Multiplication trick using estimation - By tecmath
Transcript
| 00:00 | Good day . Welcome to Tech Mouth channel . What | |
| 00:02 | we're going to be having a look at in this | |
| 00:03 | video . We're going to be looking at a way | |
| 00:05 | of multiplying all sorts of different numbers using approximation , | |
| 00:08 | using an estimation using a number of different reference numbers | |
| 00:14 | that will be able to work out as we go | |
| 00:16 | . Okay ? So I will warn you with this | |
| 00:18 | . There are multiple steps from this which might seem | |
| 00:20 | a little bit disjointed at the start , but you | |
| 00:22 | will get used to the pattern when you were doing | |
| 00:24 | these . Okay ? So bear with us , go | |
| 00:26 | through a few examples before you give up on this | |
| 00:29 | . Okay ? So let me give you example here | |
| 00:31 | , say I ask you to work out eight times | |
| 00:37 | 38 . Okay , so eight times 38 . And | |
| 00:41 | what is the estimation here ? So we would estimate | |
| 00:45 | ? No , but this is close to The number | |
| 00:48 | . This is close that's a nice number is 10 | |
| 00:50 | . The number that's close to this , which is | |
| 00:52 | a nice easy number is 40 . Now . Just | |
| 00:56 | going to give you a bit of a pre warning | |
| 00:57 | with these and you're gonna see these in the examples | |
| 01:00 | and you'll get better and better at doing these when | |
| 01:01 | you do this , you're gonna notice that the numbers | |
| 01:03 | we've also got here are also they have common factors | |
| 01:09 | in this number here Goes into 40 quite nicely . | |
| 01:12 | That's important when we're doing these , it's really good | |
| 01:14 | to choose a number where this number goes into this | |
| 01:17 | number if you can do that . Okay , so | |
| 01:20 | that's the first thing we'll get back to those , | |
| 01:22 | I think worry about those a little bit more later | |
| 01:24 | on . So this year It's very , very close | |
| 01:28 | to 10 . Okay , I'm going to put some | |
| 01:31 | numbers in brackets over here . 10 to represent his | |
| 01:34 | tent here . This 40 Is the same as 10 | |
| 01:37 | times four . Okay , we're all good so far | |
| 01:43 | . So that's that's the first step just getting these | |
| 01:46 | parties are approximation . So now I'm going to see | |
| 01:49 | how far each one of our numbers is from the | |
| 01:52 | approximate value from our estimation . So this 80 year | |
| 01:57 | Is two ways to less . That's it . This | |
| 02:00 | 40 here is too less then 10 also . Okay | |
| 02:05 | , we'll keep those down there . There's a couple | |
| 02:07 | of important numbers for us . The other things were | |
| 02:10 | going to be working here . This is a this | |
| 02:12 | seems like a bit of a strange step . I'm | |
| 02:14 | going to work out a third reference number of third | |
| 02:16 | number here , which I'm going to get by multiplying | |
| 02:19 | this number here before . Uh The Bible is 2-4 | |
| 02:24 | times minus two this morning . Right , okay . | |
| 02:32 | Now we were always almost set up to actually work | |
| 02:35 | these out . The way we do this now is | |
| 02:37 | we're going to go This number here , there's 38 | |
| 02:41 | and we're gonna take we're gonna diagonally take off this | |
| 02:44 | number here . Okay , this is 38 take away | |
| 02:46 | eight which is 30 . We're gonna times that by | |
| 02:49 | this number over here now . Okay . I know | |
| 02:51 | there seems to be the steps going everywhere a few | |
| 02:53 | times you get used to it , so 38 take | |
| 02:56 | away eight is 30 Times Times 10 is 300 . | |
| 03:04 | Okay , The last step we do . That's the | |
| 03:08 | first part of our answer . The last thing we | |
| 03:10 | do to get the second part of our answer was | |
| 03:12 | we just multiply these two numbers minus two times minus | |
| 03:15 | two which was four and we had them on over | |
| 03:17 | here so we get our final answer of 300 and | |
| 03:22 | four . So how was that ? Okay . It | |
| 03:25 | might seem a little bit confusing . None of the | |
| 03:27 | actual parts were that hard , but it's just remembering | |
| 03:30 | the order in which to do them . Okay . | |
| 03:32 | And they're not too bad . Once you do them | |
| 03:33 | a few times , you'll pick them up fairly quickly | |
| 03:35 | first . What we did is we got this 10 | |
| 03:37 | times for part . Okay . We took these away | |
| 03:41 | . We then multiply these two to get this number | |
| 03:44 | here and we took this off here . Okay . | |
| 03:46 | And almost in the same step , we just multiply | |
| 03:49 | this by the 10 here , you get the 300 | |
| 03:51 | and then we get our party . there's lots of | |
| 03:53 | little steps but they're not too bad . Okay ? | |
| 03:55 | And you will get further , faster and faster and | |
| 03:58 | faster doing that . So what about I give you | |
| 04:00 | another example to work through it ? They get to | |
| 04:02 | despondent yet if you're you're still scratching your head a | |
| 04:05 | little bit ? Okay . I'll give you another example | |
| 04:07 | to say . I was asking what ? seven times | |
| 04:11 | . Uh no , I see as an example again | |
| 04:13 | . What about 40 eighties , Okay . You're going | |
| 04:21 | to see that . This is very close here to | |
| 04:23 | 10 . This one here is close to 50 . | |
| 04:27 | Okay , so this with the numbers are going to | |
| 04:29 | be using over here are going to be ted You're | |
| 04:34 | probably gonna get this big times five . Okay . | |
| 04:38 | Put those in brackets And now let's work out all | |
| 04:43 | our little numbers down here . So this is three | |
| 04:46 | away from 10 . This one is two less than | |
| 04:51 | 50 . Now , what we do to get the | |
| 04:54 | second number is this third number , I mean is | |
| 04:56 | we multiply these two numbers , So through it minus | |
| 04:59 | three times five it's minus 15 and we're now We're | |
| 05:04 | going to take this off this number here , 48 | |
| 05:07 | take away 15 is 33 times 10 . Their answer | |
| 05:14 | Is 330 . We got it minus three Times -2 | |
| 05:22 | is six . So I'm going to add that on | |
| 05:23 | . We need the answer of 336 . How did | |
| 05:29 | you go with that ? You're a little bit better | |
| 05:30 | with that . Do you remember a few of those | |
| 05:31 | steps ? We'll tell you what yeah , we'll get | |
| 05:35 | some more of these , I'll tell you what , | |
| 05:36 | I'm gonna put a variation of this up and then | |
| 05:38 | we're going to get to some harder questions . Okay | |
| 05:40 | we'll be really a standard how to do these . | |
| 05:42 | Okay , there's some variances with these . So say | |
| 05:45 | I was now going to go instead . What we're | |
| 05:47 | gonna do is we're gonna do seven times 62 yep | |
| 05:52 | . What you're gonna notice with this is yeah okay | |
| 05:54 | we approximately once again this is a 10 and that | |
| 05:56 | this is a 60 . So we're gonna end up | |
| 05:58 | with okay getting much faster this now , we're gonna | |
| 06:01 | end up with 10 times six over here . Yeah | |
| 06:06 | . Now what you're going to see is this is | |
| 06:07 | three less But this 60 is actually 62 is actually | |
| 06:12 | two more Than 60 . Okay , so we actually | |
| 06:14 | got a plus two here . All right , well | |
| 06:16 | , we'll deal with that . It's just we're just | |
| 06:18 | gonna deal with it a little bit differently . So | |
| 06:20 | you get this next number , we multiply these six | |
| 06:22 | times -3 is -18 . And we take this now | |
| 06:27 | from 62 . Okay , 60 to -18 is 44 | |
| 06:32 | . Okay . Time's up right here we get 440 | |
| 06:38 | . Okay , Last of all we have -3 times | |
| 06:43 | positive to know the answer to that is -6 . | |
| 06:46 | Okay , so we don't add six on this time | |
| 06:48 | we take it away . So if we take six | |
| 06:50 | away from our answer here , what we're going to | |
| 06:52 | get is we're going to get the answer of 434 | |
| 06:57 | . Okay . Pretty cool . Right . All right | |
| 06:59 | . Let's get to some bigger examples of these . | |
| 07:04 | Yeah . What about what we do now is we'll | |
| 07:07 | start looking at what about okay , what about things | |
| 07:10 | that don't go entertain ? What about I do 18 | |
| 07:13 | time 77 . Okay , 18 times 77 . This | |
| 07:18 | is much closer to say 20 times 80 . Yeah | |
| 07:24 | . So we're gonna treat this a slight bit different | |
| 07:26 | . What we're gonna do is going to treat this | |
| 07:27 | like Okay , because 20 goes and 80 it's all | |
| 07:29 | well and nice . There's a reason I didn't choose | |
| 07:31 | 20 and 70 . Okay . Because 20 because 20 | |
| 07:36 | goes into 80 , so eight years ago by the | |
| 07:38 | choose . Like I said , you want this this | |
| 07:39 | number here to go into this number here ? Okay | |
| 07:42 | . So we're going to end up with 20 times | |
| 07:48 | four . It's this particular step here is the reason | |
| 07:51 | we want this number here to go into this number | |
| 07:53 | here , so we can get this proper part of | |
| 07:55 | the equation here . Okay , so This here is | |
| 07:58 | to less this here is three less . Okay , | |
| 08:03 | pretty good . So far to get that third number | |
| 08:06 | , this number of times this number is minus eight | |
| 08:09 | minus , that's four times minus two is minus eight | |
| 08:13 | . So now we're going to take this off . | |
| 08:15 | We're going to end up with 77 , take away | |
| 08:18 | eight , which is 69 and a lot of times | |
| 08:20 | it by this number here . So 69 Double This | |
| 08:24 | or Times 20 we're going to end up with 130 | |
| 08:32 | . But because it's 20 we're going to end a | |
| 08:33 | zero on this . Okay , let's take away . | |
| 08:35 | This was 69 69 . Sometimes you buy two , | |
| 08:38 | get 138 times in 2017 . 13 80 to get | |
| 08:42 | the last part -2 times -3 . This is six | |
| 08:47 | . Okay , so I'm gonna add six onto our | |
| 08:49 | answer . We're gonna get the answer of 1386 . | |
| 08:56 | Okay , what about we do another one of these | |
| 08:58 | and they're gonna get to an even more ridiculous example | |
| 09:01 | . Okay , what about we do ? Um Oh | |
| 09:07 | here we go , we'll do 16 times 68 . | |
| 09:11 | Okay , this is closer to 70 , isn't it | |
| 09:13 | ? So we could this one you might be tempted | |
| 09:16 | to say , okay let's call this one here . | |
| 09:18 | You might call it 10 , or you might call | |
| 09:20 | it 20 I'll tell you what I might call it | |
| 09:22 | . Uh I might call it 20 . Okay , | |
| 09:28 | this one here , you might call uh it's not | |
| 09:32 | gonna be called 77 20 . Doesn't go into 70 | |
| 09:34 | . We call it 80 . Okay . So what | |
| 09:37 | we're going to do with this is we're now going | |
| 09:40 | to get how far things are actually better . First | |
| 09:42 | to rideau things over here , we're gonna end up | |
| 09:43 | with 20 And to get 20-80 , we're gonna times | |
| 09:47 | for 20 times for okay , let's do this now | |
| 09:52 | . All right . Um this is four or less | |
| 09:56 | . This one here is 12 less . Okay , | |
| 10:01 | But now go this next step . Um this was | |
| 10:05 | these two times one . Another four times -4 , | |
| 10:07 | which is -16 . So I'm gonna take 16 of | |
| 10:10 | 68 . Year -16 and 68 . I'm gonna get | |
| 10:13 | the answer of 52 . Okay , 52 , i | |
| 10:17 | double it . I'm going to get the answer of | |
| 10:20 | 100 . Mhm . four . Okay , but this | |
| 10:24 | is by 20 . So 10 40 . Next , | |
| 10:30 | the last step we're just going to add , well | |
| 10:33 | four times minus four times minus 12 which is 48 | |
| 10:37 | . So I'm gonna add that on , we get | |
| 10:38 | the answer for AD 48 on 1000 and 88 . | |
| 10:43 | Alternatively what you could do with this issue could have | |
| 10:48 | Attack this a little bit better , a little bit | |
| 10:49 | differently . What I'll do is I'll keep that 1,088 | |
| 10:52 | job up here again and we'll see what would have | |
| 10:55 | happened if we hadn't done it slightly differently . We | |
| 10:57 | could have actually done this and you bought it I | |
| 11:01 | think yeah we could have done this . So this | |
| 11:02 | was a 10 and this one could be 70 . | |
| 11:05 | Okay , So this would be the same as 10 | |
| 11:09 | times seven . Are you Okay ? This is six | |
| 11:13 | more . This one here is Okay , this one | |
| 11:18 | here is to less . In fact you might even | |
| 11:20 | find that easy to turn that into a 60 because | |
| 11:22 | then you're not taking it away . Okay ? But | |
| 11:25 | this one here is too less . Okay , so | |
| 11:29 | what do we get this one times this . Six | |
| 11:32 | times seven is 42 . That's plus 42 . Okay | |
| 11:36 | , so let's add these on 42 plus 68 Is | |
| 11:43 | 1100 . Well what's up ? $110% . 10 is | |
| 11:49 | one thing as of 100 and we're going to six | |
| 11:54 | times minus two is 12 . We're gonna take away | |
| 11:57 | . We end up with this answer again . 1000 | |
| 12:01 | Okay minus 12 which is 1000 and 88 . Okay | |
| 12:08 | . Alternatively , yes , you might have actually called | |
| 12:09 | this 60 and you might have called this plus and | |
| 12:12 | you'll get the same answer . Okay , what about | |
| 12:14 | we do a harder example now . Even harder one | |
| 12:18 | . Okay , What about we go right out and | |
| 12:21 | we do say something like 97 Times 489 . 489 | |
| 12:31 | . Let's do this one . So if we were | |
| 12:33 | to do this , this is approximately 100 . This | |
| 12:36 | one here lets call 500 . Okay . So we're | |
| 12:41 | going to end up with a 100 times five . | |
| 12:46 | All right , this is three less . This one | |
| 12:49 | here is 11 less . Okay , So what are | |
| 12:52 | we doing now ? We go this one time . | |
| 12:55 | Is this one okay , minus 15 . And we're | |
| 12:57 | going to take this off this number here . 489 | |
| 13:00 | take away 15 . The answer to that is going | |
| 13:04 | to be 474 There were times that by 100 , | |
| 13:08 | wouldn't we ? So we would do that in the | |
| 13:10 | time to buy 100 . Just put a couple zeros | |
| 13:13 | there Then three times 1133 . We're gonna add that | |
| 13:17 | on . Okay , so the answer is going to | |
| 13:19 | be 4 , 74 33 . Pretty cool . Right | |
| 13:25 | beside the real party drink one . This one . | |
| 13:28 | Okay . It's going to give you guys a couple | |
| 13:30 | of examples that you can do by yourself . Hopefully | |
| 13:32 | you're getting the hang of those . Okay ? As | |
| 13:34 | you'll see you to start to get faster and faster | |
| 13:36 | and faster and faster at doing them . So what | |
| 13:39 | about a nice easy you want to start off with | |
| 13:42 | ? I'll get you to do 13 12 52 and | |
| 13:52 | then we'll go on to I'll go with this one | |
| 13:55 | first . Give this one to go , mm not | |
| 13:59 | gonna have enough working out space otherwise . Okay , | |
| 14:01 | this one here probably at that stage you probably don't | |
| 14:04 | need to write this bit down anymore . You might | |
| 14:06 | just say this is three . What am I doing | |
| 14:09 | ? It's not three , it's ted times five in | |
| 14:15 | brackets . All right , I'll move that . So | |
| 14:20 | I have a bit of space there . We have | |
| 14:22 | 10 times five and now is what we do is | |
| 14:25 | we see how far this is from 10 . This | |
| 14:27 | is three more and this one here is too less | |
| 14:34 | . What am I doing ? This is three more | |
| 14:36 | . This is two more . Okay . Maybe I | |
| 14:38 | should have been putting those particular things up there three | |
| 14:41 | times five is 15 . So we're gonna end up | |
| 14:44 | with plus 15 and now we take this off 50 | |
| 14:47 | to take away 15 . We're gonna get the answer | |
| 14:50 | of uh 52 plus 15 . We're gonna get the | |
| 14:54 | answer of 67 . Okay . This is times 10 | |
| 14:58 | . But rather than actually write anything down here , | |
| 15:00 | I'm just gonna have a quick look at this . | |
| 15:01 | This is three times two . This is six . | |
| 15:04 | So once I add this six on here , I'm | |
| 15:06 | going to have my answer . Okay , that was | |
| 15:09 | a pretty badly done one . That one . I | |
| 15:11 | apologize for that . Hopefully you did it much better | |
| 15:14 | than I did . Um Okay , what about a | |
| 15:16 | different one ? What about we do 23 . Mhm | |
| 15:20 | . Times 126 . Okay , This one here you | |
| 15:26 | might be thinking okay , 20 and this one here | |
| 15:28 | , you might think okay , 20 and 120 is | |
| 15:31 | a good number because 20 goes into 120 . So | |
| 15:34 | let's do this as 20 times six year . 20 | |
| 15:39 | times 620 . So this one is three more . | |
| 15:43 | This one here is six more . Hey , hopefully | |
| 15:46 | you're doing these six times 3 is 18 plus 18 | |
| 15:52 | . So I'm gonna add 18 to 126 years . | |
| 15:56 | So if I had 18 to 126 I'm going to | |
| 15:58 | get the answer of 1 44 and we'll put that | |
| 16:01 | one down there a number of times that by 20 | |
| 16:03 | . So I'm gonna get the center of 288 W | |
| 16:06 | numbers is so easy , isn't it ? 288 . | |
| 16:09 | But this is by 20 so 2880 . And to | |
| 16:12 | that I'm going to add six times three which was | |
| 16:14 | 18 . So if I add 18 to this only | |
| 16:16 | get the grand total of 2896 18 98 . Uh | |
| 16:25 | They don't rub that out so it looks looks nicer | |
| 16:28 | . 2898 . I don't know why aged 16 to | |
| 16:32 | it . 63 18 . Okay . So what a | |
| 16:37 | bit One ridiculous example . He are always love the | |
| 16:41 | ridiculous example or the ridiculous one that you can do | |
| 16:44 | . What about you do this 105 times 612 . | |
| 16:51 | Okay , Nice . Big one . Hopefully you're giving | |
| 16:54 | it a go . Okay , this one's almost 100 | |
| 16:57 | . This one's almost 600 . In fact , we're | |
| 16:59 | going to make this one here 100 As you can | |
| 17:02 | guess . Time six . All right , so this | |
| 17:06 | is five more . This is 12 more . Okay | |
| 17:10 | , six times five is 30 positive 30 and we're | |
| 17:14 | going to add these together . We're going to get | |
| 17:16 | the answer of That . Plus that is going to | |
| 17:18 | be 642 and then on the times that by 100 | |
| 17:22 | . So I'm going to get 642 With a couple | |
| 17:26 | of spaces there where I put zero's usually , but | |
| 17:28 | I'm more interested now what's going on over here ? | |
| 17:30 | Which is 12 times five , which is 30 so | |
| 17:33 | I can just slap those straight in 64 . What | |
| 17:38 | am I saying that 60 ? I'm losing the plot | |
| 17:41 | at the moment . Okay . Yes . In the | |
| 17:45 | alternative reality , five times 12 is 30 but today | |
| 17:48 | , well , actually , call it 60 what it | |
| 17:50 | actually is . Okay , So , we're gonna add | |
| 17:53 | 60 . All right . Anyway . Hopefully that was | |
| 17:57 | some help for you . Um and hopefully you didn't | |
| 17:59 | make as many mistakes as I tended to make today | |
| 18:02 | . I managed to catch myself in time . Okay | |
| 18:05 | , See you next time . Bye . |
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