Math Trick - multiply with lines - the five zero edition - By tecmath
Transcript
00:0-1 | Good day . Welcome to the Tech Math Channel . | |
00:01 | What we're gonna be having a look at in this | |
00:02 | video as a way of multiplying using lines and this | |
00:05 | is a bit of a , uh , an add | |
00:07 | on to a video . I've already made multiplying using | |
00:09 | lines and this is going to be looking where we | |
00:11 | are and how we can deal with it . So | |
00:13 | we had a zero in the number or numbers that | |
00:15 | are bigger numbers , they are six , sevens , | |
00:17 | eights and those sort of numbers , the numbers above | |
00:19 | five . Uh , so the type of questions we | |
00:22 | were looking at in this last year , I put | |
00:24 | a link up for this , by the way , | |
00:26 | these sorts of ones . Um , so I'll put | |
00:27 | the link up just during what I'm explaining this . | |
00:30 | Uh , it's this type of question to say we | |
00:32 | had 13 times 12 . And the way we do | |
00:38 | this is as follows , we draw the 13 , | |
00:40 | we're going to be doing it using lines . Okay | |
00:42 | . We did this using lines . So we went | |
00:43 | as follows . We did the 13 like this one | |
00:46 | , add one , 2 , 3 . Okay , | |
00:50 | that's 13 and 12 . We do this way . | |
00:52 | one that one , two for 12 . Okay . | |
00:58 | And then what we do is we separate these up | |
01:00 | into the far corner . Here on the right , | |
01:02 | is the units part . The next to going along | |
01:06 | is the 10s part and the next one going along | |
01:09 | as 1/100 part . And we simply count intersections to | |
01:12 | get our answers . I show you what I mean | |
01:13 | by this women , 123456 So the unit was a | |
01:18 | 612345 The tens was a five and the hundreds was | |
01:24 | that one ? So I answer 156 . So that's | |
01:29 | it's a good little method . So like I said | |
01:30 | , the the links should be up there uh , | |
01:33 | to do this . If not , please remind me | |
01:35 | of occasionally make that error when I do that . | |
01:38 | So I'm going to show you first off , because | |
01:41 | you can imagine first off , this doesn't account for | |
01:44 | the number zero . What do we do if we | |
01:45 | have that ? But also what we do is we | |
01:47 | have big numbers . So yeah , all of a | |
01:49 | sudden you'd have lots and lots of intersections and how | |
01:51 | we can go about uh working to eradicate that problem | |
01:56 | . So we'll have a bit of a look . | |
01:57 | Okay , look , I'm gonna be using colors , | |
02:00 | you might use a slight variance if you only have | |
02:02 | one colour using , so dash lines or dots or | |
02:05 | something like this . Okay , so I'll give you | |
02:07 | an example of how we would deal with zero . | |
02:09 | So , so we had 207 times 12 . So | |
02:17 | first off , when we do this , I'm gonna | |
02:18 | be doing a couple of different color lines are going | |
02:20 | to where we're just dealing with one . So that's | |
02:23 | where I'm going to say one and 12 I'm going | |
02:26 | to use a blue line . So that's going to | |
02:28 | denote sort of where one's a crossing one another just | |
02:31 | bear with me . I get this for a minute | |
02:33 | for zeros . I'm gonna use a different colour line | |
02:35 | which is going to be read . Okay , so | |
02:37 | I'll show you what I mean with this to say | |
02:39 | what I do 207 now , whatever they were doing | |
02:41 | is say 200 and they do one two For the | |
02:45 | hundreds part for that zero part . Sorry , that | |
02:48 | that was the hundreds part for the zero part zero | |
02:51 | Like that . Just a Red Line and the seven | |
02:55 | , I'm going to Draw seven lines . I'll show | |
02:57 | you how to deal with this . I think on | |
02:59 | the next question , we'll just deal with this variance | |
03:01 | . So 4567 at 12 we had what ? And | |
03:09 | one two . Okay , you're going to see here | |
03:14 | not to extend those out a little bit . You're | |
03:16 | gonna say , look , it's not perfect , but | |
03:19 | you sort of can visually see that this is we | |
03:22 | have the units part here , the far right part | |
03:25 | , we have the next one along and the next | |
03:27 | one along which is our tens , we have the | |
03:29 | next one's along which are hundreds and the next one's | |
03:32 | along , which is going to be thousands . So | |
03:35 | we're gonna count in sections . Now , the big | |
03:37 | difference will be here is where we're gonna have these | |
03:39 | red lines intersection and you'll see what we do with | |
03:41 | these . So first off for the units , we | |
03:43 | have 123456789 10 , 11 , 12 , 13 , | |
03:49 | 14 there . So we're gonna put four of these | |
03:51 | down . I'm gonna put the answer up here running | |
03:52 | our space down here and going to carry this one | |
03:56 | . Okay . Where we have these intersections here ? | |
03:58 | That's like zero times one . Okay . These are | |
04:01 | the ones over here a lot . One times one | |
04:02 | . And we're counting them because one times one is | |
04:04 | one these long zero times 10 times one is zero | |
04:07 | . So we're gonna be able to ignore those . | |
04:10 | So we're just going to count these where the blue | |
04:12 | ones across 1234567 Plus that one we carried is going | |
04:18 | to be eight . Once again we have where the | |
04:22 | reds crossing the blue with zero on the one cross | |
04:25 | . So we're just ignoring that and we're going to | |
04:27 | go 1234 And in the thousands we have two . | |
04:34 | So my answer is 2484 . How did you go | |
04:39 | with it ? Okay . I'll tell you what , | |
04:41 | I'll go through how I deal with the bigger numbers | |
04:45 | because we had at seven and you're sure you saw | |
04:47 | probably it was getting very are cumbersome and there's a | |
04:49 | lot of Aha . Yeah , a lot of lines | |
04:51 | and that sort of deal in intersections . That makes | |
04:53 | a little bit harder . So we do have a | |
04:55 | way that we can deal with those . Okay . | |
04:58 | So so we had a lot of about 109 . | |
05:03 | And to this we're going to multiply 72 . Okay | |
05:07 | . Now we've got a couple of big numbers here | |
05:08 | . We got the 97 . Also put a zero | |
05:10 | in there just to deal with that extra little layer | |
05:13 | of joy there . So 109 I'll show you how | |
05:17 | we're going to do this . So the 100 stays | |
05:19 | the same . Okay , the 100 . This is | |
05:21 | one and a zero part of that you probably guessed | |
05:23 | is this to do the nine I'm gonna use now | |
05:26 | with third color . Okay , I'll use black . | |
05:31 | And what this is going to be is where we | |
05:32 | get a five . Okay , So we do a | |
05:38 | a dying so that this would have a five and | |
05:42 | we have word two three , four . Okay . | |
05:48 | For the seven we're going to have yeah , we're | |
05:51 | gonna start up here . We're going to have one | |
05:53 | . You probably guessed it . 12 and for the | |
05:58 | two part , we're going to have one , two | |
06:03 | . Okay . So now I'm going to go through | |
06:05 | and separate up our unit . So I started this | |
06:07 | far bit here and I circle those . The next | |
06:11 | part . The 10th Circle . These the next part | |
06:15 | of the circle is the hundreds . The next part | |
06:18 | of the circle , I'm just going to redo that | |
06:20 | . It was a little bit rough . Okay , | |
06:22 | I'll circle That one . Did the thousands . So | |
06:29 | there's a bit of a different here . I'll talk | |
06:31 | about what we get to actually going to get to | |
06:32 | that straight away . Because what you're gonna see is | |
06:34 | where the black crosses . The blue . This is | |
06:36 | like five times one . So we're gonna count each | |
06:37 | one of these . Black crosses . Blue is five | |
06:39 | times one is five , so 5 10 , 11 | |
06:43 | , 12 , 13 , 14 , 15 , 16 | |
06:45 | , 17 , 18 . And I carry the one | |
06:48 | where the red crossing something zero times something . So | |
06:51 | it's nothing , it's zero , sorry . Uh , | |
06:54 | this one's got a few little variations . This one's | |
06:56 | got where blacks crossing black . That's for five times | |
06:58 | in 555 25 . And where Blues Crossing White one | |
07:01 | times 5 . Just five . So 25 , 30 | |
07:05 | 35 , 45 , 55 56 57 58 59 60 | |
07:11 | 61 62 63 64 . That's going to come for | |
07:15 | carry the six . The reds are all going to | |
07:18 | be counted out . So we've only got 12 here | |
07:21 | . Two plus six is I'd Okay , get rid | |
07:25 | of that . And here we have five 567 So | |
07:32 | I answer 7,848 . And that's the way that you | |
07:36 | can deal with these . Okay . Rather getting lots | |
07:38 | and lots of intersections . Okay . What about to | |
07:42 | go through a couple more where you you try to | |
07:44 | answer them , so you see how you go . | |
07:46 | Okay ? And yeah , you my my mistakes with | |
07:50 | this . It's it's It's a good little visual method | |
07:53 | . It's not necessarily always the fastest method , I | |
07:55 | must say . Okay , so 206 Times 40 . | |
08:00 | What about you ? Give that a go , pause | |
08:01 | that give it a go see how you go . | |
08:04 | Maybe we haven't got a maybe if you haven't got | |
08:08 | uh colored pen , you could use dash lines here | |
08:10 | , dotted lines of the five or certainly whichever you'll | |
08:13 | be good with . So Anyway , the way that | |
08:17 | would do this is as follows 206 . Hopefully you | |
08:19 | got the answer . I was going to start doing | |
08:20 | it now . I know you can pause me 200 | |
08:24 | at six . Did you get a oh look at | |
08:28 | that . I called the Royal colour there . I'll | |
08:30 | get rid of these . So I'll get rid of | |
08:31 | those 200 at six . We have times that by | |
08:43 | 14 . So why and why ? Two three and | |
08:52 | where that one of the four . So then I'll | |
08:54 | get to that joyous part of our trying to circle | |
08:57 | these . Okay , so this is our unit . | |
09:01 | This is going to be 10s part . This is | |
09:04 | going to be hundreds . And over here we have | |
09:08 | our thousands . Did you get something like this ? | |
09:11 | Let's can't . 5 10 15 21 2346 24 carry | |
09:17 | the two These counselor . So we just left you | |
09:20 | 56 Plus two is 8 . We have This council's | |
09:28 | out . We have 12345678 . And over here we | |
09:32 | have one to our answer is 2,884 . Okay , | |
09:38 | I'll give you one last one of these . Hopefully | |
09:40 | you went really well with that . Hopefully you're you | |
09:42 | could if you did you see where you've made a | |
09:44 | mistake ? That's okay . As you saw , I | |
09:47 | made a mistake when I started doing it . So | |
09:49 | , you know , it's easy to do . uh | |
09:53 | 607 Times 24 . Okay , last question . Give | |
09:58 | us a guy . Okay , suppose it . All | |
10:01 | right . 607 times 24 . So we have it's | |
10:05 | fairly quickly . Okay , so this is our six | |
10:09 | , A little bit bigger . 100 and 700 and | |
10:14 | seven . Hopefully you got something that looks a bit | |
10:17 | like this times 24 . So we have 24 , | |
10:21 | which is one , two and 4 one two three | |
10:28 | for . Okay , you see , I'm being fairly | |
10:31 | whatever here , as long as you can keep your | |
10:33 | what you're doing in your head and what you're doing | |
10:35 | fairly straight , you're pretty good . That's the units | |
10:37 | . It's going to be the tens , this one | |
10:41 | here is going to be our hundreds and that one | |
10:44 | there is going to be a thousands . Alright , | |
10:45 | so no problem . Let's count them 5 10 15 | |
10:49 | 2021 22 23 24 25 26 27 28 . Put | |
10:53 | the eight down there . Put the two over here | |
10:55 | across this one out because it's got the red there | |
10:57 | . Okay ? So 5 10 11 , 12 13 | |
10:59 | 14 15 16 . Put the six there , move | |
11:02 | the one over here . Then we can count this | |
11:04 | 15 10 15 2021 22 23 24 25 . And | |
11:09 | this one's counseled out . So they put that they're | |
11:12 | five there , carry the 25 10 11 , 12 | |
11:15 | , 13 14 . Our answer 14,568 . So , | |
11:22 | how'd you go with that ? That's how you can | |
11:24 | go about dealing with the fives and the Zeros . | |
11:28 | It's it's not a bad method anyway . Let us | |
11:31 | know what you think of that . Uh no , | |
11:33 | it's not gonna be great . Still when you do | |
11:34 | 99 times 99 or 99 times 998 . All right | |
11:39 | . It does still get fairly whatever with that , | |
11:42 | but that's just the way you might modify . I | |
11:45 | hope that helps anyway by |
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Math Trick - multiply with lines - the five zero edition is a free educational video by tecmath.
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