Fast Mental Multiplication Trick - Multiply in your head using base 20 and 30 - By tecmath
Transcript
| 00:0-1 | good and welcome to the tech mouth channel . We're | |
| 00:02 | gonna be having a look at in this video is | |
| 00:04 | going to be looking at using base method multiplication to | |
| 00:06 | multiply numbers in their twenties and thirties . This is | |
| 00:09 | sort of part . So we had a video before | |
| 00:11 | we were looking at using based method multiplication for multiplying | |
| 00:15 | numbers more around the number 10 . But this is | |
| 00:18 | looking around twenties and thirties . Based method multiplication by | |
| 00:21 | the way , is where we multiply two numbers , | |
| 00:23 | but we use a third number called a base . | |
| 00:26 | A nice easy number in order to help us . | |
| 00:28 | So what we're having looked at in the last video | |
| 00:31 | we shall put links up for was where we might | |
| 00:33 | multiply some numbers like 17 times 13 . And we | |
| 00:39 | would use this friendly number of base In this case | |
| 00:42 | it was the number 10 . In order to help | |
| 00:44 | us . Now we look at the base 17 with | |
| 00:48 | seven , more than 10 and 13 was three more | |
| 00:53 | than 10 . So we're riding those up there . | |
| 00:55 | But this is something you can do mentally as well | |
| 00:57 | . And then what we did is we cross added | |
| 01:00 | the so 17 plus three or 13 plus seven . | |
| 01:03 | So we got the answer of 17 plus three was | |
| 01:06 | 20 . But because it was a tens number , | |
| 01:08 | we made that into 200 And then we multiply these | |
| 01:12 | guys and we added this to our answer . So | |
| 01:14 | seven times three was 21 And we end up with | |
| 01:17 | the answer of 221 . Okay . And then you | |
| 01:22 | can do this really , really easily in your head | |
| 01:24 | . But now what we're going to be doing is | |
| 01:25 | looking at how to do this using a different base | |
| 01:28 | , not 10 , but now we're going to be | |
| 01:29 | looking at base 20 and even base 30 numbers in | |
| 01:32 | this particular video . So I'll give you an example | |
| 01:36 | . What about I get you to do this one | |
| 01:39 | here , We'll walk through this one together , I'd | |
| 01:42 | say 25 times 23 . now . Now what we're | |
| 01:46 | doing is we're using the base of 20 because 20 | |
| 01:48 | is a number which is close to these And the | |
| 01:51 | way we treat this is a little bit different from | |
| 01:53 | 10 but not hugely different . First off , we | |
| 01:56 | look at this number here and it's Five above 20 | |
| 01:59 | and this one here is three above 20 . Okay | |
| 02:04 | . And then what we do is to get our | |
| 02:06 | answer as we do the same thing . We do | |
| 02:08 | this cross addition and okay , so 25 plus three | |
| 02:13 | or 23 plus five we get the answer of 28 | |
| 02:15 | . Now I'm gonna write this very Little because often | |
| 02:18 | I wouldn't bother even write it down or I wouldn't | |
| 02:20 | even think about it for too long because we're not | |
| 02:23 | dealing with a base 10 . This time we're dealing | |
| 02:25 | with base Tony . So before we were dealing with | |
| 02:27 | base 10 , you might realize that 20 is two | |
| 02:29 | times as big as 10 . Yeah . So what | |
| 02:33 | we have to do here is we make our answer | |
| 02:34 | twice as big . Okay , so 28 times two | |
| 02:40 | is 56 . So the first part of our answer | |
| 02:43 | is 5 60 . That first number in our head | |
| 02:45 | is 5 60 then we just multiply these two numbers | |
| 02:48 | together like we did before . Okay , so five | |
| 02:50 | times three is 15 and would add that to answer | |
| 02:53 | 5 60 plus 15 is 575 . Okay . Do | |
| 02:58 | you see that difference ? Okay . So at the | |
| 03:01 | start because it's a 20 we are times in fact | |
| 03:04 | , you'll see this this little trick with throw 30 | |
| 03:07 | when we deal with 30 and that too , it's | |
| 03:09 | just a slight modification . So I'll give you another | |
| 03:12 | example here . What about we do 27 times 22 | |
| 03:19 | . And what I recommend you might even start to | |
| 03:20 | try to pause season and do them in your head | |
| 03:22 | . Okay . Because the way I'd be looking at | |
| 03:24 | this as I look at it and say 27 this | |
| 03:26 | is a this one over here is to more , | |
| 03:28 | this one , here's three more . So I'd be | |
| 03:30 | thinking , okay , this plus two is 29 I | |
| 03:33 | double it and get the answer of 58 to become | |
| 03:35 | 5 80 . And then I'd be adding Uh , | |
| 03:38 | two times 7 , getting 14 . So 5 94 | |
| 03:41 | blocks . I'm not going to do that all the | |
| 03:42 | time . Okay . Just give me an example how | |
| 03:44 | you might do it in your head , but I | |
| 03:47 | will be actually writing these down . So This one | |
| 03:50 | here is seven . More than 20 . Okay . | |
| 03:53 | And this one here is To more than 20 . | |
| 03:56 | So what we did is we go 22 Plus seven | |
| 04:00 | , which is 20 nine and then we double this | |
| 04:04 | and we get 58 . So 580 . Okay . | |
| 04:09 | Because it's a tens number Then seven times 2 is | |
| 04:12 | 14 . So we add this 14 and we get | |
| 04:16 | 500 in 94 . Yeah . How'd you go with | |
| 04:21 | that ? This will take a little bit of getting | |
| 04:24 | used to but it's a really , really powerful and | |
| 04:27 | handy technique for doing this . Okay , so Let's | |
| 04:31 | give it another go here . They are going to | |
| 04:33 | be a fair few examples . I'm going to start | |
| 04:34 | varying them up a little bit . What about if | |
| 04:36 | I do it like this sort of 128 times 19 | |
| 04:39 | . Now this as you may notice We're not we're | |
| 04:43 | still got number near 20 so we are going to | |
| 04:45 | use the base of 20 but we have a slight | |
| 04:47 | difference . This one here is eight more than 20 | |
| 04:50 | . But this number here is one less than 20 | |
| 04:53 | . So we still do this cross edition but we | |
| 04:57 | might actually end up doing a bit of subtraction . | |
| 04:59 | I'll show what I mean by this . So 19 | |
| 05:00 | plus eight which is 27 is the same as 28 | |
| 05:03 | . Take one . Okay , you see that ? | |
| 05:06 | So we get 27 again because it's based based 20 | |
| 05:09 | we double it 27 times two is 54 . So | |
| 05:14 | we get 5 40 And then we multiply these two | |
| 05:18 | numbers . Okay , 1 -1 times eight is -8 | |
| 05:22 | . So we're going to take eight off our answer | |
| 05:25 | . We're going to get the answer of 500 at | |
| 05:30 | 32 . Okay , let's do another example . These | |
| 05:38 | examples will vary but they will get progressively harder . | |
| 05:40 | Yeah , so let's do another one . Been harder | |
| 05:43 | this time . Let's do one that's 32 times a | |
| 05:45 | day . And okay , These guys are a fair | |
| 05:48 | difference from from each other , you know , I | |
| 05:50 | think it's pretty handy to chuck this sort of example | |
| 05:52 | in there . So we're still gonna use based 2020 | |
| 05:55 | is a nice central number between them . And what | |
| 05:58 | we'll do is we'll look at this one will say | |
| 06:00 | this one's now 12 , higher than 20 . This | |
| 06:04 | one in fact , is too less than 20 and | |
| 06:09 | we do that cross addition thing again . So 18 | |
| 06:13 | plus 12 we get the answer of 30 we double | |
| 06:16 | that , we get 60 so it's 60 times 10 | |
| 06:19 | is 600 and now he times these two numbers minus | |
| 06:23 | two times 12 is minus 24 . So 600 -24 | |
| 06:31 | we get the answer of 500 and 76 . How | |
| 06:37 | are you going to these ? So what you might | |
| 06:40 | be doing is you might be pausing it and giving | |
| 06:42 | it a go and then seeing how you go with | |
| 06:44 | the answers . There are a few for a fair | |
| 06:45 | few more ones to come out with . I think | |
| 06:47 | it's something you should practice a lot . So what | |
| 06:49 | about Ir give you another one ? What about we | |
| 06:52 | do um oh do this one here will do 26 | |
| 06:58 | times 35 . Okay , 26 times 35 . So | |
| 07:03 | this one here is Okay we're gonna use base 20 | |
| 07:06 | obviously again is plus six . This one here is | |
| 07:10 | 15 , more than 20 . Okay , so we | |
| 07:13 | do that cross edition again . So you do the | |
| 07:15 | cross edition . What do you get ? 35-plus 6 | |
| 07:19 | is 41 we double it 41 . We get 80 | |
| 07:22 | to 82 becomes 820 six times 15 we get the | |
| 07:30 | answer of 90 . So we're gonna add 90 . | |
| 07:35 | Giving us how much ? 910 . Okay , let's | |
| 07:44 | go through another example here . You see how easy | |
| 07:48 | this is . There are a few little tricks , | |
| 07:49 | aren't there ? Okay , let's let's do another example | |
| 07:52 | here . What about we do this one 31 Times | |
| 07:59 | 39 . Now before you start on this one , | |
| 08:01 | you might Also realize that we don't have to necessarily | |
| 08:04 | use based 20 now because we actually haven't done whether | |
| 08:07 | it's even closer To both these numbers and that's 30 | |
| 08:11 | . So I'm gonna show you really , really quickly | |
| 08:13 | how you might use base 30 and how you might | |
| 08:16 | do this . I'll put the 30 down there and | |
| 08:19 | we were using base 10 at the start , we're | |
| 08:21 | gonna now realize we went to base 20 weeks times | |
| 08:24 | are answered by two . We're going to base 30 | |
| 08:25 | with times are answered by three . That first part | |
| 08:28 | of the answer . Yeah . So this one here | |
| 08:30 | is one more than 30 . This one here is | |
| 08:34 | nine . More than 30 . Okay . And then | |
| 08:37 | we do the same . What we were doing before | |
| 08:40 | . What we go 31-plus 9 is 40 . Okay | |
| 08:44 | . 40 times three is 100 and 20 . Okay | |
| 08:48 | . So we're going to get 120 groups of 10 | |
| 08:50 | . So it's a tens one . So we're gonna | |
| 08:52 | end up with 12 11,200 . Okay . And then | |
| 08:58 | we multiply these two guys together one times 9 is | |
| 09:03 | nine . And these guys together we get the lovely | |
| 09:07 | answer of 1000 209 . Okay . What about I'm | |
| 09:13 | going to give you a bunch of examples , in | |
| 09:14 | fact , in this video because it's a bit of | |
| 09:17 | a tricky sort of thing to get your head around | |
| 09:18 | . I think at the start , I'm going to | |
| 09:20 | give you six lots of examples here . Okay . | |
| 09:22 | Each in groups of three . All right . So | |
| 09:25 | see how you go with these in the next video | |
| 09:27 | . We're going to start having a look at base | |
| 09:28 | 50 . Okay . So you might if you if | |
| 09:32 | you think you've got the hang of it , you | |
| 09:33 | might try to skip ahead to that . So here's | |
| 09:35 | a bunch of examples . I do recommend you get | |
| 09:37 | them to go . Uh , what about we do | |
| 09:41 | 23 times 22 . What about we do 29 Times | |
| 09:49 | 19 . Be careful of that one . Whatever we | |
| 09:52 | do 36 times 29 . I'll tell you what I | |
| 09:58 | recommend with that one . May be going to use | |
| 09:59 | based 30 for that one . So pause the video | |
| 10:02 | . See how you go with them . Okay hopefully | |
| 10:06 | a pause the video . Hopefully you're trying to do | |
| 10:08 | it but now we're going to walk to work through | |
| 10:09 | them . Let's we're going to use base 20 for | |
| 10:11 | this one . So this one is three above 20 | |
| 10:15 | . This one here is to above 20 . Okay | |
| 10:19 | So what we do is 23 plus two is 25 | |
| 10:22 | . We double that . We get 50 so we | |
| 10:24 | have 500 Then with three times 2 is six . | |
| 10:30 | Okay so we're gonna add that . We're going to | |
| 10:32 | get the answer of 506 . How did you go | |
| 10:36 | with that 1 ? Hopefully you went really good . | |
| 10:39 | Okay let's do this . Next one . This one | |
| 10:41 | here we're going to use base 20 again because 20 | |
| 10:44 | is a nice central number between these nines nine . | |
| 10:49 | About nine above 29 9 above 20 . Sorry , | |
| 10:52 | this one here is one below . Okay so what | |
| 10:57 | are we going to get it ? If we go | |
| 10:58 | 29 take one we get 28 . We double that | |
| 11:01 | . We get 56 so 560 and then what we're | |
| 11:07 | gonna do is going to get a negative number because | |
| 11:08 | it's a minus times a plus and minus one times | |
| 11:12 | nine which is minus nine . So we're taking nine | |
| 11:15 | off her answer . We're going to get the answer | |
| 11:17 | of 500 and 51 . How'd you go with that | |
| 11:21 | ? Did your foot did you add nine or digit | |
| 11:23 | eight ? Did you had 99 then ? Okay . | |
| 11:26 | Hopefully it took it away . All right . This | |
| 11:28 | next one I must say I was treating this as | |
| 11:31 | a base 30 . So We're going to do that | |
| 11:34 | . We're going to this 16 More than 30 . | |
| 11:37 | This one here is one less than 30 . Okay | |
| 11:42 | , so let's do this . uh 36 . Take | |
| 11:46 | one is 35 Then we multiply that not by two | |
| 11:50 | but now by three . So 35 times three is | |
| 11:53 | 105 . So we get a 1050 , we're also | |
| 11:59 | going to have to take a number off this , | |
| 12:01 | so minus one times minus six at times six Is | |
| 12:07 | -6 -1 times six is -6 . So we're taking | |
| 12:10 | six off our answer And we get the answer of | |
| 12:14 | 1000 and 44 . So how did you go with | |
| 12:19 | those ? Okay , I'll tell you what , I'll | |
| 12:22 | put the next lot of videos , I put the | |
| 12:24 | next lot of um examples up here . See here | |
| 12:28 | you go with this . I think it's a really | |
| 12:29 | critical one . You get your head around these . | |
| 12:31 | Okay , practice makes real perfectly this especially when you | |
| 12:34 | start trying to work them out mentally and this is | |
| 12:36 | possibly for me , one of the greatest mental sort | |
| 12:39 | of multiplication tricks there is . Okay , so let's | |
| 12:43 | have a look at the next one . The next | |
| 12:44 | set of examples , let's do 25 Times 22 . | |
| 12:50 | Let's do 18 times 19 , Hint for this one | |
| 12:56 | . You might use base 10 or base 20 . | |
| 12:58 | I'm going to use base 20 though . Let's also | |
| 13:02 | do 33 times 27 . Okay ? Which basically you're | |
| 13:08 | going to use for that one ? Yeah , probably | |
| 13:10 | 30 . Okay , so this one we're gonna use | |
| 13:13 | based hope the pause at first . Sorry . Now | |
| 13:17 | let's go through the answers . Hopefully you've done them | |
| 13:19 | . So let's have a look . So This one | |
| 13:22 | here we're gonna use base 20 . This one's five | |
| 13:24 | above this one's to above . Okay . 25-plus 2 | |
| 13:31 | is 27 . We double that . We get 54 | |
| 13:34 | so 540 and seven times 2 . Sorry five times | |
| 13:39 | 2 is ted we add that on . We get | |
| 13:43 | the answer of 500 50 . Our next answer I'm | |
| 13:50 | going to use base 20 but we also could use | |
| 13:52 | base 10 . Maybe you've done both . Okay we | |
| 13:55 | only use base 20 so we're actually gonna have compared | |
| 13:58 | to 20 . This is too less . This is | |
| 14:01 | one less . Okay So 18 take one is 17 | |
| 14:07 | because we're using base 20 . We double it . | |
| 14:09 | So 17 we double we get 34 so we have | |
| 14:13 | 340 and -1 times -2 minus times minus is a | |
| 14:20 | plus . Yeah so minus one times minus two is | |
| 14:25 | Plus two . Okay so 340 plus two we get | |
| 14:30 | the answer of 342 . Okay . Hopefully understood that | |
| 14:36 | if we have a minus and times it by another | |
| 14:38 | minus , we get a positive number . Okay . | |
| 14:41 | The sign here is the same when we multiply them | |
| 14:43 | , we get a positive number . It's different . | |
| 14:45 | We get a negative number . Okay , let's consider | |
| 14:48 | this last question . Okay , so we're going to | |
| 14:52 | want to use base 30 for this . This one | |
| 14:54 | here is three more than 30 . This one is | |
| 14:59 | three . Less than 30 . Okay , so let's | |
| 15:05 | have a look . Uh sorry 33 take three is | |
| 15:09 | 30 . We're gonna Because it's by 30 it's three | |
| 15:13 | times as much as 30 Times three is 90 . | |
| 15:17 | So we have not 90 but we have nine 100 | |
| 15:21 | And then -3 times three we get the answer because | |
| 15:25 | these are different signs now we get a minus nine | |
| 15:29 | . So 900 take away nine is 891 . Look | |
| 15:37 | , hopefully you've gone really , really well . Those | |
| 15:39 | I think your head is probably going to explode after | |
| 15:41 | all that . I am going to put the link | |
| 15:42 | up for the next video . I've put it out | |
| 15:43 | actually on throughout this video . This for the next | |
| 15:46 | video we're going to start considering base 50 . Okay | |
| 15:50 | . You're probably getting the idea that this is a | |
| 15:52 | really , really great technique for mental maths and I | |
| 15:55 | really recommend that's how you try to start doing it | |
| 15:57 | is mentally okay . Hopefully you enjoyed that video . | |
| 16:02 | We'll see you next time . Bye . |
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Fast Mental Multiplication Trick - Multiply in your head using base 20 and 30 is a free educational video by tecmath.
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