Rational Numbers - Free Educational videos for Students in K-12

Rational Numbers - By Anywhere Math

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00:0-1	everybody loves cookies . And if I give you the
00:02	option of having 3/4 of a cookie , 0.7 of
00:06	a cookie or two thirds of a cookie , Which
00:10	one would you rather have ? Mhm . Welcome to
00:29	anywhere . Math . I'm Jeff , Jacobson . And
00:31	today we're going to introduce rational numbers . Okay ,
00:34	so let's talk about the cookies . Three/4 of a
00:37	cookie , 0.7 of a cookie or two thirds of
00:40	a cookie . Now , I don't know about you
00:42	, but I want the most cookie I can get
00:45	. So if I'm looking at this , I want
00:47	to choose which one is greater . Well the problem
00:49	is we've got fractions and decimals . Uh so it's
00:52	a bit tough to compare . So what we need
00:54	to do is choose one . We can either make
00:56	them all fractions or all decimals . Most of the
01:00	time it's going to be easiest to make them all
01:02	decimals . Because if you try to do all fractions
01:06	then to compare , you also have to have common
01:08	denominators which we don't . So most of the time
01:12	you're gonna want to just change them all to death
01:15	because that's gonna be the quickest and easiest . Well
01:18	3/4 a decimal . Hopefully you have that memorized ,
01:21	that's just 0.75 . is already good . And then
01:27	two thirds . I don't know if you have that
01:29	memorized . Uh It's a good thing to have memorized
01:32	. If you don't hopefully you know one third That's
01:37	0.3 repeating that line means that number repeats that digit
01:42	repeats over and over and over again An infinite amount
01:46	of time . So 0.33333 forever . If that's one
01:50	third . Well the two thirds is just 0.6 repeating
01:58	. Okay , so 0.66666 . If you don't have
02:01	those memorized , try to they're going to help you
02:04	out a lot , you'll see them all the time
02:05	. But if not , you can always convert this
02:08	to a decimal by dividing two divided by three and
02:12	you will get the same thing now that they're all
02:15	decimals . Hopefully it's pretty easy to see which ones
02:19	Greater or the greatest and that is 0.75 . These
02:25	both have seven in the 10th place , but then
02:27	we have to go to the next And if I
02:29	wanted to , I could add a zero There .
02:32	So it's really 7500's compared to 7000s . Uh and
02:36	obviously that is creator And don't get confused . 0.6
02:42	repeating is like 0.66666 forever . But we don't care
02:49	about all those six is at the end or going
02:52	to infinity . We're looking here right off , right
02:56	off the bat at the tense place . Seven is
02:58	greater than 10 , so we don't even care what's
03:00	after . We already know that that's actually the least
03:04	. So if you have the option , take 3/4
03:08	of a cookie . Okay , let's first talk about
03:10	what are rational numbers When you see rational numbers ?
03:14	Think ratio . Right . It's in the word rational
03:19	. The first part is ratio . Uh So rational
03:23	numbers are just numbers that can be written as the
03:25	ratio of two integers . So a ratio we can
03:29	write like a fraction right ? A to B can
03:32	be written as a over B . As long as
03:34	B is not zero because remember if B is zero
03:38	then that's undefined . Right ? Uh So as long
03:42	as A and B are integers , okay then you're
03:45	good . You've got rational numbers now . We might
03:49	be you might be getting a little bit confused talking
03:52	integer . So I can rational numbers . And you're
03:54	thinking whole numbers and you're getting them all mixed up
03:57	. Well , let's just do a quick little a
04:00	little chart or a little graph here to help you
04:03	remember ? What's what ? Well at the very basic
04:09	we have whole numbers . Right ? That's what you
04:11	dealt with when you were a little kid . Right
04:13	. 12345678 You know , keep going . Uh no
04:17	negative numbers here . Okay . No decibels . Right
04:21	. Just whole numbers . 123 or I'm sorry .
04:25	I should have zero . There keeps going forever .
04:28	Then . We talked about integers . Right ? Well
04:32	, integers include all the whole numbers but then it
04:36	also includes let me write that into jurors . But
04:40	then it also includes the negative whole numbers . So
04:43	then we've got negative one , negative two , negative
04:46	three , negative four and so on . But it
04:49	also has all those whole numbers . Still . Now
04:51	we're getting into rational numbers . Now , rational numbers
04:56	includes all the whole numbers . It includes all integers
05:00	but now we are also going to talk about ,
05:04	I should know . Okay . We're also gonna talk
05:09	about fractions and decimals . So now that's what we're
05:13	talking about , rational numbers . So 0.534 , 0.3
05:18	repeating . Um Let's see . 0.78 negative two thirds
05:26	. Right , negative 4.5 . Those are all rational
05:30	numbers . Okay , so that's important . Hopefully that
05:34	helps kind of break it down for you . The
05:36	difference between whole numbers , integers and rational numbers ,
05:40	rational numbers include all of this stuff here . Okay
05:44	, so let's look at some examples of rational numbers
05:46	and really go over this uh definition . Okay ,
05:51	here's some examples were kind of testing , is it
05:54	a rational number ? So can we write it as
05:58	a ratio of two integers where the denominator is not
06:01	zero , so two ? Is that a rational number
06:04	? Well , yeah , we can write that as
06:06	to over 12 and one are both images were good
06:09	. Negative three can be written as negative 3/1 .
06:13	Those are both energy . Remember negative three is an
06:16	integer uh , negative a half . Well , I
06:19	can write that as negative one over two . I
06:21	can also read it as one over negative two .
06:24	Those are both energies . So that's good . 0.25
06:28	is the same as 1/4 . That's good . Those
06:32	are both integers . 0.6 , repeating if you remember
06:36	from earlier , that's the same as two thirds .
06:41	So again , those are both integers . So all
06:44	of these are examples of rational numbers . Okay ,
06:48	uh an obvious example of a number that's not irrational
06:51	number would be Pie . Right . Pie continues forever
06:55	. Never repeats . So you cannot write it as
06:58	a ratio of two integers , like a over B
07:02	. So Pie is not rational . That's irrational .
07:04	And there's other examples but uh here's someone's of rational
07:09	numbers and that's how you check . Let's do an
07:11	example . Okay , example one right as a decimal
07:15	. So each of these we're going to convert to
07:18	a decimal Uh fractions and decimals can go you can
07:21	go back and forth between the two Now -2 and
07:25	1 4th . Well I know that's two holes .
07:28	Uh So that's gonna be negative too . My decimal
07:32	point is gonna be there and then I got to
07:33	think well what is 1/4 as a decimal ? 1/4
07:37	as a decimal is .25 . Hopefully you have that
07:39	memorized . So that's simply negative . 2.25 . Now
07:45	, another way to do it . If you wanted
07:47	to you can convert it to an improper fraction which
07:50	would be right . four times two is eight plus
07:54	one is nine negative 9/4 . And then this just
07:58	means division . So I can do nine divided by
08:02	four . Well that goes twice attract I get eight
08:07	. That's one at a decimal point at a zero
08:13	four and 2 10 is too Again that's eight .
08:21	Subtract I get to bring another zero down . 4-20
08:25	is five . And remember it was negatives or negative
08:29	2.5 we get the same exact thing . Okay Um
08:33	now let's look at the next one 5 11 again
08:37	like I just said this line in a fraction that
08:42	means division . Okay that's really important . Okay I
08:50	would definitely write that down . So this means five
08:53	divided by 11 . So to convert it to a
08:57	decimal , that's all we have to do . five
09:00	divided by 11 11-5 . Well zero times . So
09:05	I add a decimal here at a decimal here At
09:10	. 0.11 into 50 goes four times . That's 44
09:14	. subtract I get six . I'm not done at
09:18	another zero . Bring it down And I get 60
09:23	11 into 60 goes five times . That's 55 .
09:28	Subtract I get five at a zero , bring it
09:32	down . 50 11 to 50 is four And you
09:37	might start to notice a pattern , right ? That's
09:39	44 . So attract I get six . It would
09:42	be 60 again . So 45 again and it's going
09:44	to keep going on forever . So the way that
09:48	I write this as a decimal since the four and
09:51	five are repeating , I'm going to write it as
09:56	0.45 with the line over the four and the five
10:01	, that means the four and the five are what's
10:05	repeating . Okay , this is called a repeating decimal
10:15	. Okay , because the four of the five repeat
10:18	over and over and over again . 40.45454545 Right on
10:24	and on and on this one it's not repeating .
10:27	It stopped , it ended . So we call that
10:30	you can think of the movie , the terminator ,
10:31	it's called a terminating mm decimal . So make sure
10:39	you know the difference between the two terminating decimals ?
10:41	They stop , they end , they terminate repeating decimals
10:46	repeat on and on and on forever . Okay ,
10:49	uh here's some to try on your own . Alright
11:00	example to write negative 0.26 as a fraction in simplest
11:06	form . Well to be able to do that ,
11:09	you need to know your place values So negative 2.6
11:13	. I'm gonna obviously my fraction is gonna be negative
11:15	so I'm not gonna worry about that yet , I'll
11:17	just kind of put that there And uh I kind
11:20	of forget about it a little bit and just concentrate
11:23	on this 0.26 . Well if you know your place
11:26	values , this is the tense place , that's the
11:29	hundreds place . So if you read it out loud
11:32	to yourself and you can say 26 hundreds , that
11:37	gives you a kind of a hint as to what
11:40	the fraction is gonna look like . 26 hundreds .
11:46	Okay , so maybe write yourself a little hit when
11:51	you're converting it from decimals to fractions . Read read
11:58	it aloud . Okay . Use those place cards and
12:01	that will give you an idea of what it's gonna
12:03	look like as a fraction now the second part ,
12:06	make sure it's the simplest form . Well This is
12:09	definitely not in simplest form , they're both even numbers
12:12	so I can divide that by two and divide that
12:14	by two and I get negative . 13/50 . Okay
12:22	. And that is now in simplest form . So
12:26	that's how you convert from decimals to fractions . Remember
12:30	just read it out loud , remember your place values
12:33	and uh simplify it at the end . Okay .
12:36	Here's some more to try on your own . Thank
12:46	you for watching . And as always , if you
12:47	like this video , please subscribe .

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