Adding and subtracting fractions - Free Educational videos for Students in K-12

Adding and subtracting fractions - By tecmath

Transcript


00:0-1	Good day . Welcome to Tech Math channel . What
00:01	we're going to be having a look at in this
00:02	video is how to add and subtract fractions . There's
00:06	going to be a couple of different parts of this
00:07	. We're going to start up by having a look
00:08	at first off adding and subtracting fractions with the same
00:12	denominators , that is the same bottom number . And
00:15	we're going to move on to ones with different denominators
00:17	. And then what we're gonna do is we're going
00:18	to have a look at how to add and subtract
00:20	fractions involving mixed numbers . So , uh , sit
00:23	back and enjoy . So the first thing we're going
00:25	to have a look at is adding and subtracting fractions
00:28	where they have the same denominators . An example of
00:30	this could be say we were to get 1/8 entered
00:34	this , we were going to add 3/8 . Now
00:38	you're gonna notice straight off , we have the same
00:40	denominator there , adding and subtracting fractions like this really
00:43	easy . All we're gonna do is we deal with
00:45	the top number , the numerator here . So what
00:48	we do is one plus three is equal to four
00:52	and we keep the denominator the same . We stay
00:55	with eighths . Okay ? We're getting 1/8 and we're
00:57	adding 3/8 . Do it . So we've got four
00:59	eights altogether . Okay , the bottom number , the
01:01	denominator stays the same . All right , this can
01:04	be simplified a bit further . Just watch out for
01:06	when you're doing these particular questions . Can they be
01:08	simplified further ? And there is a number that goes
01:11	into both the numerator and a denominator here , a
01:14	common number that will reduce it and simplify it .
01:17	So the number that goes into both of them .
01:19	And that is for So we divide by four .
01:22	Okay , the top number by four and we divide
01:24	the bottom number by four . four , divided by
01:26	four . We get the answer of one uh divided
01:31	by four , we get the answer of two .
01:32	So there's your answer , 18 plus 3/8 is able
01:36	to four eights , which can be simplified down to
01:39	a half . So what about one more example for
01:41	this ? So for our next example let's do 5/7
01:47	, And we're gonna subtract 2/7 . So you're gonna
01:52	notice first off that are denominators the same here once
01:55	again . So what we can do is just directly
01:58	take off . These are top numbers here , that
02:00	enumerators , so five take away two is equal to
02:04	three and the denominator stays the same , so this
02:08	stays as a seven . We can't simplify this any
02:11	further . So this is our answer . So they're
02:13	pretty simple those sort of our fractions adding and subtracting
02:16	those ones , but now we're going to have a
02:18	look at where they're a little bit more difficult where
02:20	we have different denominators . An example here is We
02:25	can get 3/8 and to this , we're going to
02:28	add one half and you're going to notice first off
02:31	that we have different denominators here . So how do
02:34	we go about adding and subtracting when we have different
02:36	denominators ? Well , it's not too hard . What
02:39	you really have to get with this is that we
02:41	are going to play around with either one or both
02:44	fractions here . Where are we actually going to be
02:46	using this idea of equivalent fractions to make those denominators
02:49	the same . I'll show what I mean by this
02:51	. So if we look for a common number that
02:54	both two and eight go into the lowest one we
02:57	could think of , you can think , okay ,
02:58	well both of these numbers go into eight . Uh
03:01	eight goes into eight ones , so we're not gonna
03:03	need to change this one and two goes into 84
03:06	times because two goes into 84 times . We multiply
03:10	both the top and the bottom part of the fraction
03:13	here . By that four to move it up to
03:16	eight , we're gonna end up with equivalent fraction for
03:18	a half , which is one times four is four
03:21	And two times 4 which is eight . So what
03:24	do we have now ? If I was to rewrite
03:26	this whole fraction out , I could say , okay
03:29	, we have 3/8 Plus 4/8 , and we can
03:34	work this out really easy because now what we have
03:37	is we have a common denominator here , three Plus
03:41	4 is equal to seven . And remember that the
03:44	eight stays the same , that denominator stays the same
03:47	when we're adding . So that's how we do this
03:49	. It's pretty simple , right ? Would have to
03:51	give you another example . Okay , another example we're
03:54	going to go 5/6 and we're going to take away
03:58	one quarter . Once again you're going to know that
04:01	we have different denominators here . So what we're going
04:04	to do first off is we're going to change these
04:06	using the idea of equivalent fractions to get denominators the
04:11	same on the base . So first off , what's
04:13	a common number that both six and four go into
04:17	? Yeah the lowest one I can think of is
04:19	12 . It's okay . What we multiply six by
04:22	here to get 12 and you can say okay ,
04:24	would multiply by two . So we're gonna multiply the
04:27	top and the bottom by food . Okay what would
04:30	we multiply by four here to get 12 ? Okay
04:33	, that's three . So multiplied by three . Multiplied
04:36	by three . So what have we got now when
04:38	we do this ? Okay , five times 2 is
04:41	equal to 10 . Six times two is equal to
04:44	12 . So that's the equivalent of production for 56
04:47	is 10/12 . We're going to subtract from this .
04:51	Well this fraction here , one times three is three
04:54	And four times 3 is 12 . Awesome . We've
04:58	got Common denominators here . Let us go through and
05:01	do this . So 10 take away three is equal
05:04	to seven and this denominator stays the same so they're
05:08	not too bad . All right . Last time for
05:11	example , I'm going to give you is where we're
05:13	going to be using mixed numbers and these aren't too
05:16	bad either . Okay , in this example we're going
05:18	to get three and two thirds entered this . We're
05:22	going to add 3/4 . All right . We've got
05:25	a mixed number . We've got different denominators . It's
05:28	pretty messy . Right ? These are not too bad
05:30	. We deal with just a couple of steps .
05:32	You do the first thing we're going to do here
05:34	for this mixed number . We're going to change this
05:36	into an improper fraction . Okay . So how do
05:39	we do that ? There was a video where we
05:41	looked at this . What we do device to draw
05:43	this , You can see here that we have 1
05:46	, 23 and that's cut into thirds there and we
05:50	have that . So it was to color this in
05:52	. We have these guys And that's our 3.2/3 .
05:56	So the way that we change this into an improper
05:59	fraction is once again we're gonna go three times three
06:02	here . That's these three groups of three and we're
06:04	gonna add the two . So three times three plus
06:07	two . This is equal to 11/3 . And to
06:11	this we're going to add three quarters . Okay .
06:14	So what do we do now ? Well , all
06:16	we have is different denominations now . We we've already
06:18	dealt with this kind of idea . It's not too
06:20	hard . We just have to look for a common
06:22	number that both three and four going to and that
06:25	number Is 12 . Okay so three times one equals
06:30	12 . It's three times four . So we're going
06:32	to multiply the top and the bottom by four .
06:35	Uh the bottom here is a four which we multiply
06:38	by four to get 12 and it's a three .
06:40	So we're gonna multiply the bottom by three and the
06:43	top by three . So what do we get when
06:45	we do all that ? 11 times four is 44
06:49	. Uh Three times four is equal to 12 .
06:53	And to this we're going to be adding three times
06:55	three is equal to nine and four times three is
06:59	equal to 12 . Okay what do we get ?
07:01	We get this 40 for fast , nine is equal
07:05	to 53 And that goes over 12 . We can
07:09	simplify this further because we can turn this back into
07:12	a mixed number . How many times has 12 going
07:14	to 53 while it goes in four times ? Uh
07:18	that's 4 , 12-48 and we have a five remainder
07:22	, so that's 5/12 and we can't simplify that any
07:26	further . So that is our answer . Anyway .
07:29	What about I'll give you a couple of examples to
07:32	now do yourself . So let's give you three examples
07:35	. Okay , so the first one . Nice easy
07:37	one . Same denominators , let's go 2/5 plus 1/5
07:43	. I don't think you'll have a much trouble doing
07:45	that . The second one , let's use different denominators
07:48	. Let's go one third plus three quarters and see
07:53	what that equals for the third one . Let's use
07:56	mixed numbers . Let's go two and 3/5 and we're
08:01	going to take away one and one quarter and see
08:05	what it equals . All right , give these ago
08:08	so to fits plus 1/5 . Well , we're going
08:11	to keep the bottom number the same here . They're
08:13	going to stay in fits and two plus one is
08:15	equal to three . They're really simple . So that's
08:18	right . Have you got that answer ? That's correct
08:21	. For this . Second question one third plus three
08:24	quarters . You're going to see that we have different
08:26	denominators . We're going to look for a common number
08:29	that both three and four go into which is 12
08:32	. Okay , common number they both go into is
08:35	12 . So we're going to multiply what by three
08:39	to get 12 . It's going to be four .
08:41	So we're going to do that to the top of
08:43	the bottom . And what do we multiply before to
08:45	get 12 ? That's three . So we do that
08:47	to the top and the bottom . So what do
08:50	we end up when we do this one times four
08:52	is four , three times 4 is 12 to this
08:57	. We're going to add three times three is nine
09:00	and four times three is 12 . Okay , What
09:04	do we get now ? Okay . Four plus nine
09:07	is equal to 13 And this also goes over 12
09:12	. We can simplify this further because This is a
09:17	improper fraction at the moment , 12 goes into 13
09:19	once and with one remainder , so this is one
09:24	and 1/12 . Okay , for the final question here
09:27	, two and 3/5 take away one and one quarter
09:31	. Well , we're going to first off change these
09:33	mixed numbers into improper fractions and then we're going to
09:36	have to play around the denominators . So let's first
09:39	changes into improper fractions to and 3/5 . Okay ,
09:44	two times five is equal to 10 plus three is
09:47	equal to 13 . That becomes 13/5 . One and
09:52	one quarter one times four is four plus one is
09:55	five And that becomes 5/4 . Okay , so now
10:00	let's get this common denominator here . So a common
10:03	number that both five and four go into An easy
10:07	way doing this . Sometimes if you get really stuck
10:09	, just go five times for it will tell you
10:11	a common number . They go into that . If
10:13	you can't think of one really easy . So five
10:16	and four , both going to 20 , what would
10:19	you multiply boy ? Five to get 20 here and
10:24	that would be four times four times for what would
10:27	you multiply by four here to get 20 . That
10:30	would be times five times five . So what does
10:33	that leave us with ? Okay , 13 times four
10:36	. This is equal to 52 . five times 4
10:40	is equal to 20 . We're going to be subtracting
10:44	here five times 5 is 25 , and four times
10:48	5 is 20 . What have we got now ?
10:52	All right . 50 to take away 25 is 27
10:57	. The denominator stays the same because the same denominator
11:00	. Okay . And we can simplify this further .
11:03	This becomes one and 7/20 . Anyway . Hopefully that
11:08	video was comprehensible for you . And in the next
11:12	couple of videos we're gonna be looking at more playing
11:14	around with fractions , mostly gonna put another video up
11:17	where it's going to be having a look at a
11:18	shortcut . You can take two . I save yourself
11:20	a bit of time when you do these . Okay
11:22	? Uh , so you can almost workout fractions instantly
11:25	anyway . Hopefully that video was good for you .
11:29	We'll see you next time . All right .

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