Fast mental addition of large amount of numbers using estimation - Free Educational videos for Students in K-12

Fast mental addition of large amount of numbers using estimation - By tecmath

Transcript


00:0-1	good . I welcome to take Math Channel . I
00:02	want to start this video out but asking you a
00:04	question , how fast can you add the following numbers
00:08	? One plus two plus three plus four plus five
00:12	plus six plus seven plus eight plus nine plus 10
00:17	. That's right . Can you add the numbers one
00:19	through 10 are going to give you four seconds .
00:24	Okay . Hopefully the answer you got was 55 if
00:28	you didn't . That's okay . What we'll do is
00:30	we'll have a look at how you can go through
00:33	and solve this particular question pretty much instantly . It's
00:36	a really , really great little trick . We're going
00:38	to have to look out for adding these sorts of
00:40	series of numbers . Okay , so three steps that
00:44	we do when we're doing this , the first one
00:46	is we're going to add the first and the last
00:50	number . Okay , first and last number add up
00:54	to 11 . Then we get this number and we
00:58	divided by two . We average it out so we
01:00	divided by two is two terms . So dividing it
01:03	by two gives us the answer of 5.5 5.5 .
01:09	And finally what we do is we multiplied by the
01:12	number of terms here . The number of numbers 123456789
01:16	10 times the answer by 10 . We get the
01:19	answer of 55 . So one plus two plus three
01:23	plus four plus five plus six plus seven plus eight
01:25	plus nine plus 10 Is equal to 55 . And
01:30	as you say there was not Any addition there at
01:33	all . Well start there was one plus 10 .
01:35	That was my some amount of addition . Okay .
01:38	But then we just used a few little tricks to
01:40	sort this out . So this is a really really
01:42	great little trick um Just for adding these sorts of
01:45	numbers together really really quickly . Um So what about
01:49	we go the next step up and down the numbers
01:51	1 to 10 Let's add the numbers one through one
01:57	plus two plus three . All the way through to
02:00	100 heat you can do that . I'll tell you
02:04	what let's give it a go . So remember the
02:07	steps here we add the first and the last number
02:10	here we're gonna get an average of these numbers .
02:12	So one plus 100 . And then to get that
02:16	average way dividing by two . Okay so that's the
02:20	first two steps there . Uh we're gonna get 50.5
02:24	there . Yeah . Yeah and so far . All
02:27	right . All right now how many numbers from 1
02:30	to 100 ? Well I reckon if you Canada might
02:31	be may be surprised to realize there's actually 100 numbers
02:34	there . Okay so we're gonna times that answer by
02:37	100 . Okay so 50.5 times 100 we're gonna move
02:42	the decimal place 12 times our answer is 5000 at
02:47	50 . Yeah , so one plus two plus three
02:51	plus forms . A little it all the way to
02:52	100 is 5000 and 50 . I'll tell you what's
02:57	a great little one to race your mates with and
03:00	you could do something like say okay we'll see who
03:03	can add the numbers . 1 to 100 . The
03:04	fastest . I'll tell you what you can use a
03:06	calculator . I won't and see how you go or
03:11	or what about just one last one of these .
03:14	And what about say something a little bit harder now
03:17	say . So we did something like the numbers let's
03:20	start with 20 And I'm gonna add that all the
03:24	numbers 2021 , 22 , data data data all the
03:28	way through to 35 . Okay . Now watch with
03:35	this and I've chosen this one particularly because it does
03:37	show a couple of little things just to watch out
03:40	for when you are adding these . Okay , in
03:43	fact , I'm going to go a step further .
03:45	I'm actually gonna write all these numbers down . 20
03:48	plus 21 plus 22 plus 23 plus 24 plus 25
03:55	plus 26 plus 27 plus 28 plus 29 plus 30
04:03	plus 31 plus 32 plus 33 plus 30 for plus
04:09	35 . All right , okay . We're gonna add
04:13	all these together . So first off , we add
04:15	the first and last numbers together . 35 35 .
04:19	It's over here plus 20 . The answer to that
04:21	is 55 . We're gonna get the average of these
04:24	two . So we're dividing it by two . Okay
04:26	, it's 55 divided by two equals 27 and a
04:31	half . Okay now we're going to multiply this by
04:35	the number of numbers here . Now you might automatic
04:38	look at that and say 15 . However , be
04:40	very careful here . It's actually 16 because if we
04:43	were what we used to as we used to going
04:46	123456789 $10 or 13.15 years 15 numbers there . But
04:49	we're starting from the ones number but we have this
04:52	number here also . So there's actually 16 numbers here
04:55	. Okay . And you can count them and you
04:57	may agree with me then , but there's 16 numbers
05:00	to just be very very aware of this . So
05:04	27 a half times 16 . Well if I was
05:07	trying to do this in my head , I would
05:09	do the following , I would double this answer and
05:11	have this answer . So if I double this answer
05:14	, I'd get 55 times out And then to make
05:19	that even easier , I might even double this again
05:21	and get 110 Times for the answer to this is
05:26	440 . Hey hi guy . Yeah . Just before
05:32	I let you escape and you can't escape now if
05:34	you wish . But I just want to quickly tell
05:37	you why this works okay . And it's not a
05:39	very uh difficult idea to get behind . Once you
05:43	understand , it's a really good one to get to
05:45	say I consider the numbers one through 2 , 10
05:48	, 1 plus two plus three plus four plus five
05:53	plus six plus seven plus I plus nine . And
05:57	I think the next number after that was 10 .
05:58	Yes . So if I consider the first and the
06:03	last time you're going to see the first and last
06:05	number here Add up to 11 , as do the
06:11	second and the second last number . They also add
06:14	up to 11 , 8 and three wait a second
06:18	. They also add up to 11 , 7 and
06:19	four add up to 11 , 6 and five also
06:22	add up to 11 . Okay ? So What we're
06:27	doing essentially what we're doing this trick is we're adding
06:29	the first and the last number , which is 11
06:32	. Okay . And we're just getting an average of
06:34	this . Okay . Because all these numbers are going
06:37	to be averaging it up to , You know ,
06:40	we're basically working out the average of all these numbers
06:42	. Okay , so work at the average of the
06:44	first and the last number , we're just going 11
06:46	divided by two , which is 5.5 . Okay ,
06:50	So we're working on average , we're just working on
06:52	an average of how much each digit is . Yeah
06:56	. Then we're multiplying it by these numbers because if
06:59	we averaged all these numbers out , there'll be 5.5
07:01	and then there's 10 lots of them . So at
07:03	times it by 10 and we're getting the answer of
07:06	55 Anyway . It's a great little trick . It's
07:11	a really good trick for uh playing tricks on people
07:14	and showing them how brilliant . Matthew up . It's
07:16	not a trick at all in terms of that ,
07:18	it is actually a you know , it's a good
07:20	little technique for doing such a thing . Okay .
07:23	And if you do this sort of stuff you do
07:24	, it does add to your actually mathematical abilities .
07:26	So maybe not a trick at all . Maybe just
07:29	a skill anyway . Thanks for watching this video .
07:33	I hope you enjoy that little our method of adding
07:35	numbers together . We'll see you next time . Bye
00:0-1	.

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