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In our last session, we learned about proportional and non proportional relationships. Now we'll learn how to use what we know about proportional relationships to solve real world problems that have to do with proportions.
Chapters:
00:00 Introduction
03:12 Property of proportions
06:10 Working on a real world example
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0:00
a new
0:01
section and in this section we're going
0:04
to learn how to solve proportions right
0:08
we talk about when do we get a
0:10
proportion right when we say
0:12
relationships are proportional when they
0:14
have a
0:17
constant a
0:19
constant rate right A relationship is
0:22
proportional that means that when you
0:25
take every single one of the rate uh the
0:28
the proportion they give you the ratios
0:30
they give you the same rate it's
0:31
constant right we talk about 1/2
0:34
24 uh four uh 48 and none of that step
0:38
hey can you stop doing that you make you
0:41
making too much noise all right so now
0:43
we're going to talk about why do we use
0:45
this proportion and how can we use this
0:46
proportion in real life right how come
0:49
you guys are not taking notes hands are
0:51
on the jaw just watching and some of you
0:54
guys are reading books what I'm teach
0:57
who's reading the book right now
1:01
everybody should be taking
1:03
notes it should be automatic right it
1:06
should be automatic meaning you do it
1:09
without my me saying to you take notes
1:11
it's just what it is all right
1:14
now first we need to understand what
1:18
what is a proportion right a
1:22
proportion by
1:24
definition is an
1:26
equation that states that two ratios are
1:29
equal
1:30
let me say that again a proportion is an
1:33
equation that states that two ratios are
1:36
equal right so does anybody understand
1:40
what that means yeah what does that mean
1:44
it's like the two equations are two
1:46
ratios are equal show me a real life
1:49
example where two you have equal
1:52
ratios that form in
1:56
proportion give me an example
1:59
you guys want me to start yeah all right
2:02
so I can say for
2:05
every
2:08
uh every man or every human has two eyes
2:12
every human has two eyes normally right
2:16
now say some people that can have maybe
2:17
more than two eyes or maybe not two eyes
2:20
cuz they have a problem right so that
2:22
mean so if I have two people have how
2:24
many pair of
2:25
eyes two people will be how many eyes
2:29
and then three people six six so that's
2:31
a proportion because every person that
2:34
say has two eyes every two people will
2:36
have four eyes right that's a proportion
2:38
right there that's an example so
2:40
basically it says that it's an equation
2:42
that states that two ratios are equal
2:44
right so here 1 / 3 is the same as 3
2:48
over 1 so this is the
2:50
proportion right because 1 over 3 is the
2:53
same as 3 over one why because if you
2:55
simplify 3 9 what would you
2:58
get 1
3:00
1/3 right so therefore these two ratios
3:03
are equal so therefore you have a
3:05
proportion you have a proportional
3:07
relationship right now there's a
3:09
property that we're going to learn here
3:11
right the property of
3:13
proportions now I'm going to use letters
3:15
and then later on I'm going to use
3:17
actual numbers right so for example do
3:19
you know if if then statement right if I
3:23
study I will pass my exam if I study
3:26
then this will happen right in the same
3:28
way if a b is equal to C over d right if
3:33
these two ratios are equal then if you
3:35
do the cross multiplication right this
3:37
is called a cross
3:40
multiplication if you do this cross
3:42
multiplication you're going to end up
3:44
with what a d is equal to BC this is
3:47
called the property of proportions so
3:50
now how does that
3:52
work the way we use it is this I'm going
3:55
to first give you just an example and
3:57
then we're going to work on a real life
3:58
problem right if x 3 is = 4 6 right and
4:03
I'm asking you to solve for x we're
4:06
going to use the property of proportions
4:09
we're going to do what we call the the
4:11
cross multiplication okay so you draw a
4:14
line like this draw a line here and draw
4:17
another line here you see what I did
4:19
here right so this means x * 6 right or
4:25
6X is equal to 3 * four this is called
4:31
the property of proportion if x 3 is = 4
4:34
6 then x * 6 which is 6 x isal to 3 * 4
4:39
which is 12 right this is called the
4:41
property of proportion does everybody
4:43
understand that yeah is everybody having
4:45
trouble with this property of proportion
4:47
no right this is called by the way the
4:50
the cross multiplication you can go a *
4:53
D is always going to be equal to B + B *
4:56
c as long as a b is equal to c d right
5:00
so now we have 6 x is = 12 so how do I
5:04
solve for
5:06
x
5:08
anybody divide by 6 so therefore X = to
5:12
2 right so this is called the property
5:15
of proportions this is how you use it to
5:17
solve a problem now real life how would
5:21
you use it in real life it's easy to
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solve
5:26
it first
5:30
I was
5:32
asking so why do you want to know if you
5:35
understand
5:37
it do you did you understand it all
5:41
right so how do we use it in a real
5:45
problem is what we're going to learn
5:46
right now let me read this problem to
5:48
you here the wa time to ride a roller
5:50
coaster is 20 minute when 160 people are
5:53
in line right the wa time to ride a
5:57
roller coaster is 20 minutes
6:00
when there is 160 people in line and
6:04
then at this rate they want to know how
6:07
long is the we time when 220 people are
6:09
in
6:10
line how do you think you're going to
6:12
solve this problem using the property of
6:14
proportion because somebody come up with
6:16
a solution here how would you solve this
6:18
problem using the proper the property of
6:20
proportions yeah 20 over 16 thank you
6:23
very muchal to 220 or X over 220 so 20
6:28
160 is to
6:31
what excellent I'm I'm so glad you were
6:35
able to do this you see how brilliant
6:36
that is this is actually brilliant how
6:39
did you figure that out because that's
6:41
the numbers and it just makes sense it
6:44
makes sense right we know that for every
6:47
for 20 minutes how many people are in
6:49
line
6:51
10 160 right so the key is am of minutes
6:55
it's 220 so 20 minutes correspond to how
6:58
many people
7:00
160 people 160 people waiting so for 20
7:02
minutes there's 160 people waiting in
7:04
line right now we want to know how many
7:08
people how long you going to wait if
7:09
there are 220 people so we don't know
7:12
how long you going to wait but we know
7:13
that's going to be what
7:14
x over 220 now this is the proportion
7:18
here because you know that no matter
7:20
what this is going to be proportional
7:22
right the time is always going to be
7:25
proportional what's
7:28
funny go out for go out for a minute and
7:30
go laugh out there and when you ready to
7:32
like listen you can come back I'm
7:34
listen so 20 minute 20 minutes means
7:38
there's 160 people waiting right they
7:40
want to know how long would it take 220
7:42
people how long will they wait in line
7:44
right so let's say you go to Hershey
7:47
Park and it's like oh wow the line is
7:50
like there's like 50 people and they say
7:52
for 50 people you going to have to wait
7:54
like an hour or two hours right now you
7:56
said well look you went out and you said
7:58
well you know what let me go gra a snack
8:01
and come back and now there's a lot more
8:03
people right now how would you how long
8:05
would you fig how long would you wait
8:07
it's all going to be proportional
8:09
because this is just standard they
8:10
saying that for every 160 people they
8:13
have to wait 20 20 minutes now for 220
8:16
how long you going to wait so you set it
8:18
up and now we can solve using the the
8:21
property of proportion so how would you
8:22
solve this nor I would do 220 * 20 is
8:27
equal to 160x thank you 2 20 * 220 which
8:31
is
8:32
4,400 all right whose voice was
8:37
that 4,400 = 160x and you divide it 160
8:43
all
8:44
right I
8:45
have so somebody put that in the
8:47
calculator and find out for me please
8:49
it's
8:51
47.3 333 3 33 47 333 right so you go
8:57
away no not 47 just
9:02
seven that don't make sense no
9:06
4,400 get wrong wait
9:10
4,400 ID 16 27.5 27.5 I don't know um my
9:15
calculator was not so you're going to
9:17
wait about 27 and A2 minutes right
9:20
there's 220 people that's how they're
9:22
going to wait okay so you see how you
9:24
can use this proportion to solve any
9:26
problem now what I want to do is we're
9:27
going to go to the textbook and we going
9:29
to work on a specific problem right I
9:33
it
9:40
so so let's let's do this here
9:44
right erase I
9:47
want let me give you another problem
9:49
here that we're going to work on
10:12
is
10:15
$30 not spend that much money to
10:19
Spenders
10:22
bro you
10:27
st girls where you say
10:31
dud oh yeah wait I was thinking
10:43
[Music]
10:45
something now look at this here
10:48
right Mrs hman paid $30 for four
10:51
students to visit the Bible Museum right
10:54
find the cost for 20 students I want you
10:57
to set set up the problem how you set
10:59
the up um 30 sorry 30 over okay by
11:04
kicking off 120
11:08
students uh 4 equals what and then 20
11:12
over X sorry X over 20 x 20 you have to
11:16
be careful how you set that up right X
11:18
is what x stands for the number of
11:20
students right X so know the amount of
11:23
money she's going to pay right she the
11:25
amount of
11:26
money so now we're going to do what the
11:28
cross multiplication
11:30
so know 30 * 20 right
11:32
120 equal to 4 * X right so this is here
11:37
that's 600 = 4X and she going to divide
11:41
by what four right yeah cuz 6 30 * 20
11:45
right so X will be let's see 6 4 that's
11:49
150 right so
11:52
$150 so she going to be paying
11:54
$150 for a total of 20 students would
11:57
she actually do that no right there it's
12:00
part of our budgets sometime we have we
12:01
have budgets for like school trips right
12:04
field trips and stuff like that so does
12:06
that make sense do you see how you use
12:09
proportions they are always practical
12:12
and they are easy to use so this section
12:14
is is going to be probably one of the
12:15
funnest one that you're going to have to
12:16
deal with okay wait so we're multiplying
12:18
cross and we're not like exing it out
12:20
what do you mean like divide by 10
12:22
divide by 10 why would you divide it by
12:24
10 because 20 can go 10 can go into 20
12:27
well that that would be too much work
12:29
you just doing a cross multiplication
12:30
remember you're going this way right 30
12:34
* 20 = 4X and then 600 = 4X and you
12:37
divide by four to get what the amount of
12:40
money it cost you to take a 30 students
12:43
to no 20 student to the museum right so
12:47
this is pretty much what this this
12:48
section is it's not that hard so
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