Multiplication tables for 2-9

At this point I think you know a little bit about what multiplication is. What we're going to do in this video is to give you just a ton of more practice and start you on your memorization of the multiplication tables. And if you watch enough Khan Academy videos, and hopefully you will in the future, you'll realize that I'm normally not a big fan of memorization. But the one thing about multiplication is if you memorize your multiplication tables that we'll start to do in this video, it'll pay huge benefits the rest of your life. So I promise you, do it now, you'll never forget it, and the rest of your life everything will be-- well, I don't want to make false promises to you, but they'll be better than if you didn't memorize your multiplication tables. So what are the multiplication tables? Well that's all of the different numbers times each other. So let's actually do a little bit of review. So if I say what is 2 times 1? That is equal to 2 plus itself one time. So this is equal to just 2. That's 2 plus itself one time. I don't have to say plus anything because there's only one 2 there. I could also write this as 1 plus itself two times. So that's also 1 plus 1. Well that also equals 2. Fair enough. So 2 times 1 is 2. And if you watched the last video, what's 2 times 0? Well that's 0. So you don't have to memorize your 0 multiplication tables because everything times 0 is 0, or 0 times anything is 0. So let's see. What's 2 times 2? Well, this is equal to-- we're going to add 2 to itself two times. So that's 2 plus 2. And there's only a way to do that. I could say take this 2 and add it to itself two times, but it's the same thing. And what's 2 plus 2? That's equal to 4. What's 2 times 3? 2 times 3 is equal to 2 plus 2 plus 2. It can also be equal to 3 plus 3. We learned in a previous video this statement can be written either of these ways. And in either case, what's it equal to? Well, 3 plus 3 is the same thing as 2 plus 2 plus 2, and that's equal to 6. All right. Now what is 2 times 4? Well that's equal to 2 plus 2 plus 2 plus 2. And notice, it's exactly what 2 times 3 was. 2 times 3 was that. I have that here, but now I'm just adding another 2 to it. So if we're too lazy to sit here and add 2 plus 2 is 4. 4 plus 2 is 6. Instead of doing that, we could say, hey look, we already know that this thing over here, this was 6. We figured it out in the previous line right there. We figured out this is 6, so we could just say, oh, 2 times 4 is going to be 2 more than that, which is equal to 8. And you should hopefully see that pattern. As we go from 2 times 1, to 2 times 2, to 2 times 3, what's happening? How much are we going up by? From 2 to 4 we're going plus 2. From 4 to 6 we're going plus 2. And then from 6 to 8 we're going plus 2. So you could figure out what 2 times 5 is, even without doing the addition. 2 times 5 is equal to 2 plus 2 plus 2 plus 2 plus 2. It could also be written as 5 plus 5. 2 times 4 could've been written as 4 plus 4 as well. And what's that equal to? We could add all of these up or we could add these two up. Or we could just say it's going to be two more than 2 times 4. So it's going to be 10. I'll finish the 2 times tables. And I think you see all of the patterns that emerge from it. So 2 times 6. That's going to be 2 plus itself six times. Let's see. 1, 2, 3, 4, 5, 6, which should also be equal to 6 plus itself two times. This could be interpreted either way. And that's going to be equal to 12. Once again, two more than 2 times 5 because we're adding 2 to itself one more time. So it's going to be two more. Let's keep going. So 2 times 7. 2 times 7 is equal to-- well, I could write 2 plus 2 plus 2 plus 2-- this is getting tiring-- plus 2 plus 2. Is that 7? 1, 2, 3, 4, 5, 6, 7. And that's the same thing as 7 plus 7, which you may or may not know is equal to 14. You could just say hey, that's going to be two more than 12. So 12 plus 1 plus 2 is-- 12 plus 1 is 13. 12 plus 2 is 14. All right, let's just keep going. 2 times 8. I could do all of this business here where I add the 2's or I could say look, it's just going to be two more than 2 times 7. So I could say it's going to be 14 plus 2. I'm just adding two to that one. So I could say it's 16. Or I could also say that's 8 plus 8. That's also 16. I could have done all the 2's out, but if you like you could do that for your own benefit and learning. We're almost-- well, we could go forever because there is no largest number. I can keep going. 2 times 9 times 10 times 100 times 1,000 times 1,000,000. But I'm going to stop at 12 because that tends to be what people need to memorize. But if you really want to be a mathlete you want to go up to 20. But let's go to 2 times 9. That's going to be two more than 2 times 8. It's going to be 18. Or that's 9 plus 9. Also 18. What's 2 times 10? And 10 times tables are interesting. And we're going to see a pattern there in a second when we try to complete an entire times tables. So 2 times 10? Two more than 2 times 9. It's 20. Or we could also say that's 10 plus 10. 10 plus itself two times. Now what's interesting about this? This looks just like a 2 with a 0 added. And you're going to see that anything times 10. You just put a 0 on the right. And you can think about why that is. You can view this as two 10's is 20. That's what 20 is. We're almost done. Let's do 2 times 11. 2 times 11 is going to be 2 more than this right here. It's going to be 22. Another interesting pattern. I have the number repeated twice-- a 2 and a 2. Interesting. Something to watch out for as we look at other multiplication tables. And then finally-- it's not finally, we could keep going. 2 times-- that's too dark of a color. 2 times 12. 2 times 12 is going to be two more than 2 times 11. That's 24. We could have also written that as 12 plus 12. Or we could've said 2 plus 2 plus 2 plus 2 plus 2 twelve times. It all gets you to 24. So that's the 2 times tables and I think you see the pattern. Every time you multiply it by one higher number you just add 2 to that number. So now that we see that pattern, let's see if we can complete a multiplication table. So what I want to do, I'm going to write all the numbers. Let's see. I hope I have space for this. 1, 2, 3, 4, 5, 6, 7, 8, 9. Actually, I'll just do it till 9. I'll just keep going. 9. Actually I won't have space to do that because I want you to see the entire table. So I'm just going up till 9 here, but I encourage you after this video to complete it on your own. Maybe if we have time I'll complete it here as well. So these are the first numbers that I'm going to multiply. And I'm going to multiply it times 1, 2, 3, 4, 5, 6, 7, 8, and 9. Actually I should have written this 1 under- well, what's 1 times 1? So this is the way I'm going to view it. Whatever is 1 times 1 I'm going to write here. Well that's 1. What's 1 times 2? That's 2. What's 1 times 3? That's 3. 1 times anything is that number, so I can just write 4, 5, 6, 7, 8, 9. 1 times 9 is 9. Fair enough. Now let's do the 2 times tables. I'll do that in a blue. Actually, let me do 1 in that color and now in maybe a darker blue I'll do the 2 times tables. What's 2 times 1? That's 2. It's the same thing as 1 times 2. Notice, these two numbers are the same thing. What's 2 times 2? That's 4. 2 times 3 is 6. We just did this. Every time you increment or you multiply by a higher number, you just add by 2. 2 times 4 is 8. Same thing as 4 times 2. 2 times 5 is 10. 2 times 6 is 12. I'm just adding 2 every time. Up here I added 1 from every step, here I'm adding 2. 2 times 7, 14. 2 times 8, 16. 2 two times 9, 18. All right, let's do our 3 times tables. I'll do it in yellow. 3 times 1 is 3. Notice, 3 times 1 is 3. 1 times 3 is 3. These are the same values. 3 times 2 is the same thing as 2 times 3. 3 times 2 should be the same thing as 2 times 3. So it's 6. And that makes sense. 3 plus 3 is 6 or 2 plus 2 plus 2 is 6. So every time here we're going to increase by 3. You see the pattern. 3 times 3 is 9. 3 plus 3 plus 3. So we went from 3 to 6 to 9. So 3 times 4 is going to be 12. I'm just adding 3 every time. 12 plus 3 is 15. 15 plus 3 is 18. 18 plus 3 is 21. 21 plus 3 is 24. 24 plus 3 is 27. So 3 times 9 is 27. 3 times 8 is 24. So if you were to say 8 plus 8 plus 8, it would be 24. So now I'm going to speed it up a little bit now that we see the pattern. And you should do this on your own and you really should memorize everything we're doing. You should actually go all the way up to 12 in both directions. So let's see. 4 times 1 is 4. I'm just going to go up by increments of 4. So 4 plus 4 is 8. 8 plus 4 is 12. 12 plus 4 is 16. 16 plus 4 is 20. 20 plus 4 is 24. 4 times 6 is 24. 4 times 7, 28. I'm just going up by 4. 32 and 365. All right, 5 times 1. 5 times 1 is going to be 5. Actually, we know that anything-- well, I want to keep changing colors, so I'll just do it in rows like this. 5 times 1 is 5. 5 times 2 is 10. 5 times 3 is 15. I'm just going to increase by 5. 5 times tables are very fun as well because every number you're going to add-- if we multiply 5 times-- well, we'll learn about even and odd in the future. But every other number in its times tables is going to end with a 5, and then every other one's going to end with a 0. Because if you add 5 to 15 you get 20. You get 25, 30, 35, 40, 45. Fair enough. 6 times tables, let me do it in green. 6 times 1 is 6. That's easy. You add 6 to that, you get 12. You add 6 to that, you get 18. You add 6 to that, you get 24. You add 6 to that, you get 30. Then you go 6 more, 36, 42, 48. 48 plus 6 is 54. So 6 times 9 is 54. All right, we're almost there. 7 times 1, that's 7. 7 times 1 is 7. 7 times 2 is 14. 7 times 3, 21. 7 times 4, 28. 7 times 5, what's 28 plus 7? Let's see. If you add 2 you get to 30. Then you have 5, 35. 7 times 6, 42. 7 times 7, 49. 7 times 8. Seven times is going to be 7 plus this, so it's 56. I always used to get confused between 7 times 8 being 56 and 6 times 9 being 54. So now that I pointed out to you that I always got confused between those two, it's your job not to be confused by those two. 7 times 8 you could say has the 6 in it. 6 times 9 doesn't have the 6 in it. That's the way I think of it. Anyway, 7 times 9. We're going to add another 7 here. It's going to be 63. I'll do it in the same color. All right, we're at our 8 times tables. 8 times 1 is 8. 8 times 2 is 16. 24. 8 times 3 is 24. And if we go to 3 times 8 we should also see the 24. Yep, it's there. These values are the same. So we're actually doing things twice. We're doing it when you do 8 times 3 and we're doing it when we did 3 times 8. Let's see. 8 times 4, you're going to add 8 to it-- 32. 40. Add another 8, 48. Notice, 8 times 6, 48. 6 times 8, 48. All right, 8 times 7. Well, we already pointed that one out, that was 56. 8 times 8, 64. 8 times 9, add 8 to this, is 72. Now we're at the 9 times tables. I'm running out of colors. Maybe I'll reuse a color or two. I'll use the blue again. 9 times 1 is 9. 9 times 2, 18 9 times 3-- we actually know all of these. We could look it up in the rest of the table because 9 times 3 is the same thing as 3 times 9. It's 27. Add 9 to that. 27 plus 9 is 36. 36 plus 9 is 45. Notice, every time you add 9, you go almost up by 10, but 1 less than that. So up by 10 would be 46, and then one less than that is 45. But anyway, notice, the 1's-- well, I'll talk more about it in the future. But we go from a 9, 8, 7, 6, 5 on this digit, on the second digit. And on this digit here you go 1, 2, 3, 4. So it's an interesting pattern. Another interesting pattern is the digits will add up to 9. 3 plus 6 is 9, 2 plus 7 is 9. We'll talk more about that in the future and maybe prove that to you. 9 times 6, 54. That was this one as well. 9 times 7, 63. 9 times 8, 72. 9 times 9 is 81. I don't know if you can see that. 81. There you go. Now, I could keep going. Actually, I should keep going. Well, I realize this video is already pretty long. I want you to memorize this right now because this is going to get you pretty far. In the next video I'm going to do the times tables past 9. See you soon.