 Adding. When you're adding two numbers it really depends if they have decimals or not, but you're lining things up based on their tens, right, based on their position, right? So let's say we're adding two, five, seven, six, plus seven, four, two, right? I'm covering, I know you said adding you're okay with, but subtracting is just adding negative numbers. So we'll cover adding and then we'll flip it for the subtracting, right? If you're adding these two numbers, then what you do, this is the one positions, the tens, the hundreds, the thousands, you line them up according to their position, right? So if you're going to add these two numbers, you go to five, seven, six, and that's the two, four, seven, right? Four, seven, four, two, you line them up. When you're adding them, you add. Six plus two is eight, seven plus four is eleven. If you get anything over nine you've got to carry over to the next level because that's ten plus, right? So four and seven is eleven. You put the one here and the ten goes up here and then you got six and seven is thirteen. You put one here, three. So that's adding them. Now what if you had decimals in this, right? What if this was two, five, point, seven, six plus seven, four, point, two, right? Same digits, but a decimal added, right? Then what you're really doing is you're adding based on the decimal. You're lining up the decimal because that is exactly what you were doing here, right? You're lining up based on the decimal, but the decimal is invisible because we don't have anything past the decimal, right? So the decimal for these guys is here and here and here and here, right? So we're lining up on the decimal. So if you're doing this, you line them up, point, seven, six plus seven, four, point, two, right? Now anything in the decimal that you don't have numbers for, like this goes two decimal places. This only has one decimal place. So what you have here is really just a zero, okay? It's an invisible zero. So all you do you go six plus zero is six, seven plus two is nine. Place your decimal place there, right? Five plus four is nine. Two plus seven is nine. Wow, cool number. 99.96. Easy peasy, right? Let's do subtracting. Subtracting. So let's assume we're subtracting these two numbers again. Two, five, seven, six minus seven, four, two. Okay? So again, you line them up based on the decimal. The invisible decimal that we had here is also present here, right? Because these are the single digits. These are the tens, right? The hundreds and the thousands, right? So when you're subtracting, you want to line it up with the higher number, the bigger number up top, right? With adding it doesn't make a difference. With subtracting it does. You want the bigger number up top, two, five, seven, six, and you're going to subtract seven, four, two, right? And what you do is you go six minus two is four, seven minus, seven minus, six minus two is four, seven minus four is three, and then you're going to go five minus seven, but you can't take seven away from five, right? So whenever you're subtracting, when the above number, right, is smaller than the lower number, whatever you're taking away from the above number, what you end up doing, you're borrowing one, you borrow a ten from the next number that's higher up, right? So it's not really a ten for this one, it's a hundred because this is the hundredth position, so you're bringing a thousand over, but think of it as borrowing a factor of ten, right? So seven minus, you know, seven minus five, five minus seven, you can't take seven away from five, so you borrow one from the two. So the two becomes a one and five becomes a fifteen. So borrowing one from the next number up means you're adding ten to this one. So fifteen minus seven is eight, and then you have a one here. So the answer is this two Hickey right here, okay? Cool? So that's this one. Let's do this one, but subtraction, right? Let's go four, let's go if it was two five point seven six minus seven four point two, right? Again with subtracting, you need to line up the decimals, right? I like the decimals bigger so you see them, gotta be pronounced, right? So you're gonna line things up with the decimal, but the rule stands when you're subtracting numbers, when you're doing them this way, you put the bigger number up top and subtract the smaller number, even though we're going against or not against but sort of manipulating our first mantra in mathematics which is the sign in front of the number goes with the number, right? But this is a sort of a mental note that you're going to make because what you're gonna remember is if this was 25 minus 74, then you're subtracting a bigger number from a smaller number, your answer is going to be negative. So automatically you should remember that your answer is going to be negative because you're taking away a bigger number from a smaller number, right? But we still want to make the bigger number digit-wise anyway on the top. So you're not gonna write this as two five point seven six plus seven or minus seven four point two. You're gonna write this as seven four point two minus two five point seven six. Okay, now remember this is a flip of what this is. So what we're gonna keep a note of, a mental note of, that whatever the answer is that we're gonna get here is gonna be negative, right? If you want smaller numbers, look at this. Let's assume we had here, that's four, let's go five, or in a side, right? If you had three plus five, that's an eight, right? If you have five plus three, that's an eight, right? Now what if you had three minus five, and what if you had five minus three? Well five minus three is just two, we know that, right? But three minus five, we should notice by now, the answer is negative two, but if you're gonna do the subtraction like this, which you need to do when you're dealing with bigger numbers, you need to put the bigger number up top and subtract the bottom number, and remember, mental note that the bigger number was negative, so your answer is going to be negative. So what you're really doing is doing this, you're going five minus three, that's two, but two is not the answer to this, because the bigger number was, the bigger number was negative, so the answer is really negative two. Okay, you make a mental note of it. That's exactly the way you're gonna treat this. So if you're subtracting these, you're lining up your decimal. Now remember, anything after the last digit, after the last decimal point, you can add a zero if you don't want to have an empty spot there, right? Because what you're about to do is do this, you're gonna go six, take six away from zero, well you can't take six away from zero, right? Zero minus six doesn't work, because zero is zero, zero is a smaller number, six. So what you need to do is do exactly what we did here, is go to the next number and borrow a ten value, right? So ten comes over, ten plus zero is ten, so now you're gonna go ten minus six is four, and then you go to the next number, you go seven minus, one minus seven, well you can't take seven away from one, it doesn't work. So you got to go to the next number and borrow one. So you go to the four, make this a three, so you're always kicking it down by one, the next number when you borrow it, and then you're adding the ten to one which makes it eleven. So usually you're just adding a one right in front of whatever that number was there previously. So eleven minus seven is four, put your decimal in place, and then you're gonna go three minus, well you take five away from three, same problem, right? So what we need to do is borrow one from the seven and turn the three into thirteen. So if we take one away from seven, that becomes a six, and this becomes a thirteen. Thirteen minus five is an eight, six minus two is four. Now the question is, is twenty five point seven six minus seventy four point two forty eight point four four? Well it's not because this is the bigger number. This is negative seventy four point two, so we know the answer is negative. So that becomes your answer to this subtraction. I went through this pretty fast our childhood days, but the foundation, the step-by-step process is there. Does this help you out? Does that make sense? Do you have any questions regarding this? Or anyone else for that matter? Because what I'm gonna do is, we're gonna go through the speed of Gonzales to a certain degree speed of Gonzales, right? We're doing the subtraction, we've done the addition, we're gonna do multiplication, and we're gonna do division. Okay awesome on the target age. We're gonna do division, and before we go into talking about how to move around an equal sign, we're gonna do what the little segment that we need to do, because all you need is addition, subtraction, multiplication, and division to be able to do personal finance, investing, to calculate return on investment. Crazy, right? You do need exponents as well for compound, but we'll wait up on that. Okay, so I'm gonna take this down. So that's subtraction. Let's talk about multiplication. Let's talk about multiplication. Now the first thing you have to understand about multiplication is, multiplication is an extension of addition, right? We'll multiply the tops and bottoms with 10s to remove decimals. Yes and no, right? If you have an equal sign, as long as you do it to both sides of the equation, you're okay with that, right? Because whatever you do on one side, you can do to the other side. But if you're simplifying, you can't just multiply the numbers by 10, because you're kicking up the numbers by magnitude of 10, right? So you're not going to get the final answer, right? The legit answer. By the way, gangs, apologies about if I don't catch them. Thank you for your follow-ups. Thank you for the subs if you're subbing, and thank you for the follow-ups when I'm not catching them. Technically, I'll multiply by one. Okay, it might be making it a little bit more difficult. 10 over 10. Sure, but it's extra step work that you need to do. Once you start doing and adding and subtracting with decimals and whatnot, it just becomes routine, right? That extra step might help you out initially, but in the long run, you're going to eliminate it. It's like having training wheels on a bike, right? Once you learn how to ride a bike, you know, initially when you're learning, you might have little training wheels where you're not, you know, you don't wobble over and hurt yourself when you're a little kid. But once you learn how to ride a bike, those training wheels really slow you down. Yeah, I just like to do things in a weird way. So, okay, no words, no words. So, check this out. Let's do multiplication. Multiply. Okay. Now, look, multiplication is an extension of addition. One thing I keep on saying is mathematicians are some of the laziest people you meet in the world because they like to simplify things. They like to make things speedy on Zala, so they don't have to spend too much time processing simple information. They want to move on to more complicated stuff, right? So, they've come up with shorthand and all this jazz, right? Slick, Mick, how are you doing? I feel like math is, in my school, was more about solving the problems and not learning why I was doing all this. Yeah, it's, they weren't even teaching you how to solve problems. They're, in general, they're teaching you just like a monkey, you know, a monkey-sea monkey. Do this, do this, do this. You get this. And they don't even tell you to look at the final answer to say, does that even make sense, right? Which we will be doing. Which we will be doing, right? Now, take a look at this. Multiplication is an extension of addition. So, just imagine if you had this, 2 plus 2 plus 2 plus 2, right? What's four twos out of together? Well, four, six, eight. That's eight, right? But a simpler way to do this is take your addition symbol, rotate it, right? Take your addition symbol, rotate it four to five degrees. You've got a multiplication symbol, right? That's what multiplication is. The symbol represents. And what that means is you're, you're adding the same number multiple times, right? That's what the definition of multiplication is. So, instead of writing 2 plus 2 plus 2 plus 2 is equal to 8. I can go 2 times 4 is equal to 8. Which really means add 2 together four times, right? That's all it is, okay? That's what my experience is about. Think of that, right? Multiplication is not something magic, something really necessarily novel that's been introduced in mathematics. It's just a faster way of doing addition, okay? As far as how to multiply, you do it this way. Let's assume what was the last number we have? 2, 5. I forgot what it was. It was 2, 5, 7, 4. No, there wasn't 7, 4. 7, 2, I think? Or something else? Let's go 3, 2. Times 7, 4. Something, something. 1, 2. 1, 2, right? No, that was too big. I think it was only three numbers we had. 4, 2, I believe, right? I'm pretty sure that these two numbers are up. Okay. Now, if you have a 3-digit number multiply, sorry, 4-digit number multiplied by 3-digit number, this is what you do and this is the process that you do for any digit number multiplied by any digit number. And before we do this one, let me give you a quick little, and first of all, you need to know your 10 by 10 multiplication table. So if you don't know it, learn it. Your 10 by 10 multiplication table, learn it. 1, 2, 3, 4. And then 1, 2, 3, 4. Learn your 10 by 10 multiplication table. It will save yourself a lot of time, a lot of headache. Okay, really essential. If we're doing this type of multiplication, I'm assuming you know your multiplication table and we have a full blown video out there, ASMR math video out there talking about the multiplication table. It's like an hour long or 40 minutes long or something like this of how to... I don't even know if it's about memorization. It's basically putting it into your algorithm, your program, to be able to know how to multiply, right? Seriously, I can't emphasize this enough. The first thing I tell all my students, learn your multiplication table, right? M-I-1-3-5. Thank you very much for the Twitch Prime sub. Okay, really gang. Just go chicho multiplication table. Okay, the video will pop up. Learn it, learn it, learn it. Okay, now just imagine if we're multiplying three, four digits with three digits. But before we do that, let's do two digits by one digit or two digit by two digit. So you see how the process works, all right? So here's question one but let's do a simpler one first. Let's do question two first, right? Let's assume we have two, five, three. Actually, let's go two digits. Two digits times two digits, right? Math is good but A plus B equals C is hard. A squared plus B squared equals C squared. Kenny, Kenny Roberts, are you talking about Pythagoras theorem? Exponents kicks it up a notch but we'll talk about it. If not in this live stream and in another live stream, if we're going to build basic algebra as our uncharted ace wants, we'll get into exponents maybe even in this one, right? So if we're multiplying, you'll line them up again on top of each other, just the same way you did addition, subtraction. But with multiplication, it really doesn't make a difference if the smaller number of is up top or the bigger number up top. Ideally though, put the bigger number up top, right? 25 times 12. With multiplication, what you do you do this. You go this multiplies all the digits there and that multiplies all the digits there. So two times five is 10. You put the zero here, you put the one up top. If you get any number above nine when you're multiplying two numbers together the 10th value kicks up, right? Two times two is four and then you add the top number which makes it five, right? Now think about this. What's two times 25? It's 50, right? But you're doing it piecemeal. And then you move on to the next number, one, right? Now if you're in this position and by the way with multiplication and addition and subtraction it's ridiculously important to line things up properly. Mathematics is about symmetry, really. Line things up properly. That's the way mathematics was developed to be extremely visual. Any language is very visual, right? So someone, if someone asks you to spell the word apple, right? You're gonna go apple, right? That way that person can read it, right? If someone says write down the word apple you're not gonna go apple because it's visually extremely difficult for your mind to process and we come up with languages to help us to process things faster, to retain information, right? To be able to make connections. So you want to make it easier for your mind to be able to do things instead of harder for your mind to be able to do things, right? Keep this in mind. I've seen a lot of people do a lot of mathematics where they're extremely messy. It's the equivalent of writing apple in that chaotic way. It's like no, no, no, no. First order of business, learning multiplication tables. Second order of business, tighten up your work, right? Line things up properly. When you line things up properly we've already done the two multiplication. Now we've got to go to the one. And as before this number multiplies that number and that number. But because this is in the 10th position when you go one times five you don't put it here you put it here and that's a five. And what people usually do you add a zero here, okay? Just to remember that you're starting in the second position, right? So one times five is five. There is no carryover so this one is no longer there. You have to make a mental note of that, right? And then one times two is two and then you draw the line and what did we say? Multiplication is really addition and the addition does come into play in multiplication. Here when you get down to this level you're at these numbers. Zero plus zero, zero, five plus five is 10. You put the zero here, carry the one and that's three. So 25 times 12 is 300, okay? Let's do the bigger number. Two, five, three, two, times seven, four, two. Same process, okay? Two times two is four. Two times three is six. Two times five is 10. You put a zero and carry the one. Two times two is four. Add the one you get five. Is that cool? The process is the same, right? I'm just doing a little bit faster, right? And then you move on to the four. But this isn't really four in terms of value. It was 40. It's in the 10th position. So because we moved here, you line this up. When you multiply the four times two, the result comes here. But when you moved over one, put a zero there, put a place marker there. So you know where you are, right? You don't want to, when you're doing mathematics, when you're doing algebra, you want to reduce the amount of information you have to retain in your mind. So I always say use the pen and paper as your assistant, right? Make notes on the sides of whatever it is that you're doing. If you need to remember where you are and what you need to do next, right? Putting a zero as a place marker guarantees that you don't make a mistake to go four times two is eight and put the eight there. Because that's already taken, right? So four times two is eight. You put the eight here. Four times three is 12. You put the two here and you carry the one. Four times five is 20. At the one, you get 21. And then you carry the two on top, right? Because the one's gone, right? Four times two is eight. You add the two, you get 10. Cool? Now we're into the third number. Well, if we're into the third number, that lines up here. This and this are going to be zero. Then do your multiplication. Seven times two is 14. You put the four here. You carry the one. Seven times three is 21. At the one, you get 22. You put two here and you carry the two up top. Seven times five is 35. At two, you get 37. Seven and you carry a three. Seven times two is 14. At the three, you get 17. Two. And then what do you do with these numbers? Ideally, ideally, you're lining everything up properly. Really, line everything up properly again. It's visual. Mathematics is visual. People, I've seen people do this. When they're doing this part, they got five, four here. Five, zero, six, four. And then you got zero, eight, two, one, zero, one. And then they got zero, zero, four, two, seven, seven, one. How are you gonna add this? Really? How are you gonna add this? If you need to add these guys, it's the same numbers. You got to go, okay, those guys add, those guys add, these guys add, these guys add, these guys add, these guys add, and that goes there. Man, that's a nasty way. Your mind just becomes confused, right? When you draw the lines, it's pretty straightforward, but you're not going to sit there and draw lines to line things up all the time, right? What you need to do is line it up right off the get go. Four plus zero plus zero is four. Six plus eight is 14, and that's a zero. It doesn't change anything. So 14, you put the four, carry the one. One plus zero is one, plus two is three, plus four is seven. Five plus one is six, plus two is eight. Zero plus seven is seven. One plus seven is eight, and that's a one. 2,532 times 742 is, you can put a little commas here if you want to be able to read it properly, 1,878,744, right? Easy peasy. Now, what if this had decimals? Let me take these off so we don't get them confused as decimals, right? What if this had decimals? Okay, what if this had decimals? Let's assume this guy had decimals. When you're multiplying numbers, you don't have to line up the decimals the way you did when you were adding numbers. When you're adding numbers, you need to line up the decimals to be able to add them and subtract them. You need to line up the decimals when you're subtracting numbers, right? Remember, the bigger number is always on top. Keep a mental note which number was negative. If the bigger number was negative, your answer is going to be negative. If the bigger number was positive, your answer is going to be positive, right? When you're subtracting numbers. So if you have decimals in your multiplication, you don't need to line up your decimals. You just add the total number of decimals at the end and place them there. So for example, what if this was 2.5 times 1.2? So this was 2.5 times 1.2. They line up, but that doesn't matter to us because we're not lining up the decimals. What we do is we add the total number of decimal places we have. Now, this confuses some people. When I say you add the total number of decimal places you have, you're starting off at this location, the position where you're right beside the ones, right? And you're going, okay, if the decimal was there, that's one, that's two decimal spots, so you add two decimal spots. So 2.5 times 1.2 is 3.00, which is just three, right? Let's add the decimal spot instead of adding it here. Let's add it here and here. So how many decimal spots do we have? If it's 0.25 times 0.12, we have 1, 2, 3, 4 decimal spots, right? Well, over here we multiply them without the decimals. We don't care, right? If we take these decimals away, right? And then we have four decimal spots. So we start off with the decimal is, it's an invisible decimal, and then we go 1, 2, 3. We don't have any more numbers, but we do another jump. We put the decimal there. If we have any blank spots, we put zeros, okay? So 0.25 times 0.12 is 0.03 and you don't need these two decimal spots there because zeros after the last digit in a decimal is unnecessary, right? So let's add decimals here. Let's assume this was 2.532 times 7.4, right? So we don't need to redo our multiplication. We don't because we didn't have to line up the decimals, right? If we're lining these up if we're adding, then this would have been 2.532 plus 7.42. You line them up, right? But that's not what we're doing. We're multiplying. If we're multiplying, we multiply the numbers as if there was no decimal, and then we count the number of decimal places we have total. Let's check it out. 1, 2, 3, 4, 5 decimal spots, right? So we start off where the decimal place is. So we go 1, 2, 3, 4, 5. 2.532 times 7.42 is 18.78744. Is that clear? Does that work? I hope so. Does that work on charter days? And anybody else? Any questions regarding this? Yes, that is a massive help. Awesome on charter days. Thank you very much for the follows gang square 1996 and those are some other follows that pop through, but I didn't want to break the train of thought on there. So appreciate the follows gang. Let's go to dividing. And once we do dividing, we're going to go to return on investment in personal finance so we can set up our work that we're going to do when we talk about investing in comic books in four days. Let's do division. Let's do division. Very nice. Division is just an extension of multiplication, which is an extension of addition. So they teach you everyone. They even taught me. This is the way they taught me. They said this is addition, this is subtraction, this is multiplication, and this is division. What they didn't tell you was all of these things are really just addition. Right. Subtraction is just adding negative numbers. Right. Multiplication is just multiplying, adding the same number multiple times. And division is the flip of multiplication. Right. Because for everything you can do in mathematics, you can undo almost. Okay. That's not the way it works in the physical world. Right. Try to break a glass cup. Right. Very difficult to put it back together. Right. For everything that is done in the material world, you can't necessarily undo. In mathematics, it's beautiful. You can almost undo everything that you did. I have forgot everything in mathematics almost. Micro, micro twist. I was good once upon a time. I'm horrible. Brother or sister or micro twist. One of the reasons I got into teaching tutoring mathematics was because I was very disappointed that I forgot a lot of mathematics that I had already learned. So I got into teaching mathematics as a hobby to relearn my high school mathematics because I really didn't want to lose that power that I had. It's like practicing a natural language that you might know if you speak more than one or two languages. Right. You need to practice it to retain the ability to speak it. So I got into tutoring mathematics to make sure I didn't forget how to do my mathematics because I knew it was ridiculously important in the real world. Right. Craft or how are you doing? Welcome. Welcome. Now let's do division. My spelling sucks right now. I go through periods where my spelling is good and my spelling is bad. How are you doing? Division. Let's assume we have the following. And by the way, gang, division is really just about fractions. Right. But what I'm going to do right now is I'm going to teach you long division. Okay. Because fractions, when we get into fractions, we're going to talk about prime numbers and prime numbers we're going to do in another step. I just want to teach you the process of long division right now. And the reason I want to teach you this is because a lot of people say, oh, you don't need to learn long division. A lot of, a lot of teachers actually, you don't need to, a lot of math, a lot of people to do one. You don't need to learn math, long division. I'm like, dude, learn long division. It's an exercise for the mind. It's good for the brain. It's like doing pull-ups and chin-ups. Okay. I had been, my coach was, I had been talking shit all semester to one month before summer break and my teacher said, I can't let you pass. You haven't done anything. Okay. I said, if I do the entire book and pass all the tests while I pass, yes, he said, I finished the entire mathematics a book in one month and pass all the tests. Yeah. And if you're in school and if you've been through school, you know that they take 10 months to teach you some things in their earlier years, things that, especially mathematics, right, that you could probably do in a month. Right. In grade 12, they take you, they take about 10 months to teach you something that you could learn in about two months. Okay. So if you bunker down and, you know, there's pluses and minuses of going to school, there's social activity, this, that, that, that, that, that, all that jazz. But if you want to go through schooling, education, your basic education, speedy Gonzales stuff, just to teach yourself, educate yourself. You can go and challenge tests and get stuff done. Right. And gang, don't forget, Friasage, Friasage, Friasage. Julian Assange is a publisher and journalist that has been crucified for trying to bring transparency and accountability of capitals, power to humanity. For more information, see wikileaks.org or check out our Julian Assange and Wikileaks playlist on sensor two. Let's do long division. Let's just, we had this two, five, three, two over seven, four, two. We wanted to divide these two numbers. Okay. And I'm going to do the basic long division right now. We're not going to go into the other more intricate stuff that can happen. It's because, as long as you've got the basic long division down, you're money, right? You're gold. If you're going to do this, the way you lay it out, and again, mathematics is very visual, lay it out. And actually, I should do a simpler number first, by the way. Let me do a simpler number first. Let's assume, so this is one, let's do question two first. What did we have before? 12. I want to do two, five, three divided by four. Let's do that. Okay. So 253 divided by four. This is the way you lay it out. You draw your little, what are you going to call this? Laying down L with the pointer sticking down, right? You put the four on here. You put the two, five, three here. Okay. Give yourself enough room. And when you're laying down the work, again, talking about Apple, if you're going to write the word Apple, right? You're going to write it like this. You're not going to go forget about the chaotic letters all over the place. You're not going to go like this. That's just hard to work with Apple, right? Be consistent in the spacing of the letters you put down. Be consistent in the spacing of the numbers you put down. So you give yourself enough room to maneuver, right? You want to be able to do things in there. You don't want your numbers to be staggering at different lengths and different spaces, right? You don't want to go two, five, three, two. You don't want to write 2,532 like this. It just doesn't, because when you're trying to even add, what are you going to do? You're going to put your seven here and four and two here. But why would you do that, right? Be consistent. Make it easier for yourself, right? This is how you do Long Division. You look at this number and you're dividing this into this whole thing. So you look at the first number. You go four, the, does four go into two? Does four go into two? Four is bigger than two. So it doesn't go into two. So if it doesn't go into two, you can put a zero there, but you don't need to. You just go to the next number and you put those numbers, two numbers together, and you treat that as a 25. And you ask yourself, how many times does four go into 25, right? Six times. So what you do is you put your six above the five because you're using these two numbers, right? So how many times was four going to 25? Six times because six times four is 24. So what you do as soon as you put a number up top, you bring this guy and you multiply these two numbers and you put the number there. Okay. And what you're going to do now is subtract this number from that number. So minus five minus four is one and two minus two is zero and you don't have to put the zero down. And then what you're going to do is you bring the three down. So as soon as you get down to this number, if this number is bigger than that number, you did something wrong. You didn't take this one high enough, right? Let me show you how that works just before we move on anymore. I'll put those numbers back up again, right? Let's assume you didn't know your multiplication table, right? And you ask yourself, how many times was four going to 25? And you went, oh, five times, right? Again, learn your multiplication table and make your life easier, right? Let's assume you didn't know your multiplication table, you asked yourself how many times was four going to 25? Five times, right? You go five. Five times four is 20, you put the 20 here, and then you subtract these. Five minus zero is five, two minus two is zero. You got a five here, but four still goes into five. So you have no need to bring down another number. So you just broke division, right? You don't, you can't proceed here because that number is bigger than that. So what are you going to do? You can't go, oh, four goes into five ones, but where are you going to put the one? You're still in this position. You haven't gone to the next one. So now you got to go plus one here. So that makes it six, and then four, and then one, and then you can bring the three down. And then this is now six. Oh, confusing, confusing, confusing. You got to take it to the max right off the bat, right? Know your multiplication table. How many times was four going to 25? Six times. Six times four is 24, subtract. Five minus four is one, two minus two is zero. Four doesn't go into one. That means we got as close as we could go without going over 25, and you can't go over this number, right? Now you need to borrow a number. Bring the three down. Four goes into 13. How many times? Four goes into 13. Three times, right? Three times four is 12. Cool. Right? You subtract these numbers. Three minus two is one. One minus one is zero. You're done. You don't have any more numbers here. So this is what you could write down right now. You could write down 253, 253 divided by four is equal to 63, and the remainder is one. Some people write it like this with a remainder of one. That's when they're just teaching you at the beginning stages. Yo, Graham, how you doing? That's at the beginning stages of learning division. You learned this in the first few weeks, a couple of months, and then you don't do R1 again, right? Or you can go at 63, and one is left over. One divided by four. So 253 divided by four is 63 and a quarter, which basically means, by where are you doing, which basically means four goes into 253, 63, and a quarter times. Now, if you want to represent this as a decimal, this is what you do. You come to here, you go up here, and you say, okay, I got no more numbers that I can bring down. Poop, right? There's something we can do though. We can take, we can put a decimal here, and as soon as we put a decimal there, it's sort of like putting a decimal here. And as soon as you got a decimal there, you can just add a zero, because a zero after a decimal really doesn't change anything. So there's a decimal here now, you can bring the zero down. Four goes into 10 twice. So you can put your two up there. Four times two is eight. You subtract, you get a two. Well, four doesn't go into two, but we already placed our decimal, and if we're in a decimal position, right? Then you can add one zero for every time you reach the spot, the bottom part. Okay? So you can only do it once per rotation when you hit here, right? So the zero comes down and you ask yourself, how many times does four go into 20? Well, four goes into 20 five times. Five times four is 20. You put your 20 there, you subtract, you get zero. Once you get zero, that was it. This thing went out of focus. Let's see if it'll come back. It came back. If you want, here, let me do this. Let me write this clear so you see the process, right? So we're at 20. Five times four is 20. Subtract, you get zero. Once you get zero, that's as far as you've got. You've gone. You don't need to go anymore. So 253 divided by four was 63 with a remainder of one. That's where if we stopped at this position, or 63 and one over four, or 63.25. That's what it is. Now, let's go do this. Any questions about this, by the way, on charter days or anyone else? If not, we're going to do the long division for this. Let's check this out. Seven four two, and we're going to divide that into two, five, three, two. More difficult. More difficult division, no doubt, right? But you're going to ask yourself, how many times does 742 go into two? Well, it doesn't go into 25. It doesn't go into 253. It doesn't. 742 is bigger than 253. So you've got to go all the way in, all the numbers, right? How many times does 742 go into 2,532? You can do approximations, right? Now, forget about the 32. Just call this 2,500. You want to get close but without going over. You can call this 750. How many times does 750 go into 2,500, right? Because if you're kicking this down by 32 and kicking this up, you might go over, but at least you're going to get close, right? Three times. Let's check it out. So Laugh Out Loud Tony says three times. How many 742s are there in 2532? Laugh Out Loud Tony says three. So we're using all of these numbers. So the three we're going to put on top of here, and we're going to multiply three by this. Three times two is six. Three times four is 12, two and a one. Remember, this is like doing multiplication, but on top of each other, right? 742 times three. Three times two is six. Three times four is 12, one. Three times seven is 21, 22. So this is two and two, right? Now, just for the exercise of it, just for the exercise. Now, I'm not going to do the multiplication like this anymore. We're just going to do it here. Let's assume you went over, right? You picked too big of a number, right? Let's kill this for a second. Let's assume you picked too big of a number. Let's assume you picked four. Four times two is eight. Four times four is 16. You bring the one over. Four times seven is 28. Plus one is 29. You've got to subtract this, but wait a second. 2,968 is bigger than 2,532. You're not going to do that. It's too big of a number. It's like prices, right? You went over. Oops, right? So if you went over, depending on how much you went over by, you might have gone over by a lot. In this case, we only went over by one. So we're going to kick it down to three, right? And if you go down to two, right? If you thought it was twice, then the number when you subtract it was going to be bigger than this number, and then that doesn't work because we already talked about it, right? So it's three. Three times two is six. Three times four is 12, and a one. Three times seven is 21, plus one is 22. Subtract. Now you're doing subtraction. Two minus six. Well, you can't take six away from two, so you borrow one from the three. Turn the three into a two. Oops, into a two. That's another reason you're going to give yourself space, right? Because you're going to be doing things inside here. So that's a two. And the 12, two becomes a 12. 12 minus six is six. Two minus two is zero. Five minus two is three, and two minus two is zero. So we're out of numbers, right? This doesn't go into that, rightfully so. So right now we could write our answer like this. Two, five, three, two, divided by seven, four, two, is equal to three, and because we don't have any more numbers to bring down, 306 over 402. And you can reduce this fraction, by the way, and we could have reduced that fraction as well, but we're not dealing with the reducing fractions yet until we get into fractions of prime numbers, right? So that's one answer. And again, you can reduce that fraction. Two goes into both of them, probably more. Now what if you want it as a decimal? As a decimal, we don't have any more numbers to bring down. So we're going to put a decimal here, and we're going to add a zero here so we can bring it down. Now you ask yourself, how many times does 742 go into 3060? Well, we already multiplied it by four, so we know what that came out to 29000, or 2900 something. So we know it's going to be four. Four times two is eight. Four times four is 16. Ring the one up. Four times seven is 28 plus two is 29. Zero minus eight, it doesn't work. Convert this to a five, make that a ten. Ten minus eight is two. Five minus six, it doesn't work. You've got to borrow one from the zero, but you can borrow one from a zero. Zero doesn't have anything to give you, right? You've got to go to the next one. So you're going to borrow one from the three. Three becomes a two, gives one to the zero. Zero becomes a ten. Well, now you can borrow from the ten to kick the five into 15. So ten becomes a nine, and the five becomes a 15. 15 minus six is nine. Nine minus nine is zero. Two minus two is zero. But you don't need the zero and the zero. It just confuses things, right? Take it out. Take it out. Well, we did it right because 742 doesn't go into 92, okay? We're on this side of the decimal location, right? So that means we're going to add a zero. How many times is 742 going to add the zero here? 920 once. Dolphin, how are you doing? You're going to put a one here. One times that is just 742. Again, you're subtracting it. Zero minus two doesn't work. Borrow one from here. This becomes a ten. Ten minus two is eight. One minus four doesn't work. You borrow one from the nine. Nine becomes an eight. One becomes an 11. 11 minus four is seven. Eight minus seven is one. Cool. 178. What do we do? Borrow another zero. Borrow. Add another zero. How many times is 742 going to 1780? Twice. We'll put a two here. Two times two is four. Two times four is eight. Two times seven is 14. Subtract. You can't take four from zero. You borrow one from the seven. This becomes a ten. Ten minus four is six. This is a seven. Seven minus eight doesn't work. You borrow one from the seven. Seven becomes a 17. 17 minus eight is nine. Six minus four is two. Two, nine, six. Cool. Should we continue? You can borrow another zero. Zero. Oh, so close. Look at this. 2,960. This is 2,968. Well, we know it can't be four because four will be too high. So how many times does 742 go into 2,960? Three times. Three. Let me put a barrier here. Three times that is the same thing as this. Two, two, two, six. Subtract. Six becomes a five. That becomes a 10. Four, three, seven. Oh, so close. No cigar. And so on. And you can do this until you find a pattern. Or if they say, hey, they want the answer to this to two decimal places. If they want the answer to this, you put a little approximation sign. You go 3.4 two decimal places. If you're going to round to two decimal places, you go to the one afterwards. If that number is five or more, you round up round the one to two. But it's not. It's two. Four or less, that remains the same. That's the decimal version of that. Does that work? I hope that's clear. I understand it, but we'll need to practice it. Yeah. With long division, it takes practice because it incorporates everything. You're doing multiplication and you're doing subtraction, which is really addition. Square, 1996. The unique thing why I love math is answer is always same, but the path is different to achieve it. That's where the fun is. Yeah. A Vedic math freak. And there are multiple ways to get to the same answer. And multiple ways you can manipulate numbers to give you a certain perspective on a certain situation, which shines a light on certain things. And we're going to talk about this tomorrow, by the way. Okay.