- Now what does that mean?
- Well, it means you're going to say two plus two plus two.
- Now where did the three go?
- Well, how many twos do we have here?
- Let's see, I have-- this is one two, I have two twos,
- I have three twos.
- I'm counting the numbers here
- the same way that I counted blueberries up here.
- I had one, two, three blueberries.
- I have one, two, three twos.
- So this three tells me how many twos I'm going to have.
- So what's two times three?
- Well, I took two and I added it to itself three times.
- So two plus two is four.
- Four plus two is equal to six.
- Now that's only one way to think about it.
- The other way we could have thought about this is we could've said,
- instead of having two added to itself three times,
- we could have added three to itself two times!
- And I know it's maybe becoming a little bit confusing,
- but the more practice you do it'll make a little sense.
- So this statement up here, let me rewrite it.
- Two times three.
- It could also be rewritten as three two times.
- So three plus three.
- And once again, you're like, where did this two go?
- You know, I had two times three
- and whenever you do addition, you see I have two-- oh, I don't know these--
- well, I said cherries, but they could be raspberries or anything.
- And then I have two things, I have three things
- and the two and the three never disappear.
- And I add them together, I get five.
- But here I'm saying that two times three
- is the same thing as three plus three.
- Where did the two go?
- Two in this case, in this scenario,
- is telling me how many times I'm going to add three to itself.
- But what's interesting is, regardless of which way I interpret two times three,
- I can interpret it as two plus two plus two,
- or adding two to itself three times.
- I can interpret it that way or I can interpret it
- as adding three to itself two times.
- But notice, I get the same answer.
- What's three plus three?
- That is also equal to six.
- And this is probably the first time in mathematics
- you'll encounter something very neat!
- Sometimes, regardless of the path you take,
- as long as you take a correct path you get the same answer.
- So two people can kind of visualize it--
- as long as they're visualizing it correctly,
- two different problems, but they come up with the same solution.
- And so you're probably saying,
- Sal, when is this multiplication thing even useful?
- And this is where it's useful.
- Sometimes it simplifies counting.
- So let's say I have a--
- well, let's stick with our fruit analogy.
- An analogy is just when you kind of use something as--
- well, I won't go too much into it.
- But our fruit example.
- Let's say I had lemons.
- Let me draw a bunch of lemons.
- I'll draw them in rows of three.
- So I have one, two, three-- well, I'm not going to count them
- because that'll give our answer away.
- I'm just drawing a bunch of lemons.
- Now, if I said, you tell me how many lemons there are here.
- And if I did that,
- you would proceed to just count all of the lemons.
- And it wouldn't take you too long to say, that oh,
- there's one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve lemons.
- I actually already gave you the answer.
- We know that there are twelve lemons there.
- But there's an easier way
- and a faster way to count the number of lemons.
- Notice: how many lemons are in each row?
- And a row is kind of the side to side lemons.
- I think you know what a row is.
- I don't want to talk down to you.
- So how many lemons are there in a row?
- Well, there are three lemons in a row.
- And now let me ask you another question.
- How many rows are there?
- Well, this was one row, and this is the second row,
- this is the third row, and this is the fourth row.
- So an easy way to count it is say, I have three lemons per row
- and I have four of them.
- So let's say I have three lemons per row.
- I hope I'm not confusing you, but I think you'll enjoy this.
- And then I have four rows.
- So I have four times three lemons.
- Four times three lemons.
- And that should be equal to the number of lemons I have-- twelve.
- And just to make that gel with what I just did with the addition,
- let's think about this.
- Four times three, literally when you--
- and you know, when you actually say the words four times three,
- I visualize this.
- I visualize four times three.
- So three four times.
- Three, plus three, plus three, plus three.
- And if we did that we get:
- Three plus three is six.
- Six plus three is nine.
- Nine plus three is twelve.
- And we learned, up here, in this part of the video,
- We learned that this same multiplication
- could also be interpreted
- as three times four.
- You can switch the order.
- And this one of the useful
- and interesting, actually, kind of properties of multiplication.
- But this could also be written as four three times.
- Four, plus four, plus four.
- You add four to itself three times.
- Four plus four is eight.
- Eight plus four is twelve.
- And in the U.S. we always say four times three,
- but you know, I've met people
- and a lot of people in my family they kind of learned in the--
- I guess you could call it the English system.
- And they'll often call this four threes, or three fours.
- And that in someways is a lot more intuitive.
- It's not intuitive the first time you hear it,
- but they'll write this multiplication problem,
- or they'll say this multiplication problem.
- They'll say, what are four threes?
- And when they say four threes,
- They're literally saying, what are four threes?
- So this is one three, two threes, three threes, four threes.
- So what are four threes when you add them up?
- It's twelve.
- And you could also say, what are three fours?
- So let me write this down.
- Let me do it in a different color.
- That is four threes.
- I mean literally, that's four threes.
- If I told you, say, write down four threes and add them up,
- that's what that is.
- And that is four times three.
- Or three four times.
- And this is-- let me do it in a different color,
- that is three fours.
- And it could also be written as three times four.
- And they all equal twelve.
- And now you're probably saying,
- okay, this is nice, it's a cute little trick, Sal,
- that you've taught me,
- but it took you less time to count these lemons
- than to you know, do this problem.
- And well first of all, that's only right now because you're new to multiplication.
- But what you'll find is that there are times,
- and there are actually many times--
- I don't want to use the word times too much in a video on multiplication--
- where each row of lemons,
- instead of having three,
- maybe they have one hundred lemons!
- Maybe there's one hundred rows!
- And it'll take you forever to count all the lemons,
- and that's where multiplication comes in useful,
- although we're not going to learn right now how to multiply one hundred times one hundred.
- Now the one thing that I want to give you,
- and this is kind of a trick,
- I remember my sister, just to try to show how much smarter she was than me,
- when I was in kindergarten and she was in third grade,
- She would say,"Sal, what is three times one?"
- And I would say, because my brain would say,
- Oh! That's like three plus one,
- and I would say three plus one is equal to four.
- And so I'd say,
- Oh! You know, three times one, that must be four as well.
- And she'd say,"No, silly! It's three!"
- And I was like, how can that be?
- How can, you know, three times some other number still be the same number?
- And think about what this means.
- You could view this as three ones.
- And what are three ones?
- That's one one, plus another one, plus another one.
- That's equal to three.
- Or you could do this as three one time.
- So what's three one time?
- It's almost silly how easy it is!
- It's just three.
- That's one three.
- You could write this as one three.
- And that's why anything times one,
- or one times anything,
- is that anything!
- So then, three times one is three.
- One times three is three.
- And you know, I could say, one hundred times one
- is equal to one hundred.
- I could say that one times thirty-nine
- is equal to thirty-nine.
- And I think you're familiar with numbers this large by now.
- So that's interesting.
- Now there's one other really interesting thing about multiplication.
- And that's when you multiply by zero.
- And I'll start with the analogy, or the example, of when you add.
- Three plus zero, you've hopefully learned,
- is three.
- Because I'm adding nothing to the three.
- If you have three apples,
- and I give you zero more apples,
- you still have three apples.
- But what is three--
- and maybe I'm just fixated on the number three a little too much--
- well, so let me switch--
- What is four times zero?
- Well this is saying zero four times.
- So what's zero, plus zero, plus zero, plus zero?
- Well, that's zero!
- Right? I have nothing, plus nothing, plus nothing, plus nothing.
- So I get nothing!
- Another way to think of it,
- I could say, four zero times.
- So how do I write four zero times?
- Well I just don't write anything, right?
- Because if I write anything,
- if I write one four, then I don't have "no fours".
- So this is saying--
- so this is four--
- let me write this--
- this is four zeros.
- But I could also write zero fours.
- And what are zero fours?
- Well, I just write a big blank here.
- There, I wrote it!
- There are no fours here!
- So it's just a big blank.
- And that's another fun thing.
- So, anything times zero is zero!
- I could write a huge number.
- You know, five million four hundred ninety-three thousand six hundred ninety-two
- times zero.
- What does that equal?
- That equals zero.
- And by the way,
- what's this number times one?
- Well it's that number again.
- What's zero times seventeen?
- Once again, that is zero.
- Anyway, I think I've talked for long enough.
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
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