Up next in 10
In our class today, we'll transition from whole numbers and their operations to talking about integers and one of their characteristics, the absolute value.
Chapters
00:00 Introduction
01:00 Negative numbers
01:20 Positive numbers
1:45 What's an integer?
02:58 Using integers to represent real life situations
05:25 How To compare integers
10:12 What's absolute value
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0:00
I'm recording I'm recording so by the
0:02
way um resp I
0:05
sent I sent you guys all uh an invite on
0:09
Google Classroom right did you all get
0:12
it or did you all respond to it I forgot
0:15
to do something else I all right when
0:17
you get a chance please join that so all
0:20
the videos that we recorded are all
0:22
there so if you want to go back and
0:23
watch it and someone them fun if you
0:24
want go watch and laugh show you know
0:26
you can do that the one we were talking
0:28
about functions and stuff I was
0:31
I was laughing right so today we're
0:33
going to start a new section so the new
0:35
section is integers and absolute value
0:38
again this is fun fun stuff right now
0:40
integers first we need to understand
0:42
what integers are right so the first
0:45
thing I want to discuss
0:47
is negative numbers right negative
0:50
numbers so thus far we have not talked
0:52
about negative numbers but I'm sure you
0:54
guys know negative numbers right by
0:57
definition negative numbers are that are
1:00
less than what Z zero so they on the
1:03
left side of the number line so if you
1:06
have a number line all numbers on the
1:08
left are called negative numbers all
1:12
right so those are negative numbers -2
1:14
-3 -4 those are all negative integers
1:17
okay and then we have the positive of
1:20
course the positive are anything 1 2 3 4
1:24
five they're on the right side of the
1:26
number line Beyond zero okay so negative
1:30
so if you have your number
1:34
line positives are here negatives are
1:37
here NE this is pause right positive
1:41
okay now what what's an integer by
1:45
definition does anybody have the
1:47
definition of an integer yes sir number
1:50
a number okay is that
1:52
sufficient is this just a
1:55
number what is
1:58
it what's the set of integer negative
2:00
and positive right this the set of
2:02
integers is a set of all positive and
2:07
negative numbers right so all positive
2:10
and negative numbers zero included are
2:12
called integers so those are the
2:14
integers so anything negative Infinity
2:17
all the way to what positive Infinity
2:20
that is a number okay it exclude
2:22
decimals it excludes fractions it
2:25
excludes rational numbers it excludes
2:27
radicals so all of these are called
2:30
integers -1 -2 5 0 1 2 3 all the way to
2:35
positive infinity and all the way to
2:36
negative Infinity
2:39
right again if you if you look at like
2:42
the set of real numbers the set of
2:45
integers um this is stuff that we use on
2:48
a day-to-day basis without the decimals
2:51
okay
2:54
now so we can write integers in real
2:57
life situations okay inges are used
3:01
sometimes to describe actual real life
3:03
situation for example when I say 23 F
3:07
below zero how would I write that if I
3:10
was to reuse an integer
3:13
yes3 -23 that would be the
3:15
representation of 23 fhe below zero now
3:18
is that freezing or what freezing
3:21
freezing right so -3 23 so you see -23
3:25
that's really cold it's freezing right
3:28
so -23 and when I say 11 in more than
3:32
normal what am I saying how would you
3:35
represent that eer 11 in more than
3:40
normal again how would you represent
3:43
that as an
3:47
integer think
3:49
yeah 11 in more than normal what is
3:53
normal POS 11 right so the normal so you
3:57
have a normal so more than normal that
3:59
means POS 11 cuz the normal is zero so
4:02
postive 11 or just 11 you don't have to
4:05
put plus 11 right you can just put 11
4:08
now if you playing football right a loss
4:10
of eight yards so how would you
4:13
represent that everything is
4:15
it a loss of eight
4:17
yards you know football
4:21
right- 8 right -
4:24
8 now the Washington Redskins are used
4:28
to losing your yards all the time they
4:30
not that good of a team are
4:33
they that's my my brother who's the
4:35
commanders fan here commanders Redskins
4:38
is my Wi-Fi password Redskins they the
4:41
Redskins they're not the commander I
4:43
like the
4:45
red what's your what's your team
4:50
Ravens Redskins you
4:54
redin you don't watch it what I like the
4:57
CHS you don't watch it
5:01
I just like whatever I I just like what
5:04
other team my brother likes I like I
5:06
like the what Chiefs and Chiefs and
5:11
patri patri all right that's what my
5:13
brother's like you
5:14
like CH Chiefs the 49ers all right
5:21
anyway now we're going to learn how to
5:23
compare what integers all right come on
5:25
stay with me so we're going to use the
5:27
number line to compare compare integers
5:30
okay so now here's the thing he he hey
5:34
hey hey
5:35
quiet guys guys guys that's Chicago
5:40
Bears a hockey team or a football team
5:42
that's a football team okay all right so
5:45
now we're going to learn how to compare
5:47
integers right how do I compare integers
5:49
I use less than more than or equal okay
5:52
so if I have -2 and four hey I can hear
5:57
your like I'm going to have to move you
6:01
so you better hush up so -2 and four how
6:07
would I compare these two
6:09
numbers -2 and 4 yes uh you making -2
6:14
positive I can't make it
6:17
positive no we have to compare them
6:19
right
6:22
yes NE -2 is less than four does anybody
6:25
agree there that -2 is less than four
6:28
yes or no yes why is it less than four
6:30
because -2 is where on the side of zero
6:34
on the behind zero SO2 is obviously less
6:36
than four what about
6:38
-5 and
6:41
-66 which one is so what would you what
6:43
would you put
6:45
there5 is greater or less than greater
6:47
greater right because if you were to put
6:49
down on a number line5 is here -6 is
6:52
right behind it so5 is greater than -6
6:56
okay so that's the negative integers so
6:58
the negative integers so now you can
7:00
compare positive that's pretty easy
7:01
because you know what about
7:04
this
7:06
-2 and
7:08
2 let's compare these two numbers -2 and
7:12
two yeah equal yeah equal why are they
7:17
equal because two I got double negatives
7:21
that turns out to be what positive right
7:24
I have two negatives here that gives me
7:26
what a positive okay soga -2 is the same
7:30
as saying positive2 so that means 2 is
7:33
equal to two so that that will be equal
7:34
now we not there yet but we can still
7:36
learn how to do that right so now what
7:38
I'm going to ask you to do here is to
7:40
order integers right so John and his
7:44
friends played the question in the
7:45
answer video game there scores were
7:48
1-5
7:50
01 2 and four right so what I want you
7:54
to do now is put them in order from the
7:57
least to the greatest so how would you
7:59
do that
8:00
you have
8:02
1 -5 01 2 and then four and then so I
8:07
want you to put them from the lowest to
8:09
the highest number I want you to order
8:11
these
8:28
numbers got it
8:30
so we are we are ordering this number
8:32
okay I give you a list of integers we
8:34
have one we have -5 we have 01 2 and
8:39
then four so what we want to do is is we
8:41
want to order them from the least to the
8:44
greatest right to the least to the
8:46
greatest so we can use the number line
8:48
to do that right or if you feel like you
8:50
don't need the number line you can also
8:51
do without it cuz if you know your
8:53
negative and you're positive but let's
8:54
use the number line to be
8:57
more so if you zero here what's one
9:00
one is here right two will be right next
9:03
to it right four will be somewhere here
9:05
and then zero is here1 will be here and
9:09
then five will be right here right so if
9:12
you were to list
9:22
them yeah on the left side of the
9:25
zero no this side is a positive this is
9:28
a positive
9:29
zero and this is the negative side okay
9:33
so the negatives are on the left side on
9:35
my left side so if you are here is on my
9:38
right side okay zero is here you go from
9:41
left to right cuz we are from Saudi
9:43
Arabia right you go from left to right
9:45
so left negatives and then right
9:47
positive right so
9:49
-5 -1 0 1 2 and four so this is how we
9:56
list it
9:57
okay from the Leist
10:00
to the greatest all right so I'm going
10:02
to give you another one to do in a
10:03
couple of minutes so now the next thing
10:06
we're going to discuss is absolute
10:08
value absolute value all right and a lot
10:12
of times you guys have you guys done
10:13
absolute value in uh in your previous
10:15
classes you did all right so basically
10:19
by
10:20
definition the absolute value of a
10:23
number is the distance of that number
10:26
from zero this is why the absolute value
10:29
of number is always what positive right
10:33
so for example if you see this
10:36
here that's a gap here right there's
10:38
another Gap here so if I was to find the
10:40
absolute value of -2 I'm technically
10:43
saying what is how how far is two from
10:46
zero that's what I'm looking for two
10:49
units right can we have negative units
10:51
no so this is why the absolute value of
10:53
a number is always positive okay so the
10:56
absolute value of -2 is two and the same
10:59
thing goes for the absolute value of two
11:01
the absolute value of two will be the
11:03
distance from 0 to two which is again
11:07
two unit is that making sense right so
11:10
the absolute value of two is
11:13
pos2 what's the absolute value of5
11:18
alen what would be the value
11:23
of five right five because the absolute
11:27
value of a negative number is always
11:29
what positive positive okay because the
11:34
absolute value is actually saying the
11:37
distance from that number to zero so
11:40
this is why you can't have negative
11:42
distances so the absolute value of a
11:43
number is always positive uh Kenzie
11:47
what's the absolute value of
11:53
-10 not sure all right so the absolute
11:56
value did you understand the definition
12:00
I didn't see that you didn't see all
12:01
right the absolute value of a number is
12:04
the distance that that number is from
12:06
zero does that make sense yeah all right
12:08
so therefore what's the absolute value
12:13
of-1 10 that's right 10 that's it
12:17
right uh Daniel what's the absolute
12:20
value
12:21
of
12:24
three is always what three three cuz
12:27
it's always what positive is the
12:30
distance that number is from zero it's
12:32
always positive because you can't have
12:34
negative distances right uh Kinley
12:37
what's the absolute value of
12:40
negative
12:45
20 what's the after of
12:50
20 20
12:52
20 if I can put a billion zero billion
12:55
negative is always going to be positive
12:57
because the distance has to be always
12:58
what a positive
13:01
right what's the absolute value of
13:04
negative
13:05
negative
13:07
Nega
13:09
9 uh this yeah nine it doesn't matter I
13:14
canot the consilion zero negatives it
13:17
won't change your outcome because it's
13:19
always the distance that that number is
13:21
from zero which is always a positive
13:24
number okay so it's always positive
13:27
always positive now we're going to talk
13:30
we're going to do some work now all
13:32
right so actually before we do that let
13:35
me let's work on a couple of things here
13:38
we're going to talk about the absolute
13:39
value of an expression can I eras
13:43
this yes all
13:47
right talk about the absolute
13:57
value of an expression
14:02
algebraic
14:07
expression you guys remember what the
14:10
this means algebraic expression you all
14:13
remember what is it yeah yeah
14:17
yeah
14:19
expression that's right an expression
14:22
that has an unknown or a variable in it
14:24
right so for example if I want you to
14:27
find the absolute value of x
14:30
- 2 if x is -3 so how would you solve
14:36
this I want you to find or I want you to
14:38
evaluate the absolute value of x - 2 if
14:42
x is2 so let's try and work on that you
14:45
want to do
14:46
it what is it one one how do you know
14:50
it's one what do we do because if x is3
14:55
the absolute value of3
14:59
because it's three unit Z that's right 3
15:02
- 2 which is one right so if I want you
15:06
to evaluate this what I'm asking you to
15:08
do is replace X by what -3 right and
15:12
just like you say the absolute value of3
15:15
is the distance of that number is from
15:17
zero which is what positive 3 is always
15:19
positive so that would be 3 - 2 that is
15:23
one okay so we're going to do a bunch of
15:25
problems like this to conclude the
15:27
section and then
15:29
um
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