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Welcome back to our pre algebra class, in our last session, we discussed how to find and solve problems involving unit rates. Now that you've learned how to do that, we'll talk about the use of promotional and non proportional relationships in our daily lives.
Chapters:
00:00 Introduction
00:32 What is a proportional relationship
05:06 How to identify a proportional relationship
08:51 How to find the equation of a proportional relationship
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0:01
proportional and nonproportional
0:03
relationships okay proportional and
0:06
nonproportional relationships and I'm
0:08
expecting people to write down stuff I
0:10
don't want you to have your hands folded
0:11
and looking at me I'm not a comedian I'm
0:14
a teacher so write down what I'm saying
0:18
so why is this important right it's very
0:22
important because you use a life
0:23
constantly they use it in the like
0:25
almost every field right so here first
0:29
we need to know what the definition is
0:31
right what is a
0:32
proportional uh relationship when two
0:36
quantities are
0:38
proportional that means that they have a
0:40
constant rate or ratio two quantities
0:45
that are proportional have a constant
0:48
rate or ratio what does that mean now
0:52
let's say I want to compare LeBron James
0:56
mid-range and Kobe Bryant's mid-range
0:59
rest P Kobe right so if I look at LeBron
1:04
James a midrange shot for those that
1:07
play basketball is a shot that is below
1:09
the beyond the three-point line right
1:12
that's a mid-range because you're
1:13
shooting from the perimeter but it's a
1:15
mid-range shot because it's not behind
1:17
behind the arc right so LeBron James
1:21
shot let's say in his first game 10 he
1:23
made 10 out of 15 of his shot in the
1:26
second game he made 20 out of 35 of his
1:30
shot and then in this last game he made
1:32
five out of six right it's pretty now if
1:35
you look here right there's something
1:37
that we're going to see in a second now
1:39
if you go back to Kobe Kobe made five
1:41
out of seven 10 out of 14 and then 15
1:45
out of 21 so what do you see between
1:48
these two guys here that is different
1:50
what do you see yes uh it looks like
1:53
thebr shot more you say what he shot
1:56
more right yeah oh he shot more all
1:58
right what else do you see here
2:00
mhm
2:03
yeah what else do you see theom all
2:06
different the denominators are different
2:08
all right good what else do you see here
2:10
yeah um I guess can all
2:14
multip you can multiply all of them by
2:18
seven all
2:20
right okay that's which one is divisible
2:23
by seven all of them okay well this one
2:26
is not divisible by seven this is not
2:28
divisible by seven either right
2:30
now three three all right now what what
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I want you to think about when we do
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this is this two quantities are
2:36
proportional if they have a constant
2:39
rate or ratio right now look at Kobe
2:41
here he made what five out of seven
2:43
right 10 out of 14 and 15 out of 21
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right that's that's proportional that's
2:48
proportional why because he's what
2:50
constant right he's shooting the same
2:53
way every time he should the same rate
2:55
because each one here 5 out of seven is
2:58
the same as 10 out of 14 and is the same
3:00
as 15 out of 21 right so that means for
3:03
every five seven shot that he takes he
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makes five out of it that's just
3:08
constant you want him on your team right
3:10
whereas LeBron James he made 10 out of
3:12
15 then he went to 20 out of 35 and five
3:15
out of six is inconsistent right he not
3:18
constant he's not shooting the same way
3:20
every time because in the first game he
3:22
did 10 out of 15 another gave me the 20
3:24
out of 35 and then five out of six now
3:26
if you look at five out of six and five
3:27
out of seven you think this is better
3:30
but this is not consistent because these
3:31
are not the same right the rate are not
3:34
the same you want someone that's
3:35
consistent or you want someone that is
3:37
inconsistent that it goes up and down up
3:39
and down what would you rather have
3:41
consistency or a lack of
3:43
consistency consistency right even
3:46
though this soon this look like it's
3:48
better but it's not because this sh the
3:50
same way 5 out of 7 10 out of 14 15 out
3:53
of 21 that means every time if you were
3:56
to like simplify this what's 10 out of
3:57
14 simplifi if you simplify 10 out of 14
4:00
57 what's 59 or 2175 57 57 see so he's
4:05
shoting the same way every time so we
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call this a constant rate everything is
4:11
the same nothing has changed here does
4:14
that make sense right this is constant
4:17
mean every time is the same thing right
4:19
and you guys that play basketball that's
4:21
what you want you want to be consistent
4:23
you want to be constant like in a good
4:25
way if you made one out of seven sh I
4:27
don't want you shooting the ball I do
4:29
not want you to shoo the the ball right
4:30
cuz yes you're constant but I don't want
4:32
that right yes I'm constant of Z over
4:35
zero why do you
4:38
play I'm constant for about maybe like
4:41
three out of
4:44
20 oh okay well nobody can see that so
4:47
how you going to
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know right nobody can see
4:52
that so all right now now we going right
4:59
Yeah we actually still one one way now
5:02
listen to this we we're going to learn
5:04
how to identify proportional
5:06
relationships right we just did just now
5:08
right now if you look at this
5:10
relationship here right coffee pound per
5:14
cost right so one pound of coffee cost
5:17
how much $3 $3 two pounds cost six three
5:21
cost n four cost is it consistent is it
5:24
constant yes because one over three
5:28
right so determine whether the cost of
5:31
coffee is proportional to the number of
5:33
pounds is it proportional yes why
5:36
because one out of three is equal to
5:39
what 2 out of 6 which is also equal to 3
5:42
out of 9 which is also equal to 4 out of
5:44
12 because this is true and this is all
5:46
equal to 1/3 we say that this is uh uh
5:50
proportional because this is constant
5:52
all right you have the same thing every
5:54
time 1 out of 3 is equal to 2 out of 6
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is also equal to 3 out of 9 is is also
6:00
equal to 4 out 12 this is constant
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therefore the cost of coffee uh per
6:05
pound is proportional it's a
6:06
proportional relationship right now what
6:09
if you go to a store and they tell you
6:11
this which I've heard someone some girl
6:13
told me and she thought that she was
6:15
actually giving me a good deal she said
6:17
Hey listen I walk into the store right
6:19
and that day they have what they call
6:21
like a discount right and she said if I
6:25
buy anything over $25 I get 10% off
6:29
right for $25 $25 you get 10% off and
6:33
she said also but look she said well you
6:35
can get more money off she goes if you
6:37
buy 50 now you're going to get 20% off
6:40
and she goes if I was you I would do 50
6:43
and I looked at her I said it's the same
6:45
rate it's the same doesn't change she
6:46
said no she argued with me that day that
6:49
it was better for me to spend 50 in
6:51
order to get 20% off is she right no
6:54
because it's the same thing but you see
6:56
you have people that work in these
6:57
stores I don't know what they're talking
6:59
about right right so if 25 is 10% 50 is
7:03
20 therefore 75 will be automatically
7:05
what who knows 30 right and then $100
7:09
will be obviously what 4 40% right so
7:13
this is this is proportional because
7:16
it's the same thing okay the discount
7:18
that you get is proportional to the
7:20
money that you spend right so but if
7:23
here say to me oh for $50 now you get 40
7:26
off now and then for 75 you get let's
7:30
say she say 60 off and then for 100 you
7:32
get uh let's say 50 now this is no
7:35
longer proportional right because the
7:37
more money I spend now the more money I
7:39
will save do you see this this is not
7:41
proportional because 25 over 10 is not
7:43
the same as 50 over 40 is it's different
7:46
thing so the more you spend the more
7:48
money you you save that's now this will
7:51
be not constant it's not it's not
7:53
proportional but it's a better deal
7:55
right so this is how you you do this
7:57
kind of stuff now the next next thing I
7:59
want us to learn is I want us to learn
8:01
to describe proportional relationship
8:04
right so proportional relationship can
8:07
be described in one way for example if I
8:10
say to you that my let's not use my age
8:13
anymore because you guys I've gotten too
8:16
much fun out of
8:17
that you right and so I'm not going to
8:21
talk about that anymore by the way my
8:23
wife is still M at you guys for her me
8:25
and if I call it your IDE
8:30
you know what little children hold on a
8:34
second oh you lucky cuz I I call and
8:38
have talk to you guys but we still
8:39
online anyway and tell you all peace off
8:41
B right so uh let's think about this
8:45
yeah let's let's think about this here
8:48
right so let's say
8:53
um all right let me give the guys a
8:56
little bit of a leeway here right I'll
8:58
give you guys a little bit of a so let's
9:00
say that girls IQ right is twice as high
9:04
a boys
9:12
IQ right when it comes to certain
9:18
things so's just let's just say let's
9:22
just say for the sake of certain things
9:23
you guys have a high
9:29
listen
9:32
up so
9:34
basically you you can describe a
9:37
proportional relationship using this
9:39
right it's called now proportional
9:42
relationship they can be described using
9:44
the form y = KX where K is called the
9:49
constant rate of ratio it is also called
9:51
the constant of proportionality right so
9:54
I just made a general statement I just
9:57
say that girls IQ is is twice as high as
10:01
BS IQ right no matter what girl you pick
10:05
if I'm saying that this is constant so
10:06
this is proportional that means if I
10:09
take uh if I take for example alen right
10:14
and I take gab no based on my based on
10:18
my assertion alen's IQ is twice as high
10:21
as gay based on what I say but is this
10:23
true no it's not it's not it is
10:28
not IQ is
10:33
uh but but you see here what I did was
10:38
look look look what I did was I fixed
10:42
this I I impos this but it's this true
10:44
no this is what I made I made it
10:47
proportional right I say that now if I
10:49
say now I'm going to change it I say
10:51
girl a boy strength right boy physical
10:55
strength let's call it BP boy physical
10:57
strength BPS is four times as high as
11:07
girls so which means
11:10
that arm so they are not times strong
11:19
they but they're not
11:21
four a lot of
11:24
girls yeah I'm just I'm just making I'm
11:26
just making the case I'm not saying this
11:28
is true right now now let's say for
11:31
example we looking at a circle right a
11:34
circle let's let me draw a circle here
11:37
and we're going to try to create a
11:38
proportional relationship here Circle
11:41
right a circle not a circle right a what
11:44
do you call this line in the
11:46
[Music]
11:48
circle what do you call this line in the
11:51
circle circumference what you called r
11:54
no more than the radi diameter diameter
11:56
right this is the diameter was
11:59
[Music]
12:06
dier right this is a diameter so there
12:09
is the circle the circumference of a
12:11
circle is proportional to its diameter
12:14
right the circle of the circumference is
12:17
proportional to the diameter so we know
12:19
that c right equals to something * D we
12:24
just need to figure out what is the
12:25
proportional what is the Conant of
12:27
proportionality we need to figure out
12:29
right so basically when I put C here I
12:31
mean the
12:32
circumference is proportional to the
12:34
diameter right there's a relationship
12:36
between the circumference of a circle
12:38
and it's diameter right now I know by
12:41
definition that circumference is equal
12:43
to what pi * what D so this is C = pi *
12:49
D Pi is what 3.14 right when do we get
12:53
into Pi well I'm just giving you an
12:55
example circumference of a circle I
12:57
don't have P circumference of circle is
13:00
what * so here the constant of
13:04
proportionality will be what it would be
13:06
Pi because each circle that you take any
13:09
Circle that you take anywhere a
13:10
circumference is always going to be what
13:13
the pi * what the diameter everywhere
13:16
you go the circumference of a circle is
13:18
always going to be Pi * the diameter
13:21
right circle Pi * diameter everywhere
13:23
you go no matter what Circle you take
13:25
it's always going to be circumference
13:27
equals 5 * Di so this is called a
13:30
proportional relationship right so this
13:33
chapter here is just going to deal deal
13:35
with proportional relationship or non
13:37
proportional now if you have a
13:40
relationship of this sort let's say we
13:42
have one 1/3
13:45
right 3 uh
13:48
312 and let's see we have
13:51
four uh
13:53
416 is this proportional yes is it
13:57
proportional yes or no question
13:59
yeah is that question mark 1/3 is 13al
14:02
312 no so would this be proportional
14:06
absolutely not because they don't have
14:07
this constant rate right
14:10
[Music]
14:12
yeah the only time you have a
14:14
proportional relationship is if the rate
14:17
in between the quantities is the same if
14:20
it's not constant when I say constant
14:22
you mean if it's the same then it's
14:25
proportional if it's not the same is
14:27
nonproportional all right so this is
14:30
pretty much it for this
14:32
chapter this
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