Graphing Fractions and Decimals on the Number Line - Free Educational videos for Students in K-12

Graphing Fractions and Decimals on the Number Line - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff , Jacobson .
00:02	And today we're gonna be graphing fractions , decimals on
00:05	a number line . Here we go . All right
00:26	, today we're going to be dealing with fractions and
00:28	decimals . Now you should know that with integers .
00:32	There's positive and negative integers with fractions and decimals there's
00:36	also positive and negative . Right ? So for the
00:40	first example we're gonna graph each number and its opposite
00:44	. Okay , every fraction has its opposite , right
00:47	? A positive fraction would have a negative uh opposite
00:51	fraction would be negative , A negative decimal . The
00:54	opposite would be a positive decimal . So we're gonna
00:56	grab both for the first example . Uh So pretty
01:00	simple . I'm gonna start just with Okay , number
01:03	one . Uh Now it's 3/4 . Well I know
01:06	3/4 is in between zero and one . Uh If
01:11	I'm thinking well how am I going to graph that
01:14	? Right , it's in between here , Well it's
01:17	in four , so let's break it up into four
01:18	pieces , so that would be 1/4 to 4th .
01:22	3/4 . Uh and I'll just I'll label that 1
01:27	4th to fourth which is a half . Maybe you'd
01:30	be better if I simplified it 1/2 and there's 3/4
01:35	right there . So when I'm graphing three forth ,
01:40	I'm gonna put a big point right there . Now
01:44	the opposite of 3/4 would be negative 34 So same
01:48	thing that's going to be in between zero and negative
01:51	one . So negative 1 4th -1/2 and -3 4th
02:01	. So the opposite of three forces , not your
02:03	three force . And I grabbed that point right there
02:07	. So there's our first part , the first part
02:09	of our first example . Let's try part b .
02:11	uh so we're gonna graft negative 1.6 and its opposite
02:15	the same thing . I'm going to start with a
02:18	number line I know negative 1.6 is in between negative
02:24	one and negative two . Right ? It's farther negative
02:30	or farther to the left . The negative one but
02:32	not quite all the way to negative two . So
02:36	I'm going to start with zero . There is -1
02:42	. There's negative too . There's one there's 2 .
02:47	Uh Now I know negative 1.6 . Negative 1.5 would
02:51	be exactly in between Right ? That would be negative
02:54	1.5 . So negative 1.6 is going to be a
02:58	little bit farther negative right ? So probably about there
03:05	And I'm just gonna label that above negative 1.6 .
03:09	Yeah , The opposite of that would be 1.6 positive
03:13	1.6 . So again halfway between one and two would
03:17	be 1.5 . So it's going to be a little
03:21	More to the right than 1.5 . So I'm gonna
03:25	put that just on the other side there , That's
03:29	gonna be a positive 1.6 . Okay so we graft
03:36	uh each of these numbers and their opposite . Okay
03:40	uh notice they're both the same distance away from zero
03:45	. Right ? This is positive 1.6 away . That's
03:49	also the distance is 1.6 away here , it's just
03:51	in the negative direction . Same thing here . 3/4
03:55	from 0 to 3/4 and from zero to negative 3/4
03:58	the distance It's also 3/4 . Okay here's some to
04:01	try on your own . Okay here's example number to
04:11	compare negative 1/2 and -3/4 . Now there's multiple ways
04:15	to do this , I could make a common denominator
04:17	compare them that way but I'm gonna show you how
04:20	to do it graphene using a number line . So
04:22	here is my number line . I know that uh
04:27	they're both negative so I don't really need to worry
04:29	about graphing too much in the positive direction . So
04:33	here's zero . I know that both of them are
04:36	in between zero and negative one . So I'll put
04:38	negative one here uh halfway in between is negative one
04:44	house . So that's easy . Now I know negative
04:48	3/4 to be able to draft that , I need
04:50	to break us into force so I'm gonna put negative
04:54	1/4 there and negative 3/4 there . So now with
05:01	that setup it's pretty easy to grab my point .
05:04	Negative one half is right here , put a big
05:07	point , their negative 3/4 is right here , put
05:10	a big point there . Okay now Hopefully this makes
05:16	it easy to be able to compare the two .
05:19	I know that as I move left on my number
05:23	line , the value is decreasing as I moved to
05:27	the right , I'm increasing in value . So if
05:31	I look -3 forces the farthest left , which means
05:36	it's the least value has the least value negative one
05:40	half has a greater value than negative 3/4 . Even
05:44	though they're both negative right ? It still has a
05:47	greater value than negative 3/4 . Therefore negative one half
05:52	is greater than negative three forth . Okay . Ah
05:59	Let's do another example . All right . Here's the
06:01	second part of example to compare negative four and 56
06:05	and negative four and 16 Same thing . I'm going
06:08	to use a number line to help me do that
06:11	make it big . Uh hopefully when you look at
06:15	this , you notice that both of these mixed numbers
06:17	are in between -4 and -5 . Uh If zero
06:22	is way up here , negative four would be here
06:25	going this direction values decreasing . So I'm gonna put
06:29	negative five . Way down here , right in the
06:33	middle would be negative four and one half . Uh
06:41	but if I'm gonna be able to graft these ,
06:43	I want him in 16 . Uh so that would
06:46	be the same as 36 . So let me see
06:49	if I put negative four and 16 their negative four
06:54	and 26 there , then that would be negative four
06:57	and 36 which is the same as negative 4.5 .
07:01	Uh Then it would be negative four and 46 which
07:07	is two thirds , but I didn't simplify that ,
07:10	so I'm not going to simplify this one and negative
07:13	four and 56 would be there and then one more
07:16	six would give me two negative five . Now I
07:20	can graph uh and plot my points -4 and 56
07:24	is right here -4 and 16 is all the way
07:29	down here And again as I move to the left
07:35	, the value is decreasing on my number line ,
07:38	which means negative four and 56 is less than right
07:45	? -4 & 16 . Okay . And if you
07:50	wanted you would be even be able to tell what's
07:52	the distance between them ? Right ? 16263646 . Right
07:58	? Which we can simplify to just two thirds .
08:01	Let's try one more example for our last example we
08:04	are comparing to negative decimals . We've already done mixed
08:08	numbers and fractions . Let's try decimals . Uh So
08:11	with this negative 3.8 and negative 3.8 . Or if
08:16	I want to think of it as negative three and
08:19	eight hundreds And -3 and 8/10 . If you say
08:25	it that way , hopefully that will help you realize
08:28	how we're gonna graph this . Um You should realize
08:31	that both are gonna be between -3 and -4 .
08:36	So , if I'm going to start with my graph
08:40	, Uh again , negative three is going to be
08:42	here . Remember Zeros down this direction ? Okay ,
08:45	I'm going this way , we're getting more and more
08:48	negative . So -4 would be here . Now We've
08:53	got a couple options . If I want to think
08:56	about how I'm gonna graft native three and 800s .
09:00	Do I really want to break uh my space between
09:04	negative three and negative four and two hundreds ? That
09:07	would mean I'd have to have 100 little uh little
09:10	lines . That doesn't sound very nice . Or if
09:14	I want to do negative three and a tense ,
09:17	I could break this up into tents . Just 10
09:20	little lines . That sounds a little bit more reasonable
09:23	. So I'm gonna do that halfway . That would
09:28	be negative . three and 5 tents . They get
09:31	3.5 . So I'll be negative 3.1 . Now you're
09:36	3.2 A EUR 3.3 and There were 3.4 . I'm
09:43	just putting some of them above because they don't have
09:45	a whole lot of space . Uh negative 3.6 ,
09:49	negative 3.7 , negative 3.8 and negative 3.9 . Okay
09:57	. Um Now let's graph , I'm gonna hold off
10:02	on this one for just one second . Negative three
10:05	and 8/10 or negative 3.8 . That's easy . That's
10:08	right here . Mhm . Now , how about -3
10:14	and 800s ? Well , notice 800 . It has
10:18	zero tents . Okay . It doesn't even have 1/10
10:23	. So hopefully you realize that it's between negative three
10:27	and negative 3.1 or negative three and 1/10 . So
10:31	that if I broke this section up into hundreds ,
10:38	right ? Uh I would just need , basically you
10:42	can think of that as 800s . This would be
10:46	uh 10 hundreds , Right ? So 800s would be
10:51	right about there . Okay and in this situation to
10:56	be able to compare it it doesn't matter . You
10:59	don't have to be real specific . Just as long
11:01	as you know that negative three and eight hundreds Is
11:05	gonna be between -3 and -1 . You're okay ?
11:08	Okay . Um just notice that it doesn't even get
11:12	to negative 3.1 negative three and 1/10 because there's zero
11:17	in the 10th place here . Okay so now again
11:21	as we go to the left the values decrease .
11:24	So that means uh I'll just go with blue NATO
11:28	three and 800 is greater then negative three And a
11:37	10th . Okay and that seems a bit weird to
11:40	think about but if you look at it on the
11:42	number line , remember the farther we go left ?
11:45	Uh The less our value becomes Right , zero is
11:50	up there . Okay when we go to the right
11:52	our values are increasing so that negative 3 800 is
11:58	actually greater than negative three and 8/10 . Okay ,
12:02	here's some to try on your own . Thank you
12:11	so much for watching . If you like this video
12:13	, please subscribe .

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