Fractions addition and subtraction the fast way with mixed numbers - cool math trick - Free Educational videos for Students in K-12

Fractions addition and subtraction the fast way with mixed numbers - cool math trick - By tecmath

Transcript


00:00	good and welcome to the Tech mouth channel . What
00:02	we're gonna be having a look at this video is
00:04	how to add uh , fractions of mixed numbers ,
00:08	Okay . With different denominators . So a bit of
00:11	a few things here and we'll have it of a
00:12	look . Okay , so I'll start to do this
00:15	. This is how to do these really , really
00:17	quickly without having to worry about working at lowest common
00:20	denominators and the like . So anyway , so here
00:23	you go . So an example I'll do here you
00:26	say 2.5 and I'll add this to three and 1
00:32	3rd . OK . Now , the way that we
00:34	do this is first off , if we have a
00:37	mixed number , we have to turn this This is
00:39	a mixed number here where we have a normal number
00:42	and a fraction together as one number . We have
00:44	to turn these into what is known as an improper
00:47	fraction . Now , an improper fraction is where we
00:49	have a fraction , but it has a bigger number
00:52	on the top and a smaller number on the bottom
00:55	. And the easiest way to do that is this
00:57	first off , what we do is we put the
01:00	bottom number , there's the same number then to get
01:04	the top number . What we do is we get
01:06	the whole number here . We times it by the
01:08	bottom number and then we added to the top number
01:11	. So I'll show you ahead of this too .
01:13	Times two is four plus one is five . Yeah
01:17	, We've turned it into an improper fraction . So
01:21	Okay , the plus um we'll do the same thing
01:22	over here . So we keep this bottom number the
01:25	same . Then we go three times three plus one
01:31	, which equals 10 . Okay , so how do
01:35	we deal with this now ? Well , let's have
01:37	a look . Well , what we do with these
01:39	is to get the bottom number . The easiest way
01:42	to do that . Rather than working at lowest .
01:45	Common denominators and and and common denominators , rah ,
01:48	rah , rah . What we would do is we
01:50	, the simplest way is just to multiply the two
01:53	bottom numbers together . So two times three , six
01:56	years ago and I got the bottom number . Then
02:00	what we do is we start on the top left
02:02	over here and we multiply this by its diagonal are
02:07	pair over here on the bottom . Okay , so
02:09	you'll see this the denominator , the bottom number over
02:12	here on the bottom . So many times these two
02:13	guys together . So five times three is 15 .
02:16	It's pretty important to start in the top left .
02:18	Okay . Especially Later on when we get into subtraction
02:21	and things like this . Okay , so that was
02:23	15 . We add these guys together . Then we
02:28	go to the right over here and we multiply this
02:33	By the diagonal over there . Okay , so 10
02:35	times too it's 20 . Okay , So we have
02:39	15 plus 20/6 . So we go 15 plus 20
02:43	which is 35 . And the bottom number stays the
02:48	same . So we have the fraction . 35/6 .
02:52	Okay . We can actually turn this now . And
02:55	a lot of teachers like their students to do this
02:58	, they like the students to turn this back now
03:00	into a mixed number at the moment . An improper
03:02	fraction . It's a bigger number over a small number
03:05	. So What we do to do this is we
03:08	go 35 . This line here means divided by so
03:11	we divide six into 35 . So 35 divided by
03:14	six is five and there's five left over That five
03:20	. We put as the top number of our .
03:22	There are a fraction here and we put that over
03:25	six . This same as is still behavior . Okay
03:29	. That wasn't too bad . Yeah . What about
03:30	I'll do another one . I'll rub those out And
03:37	let's have a look . Okay , I'll make up
03:40	another one on the spot here and I'll do something
03:42	like uh five and a half plus one and 2/3
03:50	. Okay . And so what do we do 1st
03:54	1st off , because we have mixed numbers here ,
03:56	we have to turn them into improper fraction . So
03:59	do you remember how to do that ? Yeah ,
04:02	we keep the bottom done with the same . So
04:04	the two We get this , we multiply it by
04:07	this . So five times two is 10 plus one
04:12	. Okay , five times two is 10 plus one
04:15	is 11 . We put the plus there and then
04:19	for this one we keep the bottom number the same
04:22	one times three is three plus two is five .
04:26	There you go . We've got them written out now
04:28	and they're written as to improper fractions we're adding together
04:31	. So let's uh do this little trick . So
04:34	what we do to get the bottom number two times
04:37	three is six . And then what we do is
04:44	we start over here and we multiply these two numbers
04:47	. So 11 times three is 33 . We keep
04:51	the plus and two times 5 it's 10 . This
04:55	equals 33 plus 10 is 43 . And we put
05:01	that over six . So as you see , we're
05:05	stuck with a improper fraction here , so we'll turn
05:07	that into a mixed number . So 43 divided by
05:10	67 Sixes are 42 so we get seven with one
05:15	left over one . This number is going to be
05:18	the same . So six 716 Okay , I'll try
05:23	this with a subtraction number . Rob those out .
05:30	So here's our subtraction . Let's go what ? Three
05:35	and a quarter and will take away one and a
05:39	third . All right , So first off , let's
05:43	what do we do ? We got mixed numbers here
05:45	. We're going to turn them into improper fractions .
05:47	Okay , The same sort of process . Okay .
05:49	It's just taking away this time . So three times
05:53	four is 12 . Actually put the four down here
05:55	. First three times four is 12 plus one is
05:59	13 . Take away three down here one , top
06:03	3 is three Plus one is 4 . Okay then
06:09	what we do is okay to get this bottom number
06:13	three times four is 12 . Again , we start
06:17	at the top left here . This is where minus
06:20	is really important because you know , it actually matters
06:23	what take away what it affects our answer . Um
06:26	so 13 times story is 39 . We put them
06:32	on us there And then we have four times four
06:35	which is 16 That equals 39 . Take away .
06:41	16 is 23 And this goes over 12 . Okay
06:49	? As you see this as an improper fraction so
06:51	we can simplify it further . 23 divided by 12
06:55	. It goes once and it has 11 left over
06:58	. So we put 11 over 12 . Not too
07:02	bad . Right what about I go one last one
07:06	, another subtraction one , then I'll leave you be
07:11	on this one . So what about we go um
07:16	6.5 and we take away three and three quarters .
07:26	Okay So how do we do this again ? We
07:29	have mixed numbers here . We have to turn them
07:31	into improper fractions . So we have the two on
07:34	the bottom here . Six times two is 12 plus
07:37	one is 13 . Take away . Yeah four on
07:40	the bottom Three times four is 12 plus three is
07:45	15 . Okay so let's uh now do our cross
07:51	multiplication type thing so we'll get to the bottom number
07:53	first . Two times four is eight . 13 times
07:59	four . That's a bit of a harder question .
08:01	Is that 13 times for the answer to that ?
08:06	It's 52 And we take away two times 15 which
08:11	is 30 So this equals 50 to take away 30
08:16	over 850 to take away 30 is 22 . And
08:22	that goes over . Now this is a good one
08:24	because we actually not only have a improper fraction which
08:28	is left , but we're also going to have to
08:29	simplify it a little bit . So let's simplify it
08:32	first . So there's a number that goes into both
08:34	two and eight . That will be too two goes
08:37	into 22 11 times And it goes into 84 times
08:44	. So we have 11/4 . Then we can turn
08:47	that's simplification . We can't divide anything further into it
08:50	, so let's just get rid of this are improper
08:52	fraction turned into a mixed number . So 11 divided
08:55	by four . It goes in twice , three left
08:58	over , so that three goes over four . So
09:01	I hope that was for some help . Anyway ,
09:04	Thanks for watching . See you next time .

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