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# Basic multiplication

## Video transcript

let's learn to multiply mu l TI pl why 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 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 review you could think of if you had two I don't know to magenta that this color cherries and I wanted to add to it three blueberries how many total pieces of fruit do I now have and you say oh one two three four or five or likewise if I had our number line and if we see and you probably don't need this review but it never hurts never hurts to reinforce the concept and if this is zero one two three four five if you are sitting to to the right of zero and in general when we go positive we go to the right and if you were to add 3 to it you would move three spaces to the right so if I said you know if 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 or timesing something is it's just a it's just a simple way of doing addition over and over again so what this 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 what does that mean what means you're going to say two plus two plus two now where did the three go well how many how many twos do we have here let's see I have this is a 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 add one two three blueberries I have one two three two so this 3 tells me how many twos I'm going to have so what's 2 times 3 well I took 2 and I I added it to itself three times so 2 plus 2 is 4 4 plus 2 is equal to 6 now that's only one way to think about it the other way we could have thought about this is we could have said instead of having to added to itself three times we could have added 3 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 2 times 3 it could also be re-written as 3/2 times so 3 plus 3 and once again you're like where did this to go where do you know I had 2 times 3 you know and whenever you do addition you see I have 2 I don't know what these well I said cherries but they could be raspberries or anything and then I you know I had two things that three things and and the two of the 3 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 to go to in this case and this scenario is telling me how many times I'm going to add three to itself and once but what's interesting is regardless of which way I interpret two times three I can interpret it as 2 plus 2 plus 2 or adding 2 to itself three times I can interpret it that way or I can interpret it as adding 3 to itself two times but notice I get the same answer what's 3 plus 3 that is also equal to 6 and this is probably the first time in mathematics you'll encounter something very neat then 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 you know when when is this when is this multiplication thing even useful and this is where it's useful sometimes it simplifies counting so let's say I have I have a a well I let's let's stick with our our fruit analogy and an analogy is just when you kind of use something as as an egg 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 so then I'll draw them in rows of 3 so I have 1 2 3 well I'm not going to count them because that'll give our answer away just drawing a bunch of lemons now you could if I said you tell me how many lemons there are here and if you 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 you know there's 1 2 3 4 5 6 7 8 9 10 11 12 lemons so I actually already gave you the answer we know that there are 12 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 a 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 how many rows well that this was one row then this is the second row this is the third row and this is the fourth row so an easy way to count it as I say I have three lemons per row and I have four of them so let's say I have three lemons per row and I hope I'm not confusing you but I think you'll enjoy this and then I have four rows so I 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 out the word four times three I visualize this I visualize 4 times 3 so 3 4 times 3 plus 3 plus 3 and if we did that we get 3 plus 3 is 6 6 plus 3 is 9 9 plus 3 is 12 and we learned and in up here at this part of the video we learned that this same multiplication could also be interpreted as 3 times 4 you can switch the order and this is one of the useful and interesting actually up kind of properties of multiplication but this could also be written as 4 3 times 4 plus 4 plus 4 you add 4 to itself 3 times 4 plus 4 is 8 8 plus 4 is 12 and in in in the US we always say 4 times 3 but you know didn't I've met people and a lot of people my family they kind of learned in the I guess you could call it the English system and they'll often they'll often call this for threes or three fours and that in some ways 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 is to 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 12 and you could also say what are three fours so this is so let me write this down this is let me do it in a different color that is four threes I mean literally that's four threes if I told you to say write down four 3s 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 that in a in a different color that is three three fours and it could also be written as three times four and they all equal 12 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 these these lemons then till 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 there are times there are times and there are actually many times and 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 a hundred lemons and maybe there's maybe there's you know a hundred rows and then would take you forever to count all the lemons and that's where multiplication comes really useful although we're not going to learn right now how to multiply a hundred times 100 now the one thing that I want to get you in 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 3 times 1 and I would say because my brain would say oh that's like 3 plus 1 and I would say 3 plus 1 is equal to 4 and so I say oh you know 3 times 1 that must be 4 as well and she'd say no silly it's 3 and I was like how can that be how can it you know how can the 3 times some other numbers still be the same number and think about what this means you could view this as 3 3 ones and what are 3 ones that's 1 1 plus another 1 plus another 1 and that's equal to 3 or you could view this as 3 one time so what's 3 1 time it's almost silly how easy it is it's just 3 that's 1 3 you could write this as 1 3 1 3 and that's why anything times 1 or 1 times anything is that anything so in 3 times 1 this one titled one times three is three and you know I could say a hundred times one is equal to 100 I could say that one times 39 is equal to 39 and I think you're familiar with number is 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 when you add 3 plus 0 you've hopefully learned is 3 because I'm adding nothing to the 3 if I have 3 apples and I give you 0 more apples you still have 3 apples but what is 3 and I maybe I'm just fixated on the number 3 a little bit too much what else let me switch what is 4 4 times 0 well this is saying 0 4 times so what's 0 plus 0 plus 0 plus 0 well that's that's 0 right I have nothing plus nothing plus nothing plus nothing so I get nothing another way to think of it I could say 4 0 times so how do I write 4 0 times well I just don't write anything right because if I write anything if I write one for then I don't have no fours I thought this is saying so this is this is for let me write this this is for zeros but I could also write 0 fours and what is zero 4s well I'll 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 0 is 0 I could write a huge number you know five million four hundred ninety-three thousand six hundred and ninety two times zero what does that equal that equals zero and by the way what's this number times one what's that number again and what's zero times you know I seventeen once again that is zero anyway I think I've talked for long enough see you in the next video