Math Trick for Fast Multiplication - Free Educational videos for Students in K-12

Math Trick for Fast Multiplication - By tecmath

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00:00	Can I welcome to Tech Math Channel . You're gonna
00:02	do another math trick video . I haven't done one
00:04	of these in the wall . So This line straight
00:07	into it . How fast can you multiply the following
00:10	two numbers ? I'm gonna give you five seconds .
00:12	We'll do 35 times 95 . Okay . All right
00:22	, Time's up . Did you get the following answer
00:24	? Did you get 3325 . If you did .
00:28	Congratulations . If no one look , you're not going
00:31	to show you how to do this . So sit
00:33	back and enjoy great math trick video . And if
00:36	you like this video , please remember , do like
00:39	. And please please please subscribe . Also , comments
00:42	are always welcome as well . So let's just launch
00:44	into how to do this trick and at the very
00:45	end , I'll show you why this trick works .
00:47	So , uh , first off how to do this
00:49	particular trick . Now this multiplication trick First off only
00:53	occurs and only works when you're multiplying numbers . That
00:57	end in five . Like these two numbers here ,
00:59	35 and 95 , both end in fives . What
01:01	we're gonna be having a look at is we're gonna
01:03	be looking at the numbers before the five . To
01:04	work out Our answer here , we're gonna be using
01:07	the three and the nine and we're gonna do a
01:09	couple of things . The first thing we're gonna do
01:12	is we're going to multiply these two numbers , so
01:15	three times nine is equal to 27 . The second
01:20	thing we're gonna do is we are going to work
01:22	out the average of these two numbers , the average
01:25	of the three and the nine . That is to
01:26	say we're going to add them together , divide by
01:28	to work out the number halfway between three plus nine
01:31	is equal to 12 , divided by two is equal
01:35	to six . Then what we're gonna do is we're
01:38	going to add these two numbers together are two things
01:40	that 27 now six , So 27 plus six is
01:44	equal to 33 you'll notice this is the first part
01:46	of our answer here . Okay . 33 . All
01:49	right . So it's going to put that down .
01:52	The next thing I do is we're gonna multiply this
01:54	number by 100 so 33 times 100 Is 3300 .
02:00	Finally , we're going to add 25 to our answer
02:03	. So we do that . I just rub those
02:05	out and you're gonna see that our answer here is
02:08	3,325 . Hey , pretty easy trick . Right ?
02:13	Hopefully you like that . What do you think ?
02:15	Nice , easy math trick . Tell you what ,
02:16	go through a couple more examples . These will get
02:19	a little bit harder . There's a couple of little
02:20	tweaks to it , but nothing too ridiculous . All
02:23	right . For the second example , what about you
02:24	give this one to go 45 times 85 . You
02:29	know , this is going to work . They both
02:31	finish in fives , so give it a fly .
02:34	All right . I'm gonna be using the four in
02:36	the 8th . 1st thing we do four times eight
02:39	. I reckon you'll be able to know that is
02:41	32 . The next thing we do is we work
02:43	at the average of the four in the ideas of
02:45	4-plus 8 is 12 . And Uh run that by
02:49	two . We get six , add these two guys
02:52	together , we get 38 . Okay , So this
02:54	is going to be 38 times 100 and 3800 .
02:57	3800 . Finally , what we do is we add
03:01	25 to our answer . All right . 3825 .
03:06	That's pretty rapid way of doing it . Right .
03:08	It's pretty good . What about to go to one
03:10	where there's just a little tweak to it . Okay
03:14	. Alright , for this example we're going to do
03:16	what about we do 45 times or 95 ? You
03:22	give it a guy Okay . Both end in five
03:26	. You're gonna see here , we're going to go
03:27	once again , four times nine is equal to 36
03:32	. Then we're going to work out the average of
03:34	49 so four plus nine is equal to 13 .
03:37	If you have 13 , you're going to get the
03:39	average of 6.5 . Okay , So 6.5 add these
03:44	together , you're gonna get 42.5 . So you multiply
03:48	this now by 100 . We're gonna get 4250 .
03:53	All right , just a little bit different . There's
03:55	not ending in the hundreds this time To this we
03:57	are going to add 25 . So 50 plus 25
04:02	is going to give us an answer of 4,275 .
04:07	I'll tell you what let's do an even bigger number
04:09	now . Alright , for this example , Let's go
04:13	. Well , what about we do 135 times 85
04:21	. All right , nice big number here . So
04:24	you should be able to do the same thing .
04:25	There's going to be a bit nastier though now because
04:27	you're gonna have to be multiplying 13 times eight .
04:30	Okay . So what is 13 times eight ? Hopefully
04:33	this is one you can do in your head .
04:35	You might look at it and say okay , it's
04:36	24 plus 80 which is 100 and four . Okay
04:41	. The average of 13 8 . Well , 13
04:43	plus eight is equal to 21 half of that is
04:47	10.5 . So , we add these together . What
04:49	are you going to get ? You're gonna get 114
04:54	0.5 . All right . So what do we do
04:57	now modifies 501 14 50 . All right . And
05:05	we're gonna add 24 to it . All right .
05:08	50 plus 25 is going to be 75 , 11475
05:16	. All right . So , what do you think
05:17	of that ? Do you like that particular type of
05:19	method ? I think it's I think it's actually pretty
05:21	handy . Okay . It's obviously it's got its limitations
05:23	, but it's pretty cool . But I'm going to
05:25	show you now why this works . If you do
05:27	like this , by the way , this particular method
05:29	, don't forget to hit like So , let's show
05:31	you why this particular method works To do this .
05:34	I'm just going to put an example . Let's do
05:37	35 times 65 . Okay , so When we're doing
05:42	this , you can imagine this 35 being or any
05:45	number that we're starting with as being 10 x plus
05:48	five . And what I mean by that is in
05:50	this particular case the X Arabic or +33 times 10
05:54	is 30 plus five . We could be dealing with
05:56	45 or 55 where X is changing our value .
05:59	And that's dealing with that first number there for our
06:01	second number , this one we're going to think of
06:04	this as 10 Y plus five . Okay , once
06:08	again this number is represented . Are the wire here
06:11	. So in this case it's 66 times 10 is
06:13	60 plus five . And we're multiplying these two numbers
06:16	together . So what happens when we do this ?
06:18	First off we multiply these two parts . When we
06:21	do this we get 10 X times 10 Y ,
06:23	which is equal to 100 X . Y . To
06:28	this , we're going to get two things , we're
06:31	gonna get five times 10 y . and five times
06:34	10 x . Now five times to my is 50
06:37	Y . And five times 10 X . Is 50
06:39	X . So we could write , this is following
06:41	, we could write this is 50 X plus Y
06:46	. Okay , because 50 times X . Is 50
06:49	X . And 50 times why is 50 Y .
06:51	So everything is good so far . And this leaves
06:53	us finally with five times five , which is 25
06:56	. So I was just expanded out those brackets .
06:59	Now we can take this a little step further .
07:01	What we could do is we could factories this a
07:04	little bit . So if we divide by 100 I'm
07:07	just gonna put the 100 . Here , We divide
07:09	this by 100 . This particular term here , we're
07:12	going to get X . Y . We divide this
07:15	by 100 . We're going to get X plus y
07:18	. The whole lot divided by two because 50 divided
07:21	by 100 and a half . Yeah to this we
07:25	get 25 on the end . Okay , we still
07:28	have 25 on the end . So what have we
07:31	got going on here and then you'll see what why
07:33	this works . What we started doing is we started
07:36	in this particular case going 6 35 times 65 X
07:40	. And y . We got three times six .
07:42	This was our X times Y bit . Then what
07:44	we did to that was we added the averages as
07:46	this party . So we add those together , we
07:49	multiply them by 100 . That's what's going on here
07:52	. And to our answer we added 25 and that's
07:56	why this particular trick works . Hopefully you like that
07:58	trick . Hopefully you like the explanation of why it
08:00	works as well . I think it's a pretty good
08:02	thing to know . Anyway , please like please subscribe
08:06	. Look , it's lovely to be making math trick
08:09	videos . Any comments are always welcome . Thanks for
08:13	watching . See you next time . Bye .

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