Up next in 10
We've already learned how to divide positive fractions and also learned how to multiply rational numbers. Now we'll learn how to divide positive and negative fractions as well as mixed numbers. And then we'll also learn how to divide algebraic expressions
Chapters:
00:00 Introduction
00:52 How to find the multiplicative inverse of a number
04:23 How to divide and simplify fractions
10:22 How to divide mixed numbers
13:32 Solving a real world problem
17:44 How to divide algebraic expressions
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0:01
so we are talking about
0:05
dividing rational numbers everybody know
0:08
what a rational number is by now it's a
0:10
fraction right a number that can be
0:13
written as a fraction is called a
0:14
rational number you know that you know
0:16
what whole numbers are you know what
0:17
integers are you know what irrational
0:20
numbers are so you know okay now the
0:23
first thing that we need to learn in
0:24
this new section which I expect that you
0:27
guys are all going to be writing down
0:28
information I don't want to see anyone
0:31
not writing down anything because I
0:33
don't want to have to well I don't
0:34
remember how to do this so you better be
0:36
writing down stuff I better see you with
0:38
your notes better I see you writing down
0:40
things everyone no
0:43
exception yes yeah go ahead yeah right
0:47
so the first concept that we going to
0:50
learn is called the multiplicative
0:52
inverse everybody says that multip
0:55
multiplicative
0:58
multiplicative right so what does that
1:01
mean what is the multiplicative inverse
1:04
of
1:06
1/3 what is that yeah you want to Define
1:08
it yeah the definition of the word all
1:11
right the product of the number and it's
1:13
multiplicative inverse is always equal
1:15
to one what does that mean if a number
1:18
times is multiplicative invers is one
1:21
what does that mean yeah can we just
1:22
call
1:23
mi if you want yeah if you take a
1:27
fraction and then times it by the
1:29
fraction two invers it's always going to
1:31
equal one exactly exactly how you define
1:33
it right so if you take a number and
1:35
flip it and multiply by a flip um self
1:42
you get one right 1/3 * 3 is equal to 1
1:45
so that's what this means here right so
1:47
if I have a b * B A I'm always going to
1:51
get one because guess what by the
1:53
butterfly effect right butterfly
1:55
whatever the A's are going to cancel out
1:58
and the B's are going to cancel out and
1:59
you going to get what one cuz basically
2:02
you technically getting what AB over a
2:06
which is equal to one so if you time the
2:08
number by multiplicative inverse you get
2:10
one yes how didn't know which number to
2:12
flip say it again I don't know which
2:14
number to flip say that again how do you
2:17
know what you oh you will find out we'll
2:20
get right now we just understand the
2:22
concept right and then we going to see
2:24
how this applies to division of rational
2:26
numbers right so for example 2/3 * 32 is
2:31
= 1 because this technically 6 over 6
2:34
right
2:35
now let's try and find some
2:38
multiplicative inverse and then we're
2:39
going to go to div yeah go ahead right
2:42
for example what is the multiplicative
2:45
inverse of 76 7 over 16 what would it be
2:48
16 16 over 7 does that make sense to
2:51
everyone right you just have flipping it
2:54
that's all you doing just you're just
2:55
flipping it right now what is the
2:58
multiplicative of
3:02
three 1/3 does that make sense to
3:05
everyone because three is like
3:07
technically 3 over what one right so if
3:09
you want to find the multiplica inv of 3
3:11
is
3:12
1/3 now we have a mixed fraction here so
3:16
what is the multiplicative inverse of -6
3:19
and 1/3 hold up what do we do first I
3:23
got it yeah I don't know 37 say it
3:27
again so we going to to first six * 3
3:30
right which 18 + 1 19 so we have to turn
3:35
this into improper fraction that is Nega
3:38
what
3:39
193 so therefore the multiplicative
3:42
inverse of9 /3
3:44
is 319 right 319 so that will be the
3:48
multiplicative inverse of this number so
3:51
pretty simple now that we understand
3:54
what a multiplicative inverse is we're
3:55
going to see how that relates to
3:57
fractions right so now dividing
4:00
fractions so when you divide a fraction
4:03
what you're technically doing is this if
4:05
I'm dividing A over B / c d what I'm
4:09
doing is I'm multiplying a b by the
4:12
multiplicative inverse of C
4:14
D okay that's a lot of terms so
4:18
basically a b / c d is technically a b *
4:23
D over C yes um like I think I know this
4:28
is multiplying by
4:31
reciprocal that's why reciprocal right
4:33
and the way you reciprocal is r e c i
4:37
reciprocal so when you divide a fraction
4:40
you what you do is you multiply the left
4:43
hand fraction by uh the reciprocal of
4:47
the right and fractions this is the left
4:49
this is the right so a/ B / C over D is
4:53
basically a b * d c does that make sense
4:57
right so now for example if I have 1/ 9
5:01
and I'm trying to divide that by
5:03
52 first we're going to learn how to
5:05
divide fractions by fractions right 1 9
5:09
/ 52 is 1 9 * 12 5 okay now since we
5:16
learn how to do multiplication yes um
5:20
when you're doing when we dividing um
5:22
the fact
5:25
I the butterfly yes I was going to talk
5:28
about that so you actually ahead of me
5:30
right so since we are
5:32
multiplying when you have a
5:34
multiplication we always think about
5:35
what simplifying the fraction right
5:38
because going forward any fraction
5:40
that's not simplified is not totally
5:42
complete right in my algebra 2 when they
5:45
don't simplify I take some points off
5:48
and they why I said well because you
5:50
have you have to simplify it's a rule in
5:52
mathematics that you have to simplify
5:54
any fraction right every fraction so now
5:58
I have 1 9 and 12 5 so how do I simplify
6:01
this
6:03
fraction um
6:05
mhm by
6:08
what if I look at these two does is
6:11
there a relationship between one and
6:12
five none right what about 9 and
6:16
12 what goes into n that goes into 12 th
6:20
right so if you divide this you get four
6:23
divide this you get three so that's
6:24
basically 1 over 3 * 4 5 right and then
6:28
now to multiply you multiply
6:30
across okay so this becomes 4 over 15 so
6:36
this is how you're going to do this WR 4
6:38
over 15 that make sense now what am I
6:41
going to do here I want you all to try
6:43
this 37 / 8 and tell me how you did it
6:47
so how would you divide this fraction 37
6:50
/
6:55
8 what 37 and you're trying divide that
7:00
by eight okay so tell me how you first
7:01
set it up and then divide it and then
7:04
finish it so
7:06
first I want you to do it on your own
7:14
first
7:17
by you can use
7:21
it okay I'll give you one hold
7:26
on thank you
7:29
if you got the tell what you
7:32
got Havey what you
7:38
got did you do
7:41
it all right so what you
7:45
got I started by taking the eight and
7:50
turning turning that into a fraction and
7:53
then I multip by the
7:56
recipal and so I got 3 over7 * 1 over8
8:02
okay and I got 356 356 because there's
8:05
no number I remember that goes into
8:09
eight right so therefore it's 3 over 56
8:11
are we clear on that wait simplify that
8:15
you can't because there's no
8:16
relationship between three and there's
8:18
nothing I mean like 3 56 because b six
8:22
this 56 it's not a it's not 5 * 6 it's
8:25
56 three does not go into 56 right
8:30
yeah um how come
8:33
swap
8:36
only cuz we don't swap this one we only
8:39
swap the one on the right hand side
8:41
right the only one that's always swapped
8:43
or flipped is the one on the right hand
8:45
side does that make sense okay now let's
8:48
try this 4 five right times divided
8:54
by
8:55
um 20 so go ahead and do that 4 five by
8:59
20 and see what you
9:16
get next what you got um 12 so tell me
9:21
how you did it um so I turn the 20
9:27
into 12th okay
9:30
and then you multiply
9:32
right M right I M
9:37
cross the 4 20
9:42
into and and that's 125 125 that's
9:47
correct 125th right because the four
9:49
goes into 25 so you got 5 * 5 that's 25
9:53
12 okay we're going to move on from this
9:55
and now we're going to talk about how do
9:57
you divide and mix number right mixed
10:01
number now we got -4 and then 2/3 / 3
10:06
and 1 you guys try it on your own and
10:08
see what you
10:14
get4 2/3 and then divid by 3 and then 1
10:28
n
10:58
okay for
11:35
all right so how do youall do it yes um
11:39
Abby so then
11:42
I so first it was negative I made the
11:46
fraction into a uh improper yes improper
11:51
fraction that's
11:54
1443 okay
11:56
289 and then I 28 over 9 right everybody
12:01
knows how she got that no no no no sorry
12:03
yeah 28 over 9 right I'm not M and then
12:08
oh
12:09
yeah I did um I switched the n
12:16
and symb
12:19
into
12:22
14 143
12:24
* um 9 * 9 28
12:29
okay and
12:30
then
12:34
meod
12:37
14 24
12:43
tce can go into three
12:47
times okay so I
12:51
got 3 two that's right3 23 over2
12:57
right oh you can you can leave it like
13:00
this so you can turn this back into a
13:01
mixed number which is one one2 right you
13:05
have two option you can leave it like
13:06
this there's nothing wrong with this or
13:09
this one all right now let's try to work
13:11
on the word problem which I know you
13:12
guys love so much right
13:15
yeah go ahead and make sure so I don't
13:19
know about you but my dogs don't like
13:21
dog food they hate it I have to cook for
13:24
them maybe 3 days they won't eat any dog
13:27
K yeah that's spoil dog
13:30
absolutely they're not
13:32
spoiled you know why because dark food
13:35
first of all is processed it's like you
13:37
EA living on McDonald's every day would
13:39
you do that no yes no is James a boy or
13:42
a girl with this James is a boy James
13:45
feeds her dog oh well let's call it
13:49
Jamie
13:50
then if he if
13:53
she right so Jamie feeds her dog three
13:57
and three quarter cups of dog food per
14:01
day if she buys a bag of food way too
14:03
specific that contains 165 cups how many
14:07
days will it last I want you all to try
14:09
to solve this problem right so Jamie
14:12
feeds her dog with three and three cups
14:14
a day and she buys a bag that had about
14:17
165 cups so how many days do you think
14:19
that would last so how would you do this
14:21
problem how would you that depends on
14:22
how much the dog eat no you have the
14:25
information and she Fe how much does the
14:28
dog eat every day a lot a lot too much
14:32
what is it what's the number how much is
14:35
dog eat three and 3/4 so we know how
14:37
many cups did she buy I need another
14:40
marker 165 right so how would you set
14:44
this up so far so good I need another
14:47
marker
14:48
please all these markers are bad are you
14:51
like literally like drinking the ink
14:53
those markers how you finish things
15:04
that all right does
15:06
anybody I want to know how you set it up
15:08
first before you even go so yes nor how
15:10
you set it up 3 and
15:12
34
15:14
165 over one all right good we way to
15:18
set it up so it's 165 right divided by
15:23
what three and 34 right so now what we
15:27
do from here so we mhm um switch it and
15:31
make it um we switch the we put
15:36
65 we switch we switch we switch this
15:39
guy right first we have to turn this
15:40
into what mix uh improp fraction which
15:44
is what four 15 4 15 it's 15 over four
15:48
but 15 over four right and then after
15:50
that let's go step I said it's 3 * 4
15:53
which is 12 well I'm slow so let me go
15:56
little by little right 3 * 4 is 12 12 +
15:58
3 is 15 15 over
16:00
4 right that's what I'm saying I'm very
16:03
slow so now we have 165 over one and
16:06
then times 4 over 15 now what we do from
16:10
here
16:12
do I got it
16:15
butterfly um 15 and 165 15 goes into 165
16:20
11 times 11 times is that right no I use
16:23
my calculator I don't think that's right
16:25
cuz 4 * 15 is 60 so it goes by five time
16:29
let's do at least five we know this is I
16:31
don't know and this will be what's 165
16:34
of five it says 11 11 here wait hold 165
16:40
16 15 oh so this is 11 all right so that
16:43
will be 11 yeah is 11 so this is 11 1 *
16:47
4 over 1 which is what 44 right so how
16:52
long will food last 44 days 44 days
16:56
those dogs arey
16:59
has 150 cups of dogs well if you have
17:01
big dogs you know that's that's good
17:04
yeah dog e a lot
17:07
what it's called gig all right now Emily
17:12
you skipped the word problem just in
17:13
time okay now we're going to learn how
17:14
to um I know now we're going to learn
17:18
how to use this to uh solve um what we
17:21
call algebraic expressions okay great so
17:25
now we're going to talk about algebraic
17:26
expressions which I know you guys also
17:28
love
17:29
so how do you divide them so if I have 5
17:33
over 3 a right and I'm trying to divide
17:36
that by um
17:39
15 over ABC so now I'm going to try to
17:42
solve this in front of you guys real
17:43
quick right so look I have letters I
17:47
have variables right it does not change
17:51
it does not change the problem that much
17:52
it's the same principle that we using
17:55
Okay so let's let's pause for a second
17:59
it's easy so it's going to be 55 over 3
18:02
a
18:03
right gab I can hear you from
18:06
here I can hear your
18:09
voice don't move him back there with
18:10
Emily Emily can't do that I will
18:13
actually fight
18:15
somebody I'm not saying that way I'm
18:17
just saying like are we following here
18:21
right right for a second so we have 5
18:24
3ab time abc 15 right yeah
18:30
so now if I'm going to simplify this I
18:33
need to go numbers and numbers and then
18:37
variables and variables right so now
18:39
five and 15 five goes into 15 three
18:43
times right and now a b c watch this A
18:48
and A are going to cross up B and B are
18:52
going to cross up correct so I'm only
18:54
left upstairs with what c c is the only
18:58
one left up stairs and then downstairs I
19:01
have what 3 * what 3 which is 9 so the
19:06
final result is C over9 so a lot of
19:09
people get intimidated when they see
19:11
letters you shouldn't be right now let
19:13
me twist it up a little bit and see if
19:15
you guys can figure this out now what if
19:17
I had 3 a 2 over 5 times
19:25
um noid by doing exponent one second one
19:33
second
19:36
I'm just the number A
19:41
B let's see if you guys can use your
19:44
brain to figure this out right it's not
19:46
that hard right just
19:49
because do you guys know expon yes or
19:53
no no all right let's this
19:57
here take number
20:01
I have hiup which is a
20:04
goodi
20:07
yeah 2 power three right let me explain
20:10
this to you real quick pay
20:15
attention 2 3 power is literally 2 * 2 *
20:20
2 hey hey hey hey hey hey hey that's
20:23
enough right so a to the^ two is a * a
20:31
that's all it is so it's not
20:32
intimidating so now I'm going to go 3 *
20:36
a * a over 5 right and I'm going to flip
20:40
this guys so that becomes a * B over 10
20:45
now I can simplify this can I yeah right
20:50
actually I was let me change this let me
20:53
let me do something different here I
20:54
should have done it you can the a yeah a
20:57
over 10 let's do it this way right so
21:00
now I'm going to do this so I'm going to
21:01
have 3 * a * a over 5 right
21:07
times 10
21:10
time
21:11
right so now can I simpli this yes right
21:16
the a are going to
21:17
what out right 5 is two so now 38 * 2
21:23
which is what 68 and then over what have
21:27
anything down say is over one so it's
21:29
basically
21:30
68 right so that's what I'm
21:33
saying and they get kind of this is so
21:36
hard really simple stuff all right okay
21:39
so this is the today's lecture now we're
21:42
going to work on some
21:43
problems and I'm going to give you stuff
21:45
to work on it's not homework is it
#Mathematics