Multiplying Fractions - Fast Math lesson - Free Educational videos for Students in K-12

Multiplying Fractions - Fast Math lesson - By tecmath

Transcript


00:0-1	Good day and welcome to Tech Math Channel . Why
00:02	don't we have a look at this video ? Is
00:03	how to multiply fractions together . So I'm gonna start
00:06	out some pretty easy examples are these these examples to
00:09	explain how to do it . And we're gonna move
00:11	into some harder examples . And then there are some
00:13	ones that you can try on your own . So
00:15	without much further ado uh , the type of thing
00:17	, you'll be multiplying when you multiply fractions is as
00:20	follows . You might get say something like one that
00:22	looks like this and its most simple . Say ,
00:24	say a half times three quarters . Yeah , what
00:30	this actually means is a half of three quarters .
00:32	So we're going to get a smaller answer here .
00:34	So you might be able to think of half or
00:36	three quarters and you might be able to think of
00:37	what that is . But I'm going to show you
00:39	how to do this mathematically . So the way we
00:42	do this is as follows , basically the top numbers
00:46	here and the bottom numbers here . So what we've
00:49	got is the numerator denominator . So what we're gonna
00:51	be doing is we're going to multiply the two top
00:54	numbers together to get our first part of the answer
00:56	to bottom numbers together to get our bottom part of
00:58	the answer . Okay , so one Time Street ,
01:01	it's three , two times four , So the answer
01:06	is 3/8 and that's how easy , are . yep
01:11	. Okay for another example I'll show you how I
01:13	used to remember this as a kid when I wasn't
01:15	sure this , remember my bigger brother coming home and
01:17	telling me that what what what it was was a
01:19	half times a half and I remember him telling me
01:23	what it was and that actually stuck with me because
01:26	I always thought it was very strange at the time
01:27	until you sort of think of why that is .
01:29	But if we work out what half times a half
01:30	is one times one is one and two times two
01:34	is four . And I mean this is a really
01:35	little kid thinking how strange it was that half times
01:38	a half has given me a quarter . This is
01:39	like a smaller answer . I thought surely it's one
01:42	, isn't it ? But that would be half plus
01:43	a half . If we can think about this half
01:46	of a half an emergency layer , a pizza here
01:50	and we have half this pizza here , well we
01:53	have here section here which is a half , but
01:55	if we then cut that in half again a half
01:58	of a half we're gonna end up with a quarter
02:02	. Okay , So hopefully that that might be a
02:05	way that you might remember how to do that .
02:07	So I'm gonna give you another example here . So
02:10	you might try this one on your own . Say
02:11	let's do what is 3/4 Times What about 2/3 ?
02:18	Okay , give that a go . All right .
02:23	Hopefully you get a positive . You still need a
02:25	bit of time but I'm gonna go through the answer
02:26	right now . So three times two is six and
02:30	then four times three is 12 . And you're going
02:33	to see that we can actually take this down even
02:35	further because there's a number that goes into both our
02:37	denominator and numerator over the top and the bottom number
02:40	. And this common number that goes into both of
02:42	is six . So six goes into six once and
02:46	six goes into 12 twice . So this is the
02:48	same as a heart . Okay , how did you
02:52	go with that ? All right . We're going to
02:55	put a couple harder examples up . Okay , so
02:58	the example I'm gonna put up now are involving mixed
03:01	numbers there . Mixed numbers and numbers that look like
03:03	this . So we have something like you say 2.5
03:07	times that by three and one quarter . Now to
03:11	multiply this is all of a sudden , a bit
03:13	more difficult , but not much more difficult . It
03:15	just requires one extra step . And what to do
03:18	this . What we have to do is we have
03:19	to actually change our number here into this is a
03:22	mixed number . So it has a mix that's got
03:24	a whole number and part number . So it's called
03:27	a mixed number into an improper fraction . Now these
03:30	are proper fractions , but an improper fraction would be
03:32	one where this number up here . The top number
03:35	is bigger than the bottom number . So I'll show
03:38	you how to do this and its most simple because
03:40	there's they're the easiest way to do this is this
03:45	is to the bottom number stays the same , then
03:48	two times two plus one is five . Now ,
03:51	I'm just gonna show you conceptually why this works .
03:53	Well , an idea of what this works . It
03:54	was the draw 2.5 . So this boy 2 1/2
04:00	. Okay . You might be able to count how
04:03	many have there are ? There's 12345 Okay . There's
04:07	two lots of to this is our two times two
04:10	part , which is this part plus one . Which
04:13	is this ? This is giving us a top number
04:15	. There's 5/2 . Okay , Bottom number , which
04:20	is two . There's a harms . Okay , so
04:21	this is where we end up with five over to
04:24	the easiest way to do this is you keep the
04:26	bottom number the same . So the two stays the
04:29	same and then we go two times 2 because there's
04:34	too lots of these plus one . Okay , so
04:39	it's 1 , 2 , 3 , Okay ? So
04:42	using that same idea , So you get 5/2 of
04:45	them and multiply , that Changes one here . Same
04:49	way three times 4 plus one . So three times
04:52	four is 12 plus one Is 13 . The bottom
04:55	number stays the same . Okay , what does this
04:58	equal five Times 13 to get our top number .
05:03	What do you think the answer to that is ?
05:05	Hopefully get 65 . Okay , and this is going
05:09	to go over . Right . All right . How
05:13	did you go with that particular question ? We can
05:16	change this a little bit further there because what you
05:18	might look at as you might say , well ,
05:20	65 you don't might not like that because this number
05:23	here is bigger than this number here . So we
05:24	can actually change this back into a mixed number .
05:26	And the way we do is as follows this 65/8
05:30	. Okay this I would probably pronounce it the wrong
05:34	way . This line here , I'm pretty sure it's
05:37	code vin told them but I'm wrong with this .
05:41	I actually think this is this divide . So this
05:43	here It's mid 65 , divided by 65 , divided
05:47	by eight . What did you get what you get
05:50	for that ? So 65 divided by eight . The
05:54	answer to that ? 88 , And there is one
05:59	left over . So this one we put over eight
06:03	so we have 18 where Okay notices bottom number here
06:06	stays the same with the one that remained a part
06:09	of our 65 divided by eight . Okay let's charge
06:15	another example here then I'm gonna give you a whole
06:17	bunch to do by yourself . So what about I
06:20	do this one ? Um What about I do 1.5
06:24	and I'm gonna time's up by what the times that
06:27	by 2.5 . Okay so first off we're gonna changes
06:32	in to improper fractions these mixed numbers . So one
06:37	times two plus one is 3 , 3/2 times two
06:43	times 2 plus one , two times two is four
06:46	plus one is five . Bottom number . Stages are
06:49	too And then we just multiply Australia across the three
06:53	times five is 15 And two times 2 is four
06:57	. And we can take that to the next step
06:59	because 15 divided by four . We can do it
07:01	15 divided by four . This goes three times because
07:05	3412 and I'm sorry that you have an email come
07:11	through and we have three left over . Okay so
07:14	three we're gonna put that over four . Okay so
07:21	I'm gonna give you a couple of examples to go
07:22	with this . Hopefully you did pretty good with that
07:28	. So what I got a couple of examples .
07:30	Okay so let's give you I'm gonna give you three
07:33	examples here and these are they what I'm going to
07:37	start with a nice easy one which is gonna be
07:39	what is to over three times 5/7 . Okay .
07:45	57 not a commonly used fraction . Look I tend
07:48	to prefer to use the quarters and the haves and
07:50	the third and that sort of deal but let's let's
07:52	get out there . Um So we might do another
07:54	one which I'm going to do which is one and
07:56	a quarter a number of times that by two and
07:59	one third . See here you go with that .
08:02	And then the last one we're gonna do is I'm
08:04	going to get you to do 2.5 and I'm gonna
08:07	get you two times that by three and 3/4 ,
08:11	3 quarters . Okay , let's see how you go
08:15	. So pause the video , give him a guy
08:17	them come back . Okay ? Hopefully pause it .
08:22	Let's see how you go . So I'm going to
08:23	work through them there . So two times 5 is
08:26	10 , three times 7 is 21 And there's not
08:32	a number that goes into both of those , so
08:33	that's our answer . 10/21 . Okay , this one
08:36	here one . These are mixed numbers are going to
08:39	change those into improper fraction , so one times four
08:42	is four plus one is 5/4 plus two times three
08:48	plus 12 times three is six plus one is seven
08:52	over three . And then I multiply these straight across
08:55	, going plus in there . I don't know why
08:57	I'm placing this is in fact a times . Okay
09:01	, let's make little mistakes every now and then .
09:03	Are we ? As long as we fix them up
09:04	as we go . So five times 7 is 35
09:09	And this is Times four times 3 which is 12
09:13	. Okay ? And so 35 this goes in to
09:19	There's 2 12 24 And there is 11 left over
09:23	11/12 . Okay , How did you go with that
09:29	? All right , let's do this last one .
09:30	So let's change these mixed numbers into improper fractions .
09:33	Two times two is four plus one is 5/2 .
09:37	And this one here is going to be three times
09:39	four plus 33 times four is 12 plus three Is
09:45	15/4 . It's time seize across five times 15 .
09:51	The answer to that is . What did you get
09:53	from the answer to this ? Hopefully you're gonna get
09:56	five times 15 , which is 75 and then two
10:02	times 4 is eight , so 75 divided by eight
10:08	equals what ? Okay so I recommend you go 298-72
10:13	so equals nine that there is 72 2 , there's
10:17	three left over three over I so hopefully that's the
10:22	answer you got . So let me know how you
10:24	went with those . Hopefully you're really , really good
10:27	and we'll see you next time . Okay . Bye
00:0-1	.

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