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How To Add & Subtract Like Fractions
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Feb 19, 2025
Welcome back to our Prealgebra class, we are currently in section 3.5, which deals with adding and subtracting like fractions. So fasten your seatbelts and let's get started. Chapters: 00:00 Introduction 00:51 How to add like fractions 04:06 How to add mixed numbers 09:56 How To subtract like fractions 11:22 How to subtract mixed numbers 14:08 Working on a real world example 18:41 How to add and subtract algebraic fractions
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0:01
so a fraction that have the same
0:03
denominator are called like adding
0:07
adding subra like fractions right when
0:09
they have the same denominator right a
0:12
fraction has two things a numerator and
0:15
a denominator so when a fraction has the
0:18
same denominator you have two fractions
0:21
with the same denominators you can add
0:24
them up straight up right now I've seen
0:27
a lot of people do funky stuff it's this
0:30
uh fractions that I want I want to
0:32
prevent that so first I'm going to give
0:34
you the symbols and then after that
0:35
we're going to do an example right hey
0:39
pay attention no more that right SC pay
0:42
attention here so we have a c plus b c
0:49
hey get attention now it's not the time
0:52
to be doing that so close
0:56
that and then keep your eyes here a/ C
1:01
plus b over C right it's a + b over C so
1:06
what does that mean if I have a fraction
1:08
here right I have 7 /
1:11
10+ 6 over 10 right what's the
1:15
denominator here 10 10 because the
1:18
denominator is the same I can add the
1:22
numerators yes when will I ever do this
1:25
in my life well that's not for me to
1:27
answer that question right now
1:30
it doesn't make sense to learn it if
1:31
we're not going to use it I can't answer
1:33
that question right now I get to so
1:36
first I want to get through the lecture
1:37
and I will answer that question
1:39
later right so I have 7 over 10 plus 6
1:43
over 10
1:45
right how you add it is the fraction
1:48
have the same denominator 10 is under so
1:51
I'm just going to add the numerator 7 +
1:53
6 that is 13 over 10 now if you want to
1:56
turn this to a mixed fraction you are
1:58
welcome to do so if you don't that's
2:01
okay here's what I've seen some people
2:03
do and I want to prevent that I've seen
2:05
it last year I've seen it the year
2:06
before I've seen it again and again you
2:09
have fractions like this 7 over 10 plus
2:12
6 over 10 and some people give me 13
2:14
over 20 because they add the
2:17
denominators that is not how you do it
2:20
this is not how you do it okay you don't
2:23
add the
2:25
denominators as long as the denominators
2:27
are the same you just add the numerators
2:30
and keep the denominator the same this
2:32
is why they called like fractions
2:34
denominator not the same that's going to
2:36
be something we're going to discuss on
2:37
Wednesday we're going to try to figure
2:39
out how to find the lowest common
2:41
denominator that's not today that's
2:42
probably Wednesday or Thursday right
2:44
right now we still doing the light stuff
2:46
okay so now I have 5 over
2:49
8 plus -7 over 8 right
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remember when we have stuff like this
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okay we we we learn not to add numbers
3:01
whole numbers right 5 +
3:03
-7 yall should know that by now it's
3:06
automatic -2 right it's not 12 it's not
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-2 you have five bag of dirt and you
3:15
have seven holes right if you feel you
3:18
still have two holes left this is why
3:20
this is -2 over 8 and then we also learn
3:23
how to simplify
3:25
fractions right simplify now I'm hoping
3:28
that here's the thing I'm hoping that
3:30
everybody knows this stuff like tomorrow
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you don't come back here and say I don't
3:33
remember nobody's taking notes save
3:37
Kenzie and
3:38
Dexter that's the only two people that
3:40
are like writing this thing down no
3:42
everybody else is looking at me question
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yes is there going to be a question
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tomorrow no I warn tomorrow what we
3:49
doing tomorrow right so this gives you
3:52
-2 over8 and then you simplify the
3:55
fraction that gives you one4 right
3:58
because two goes into two two goes into
4:00
eight you left with netive 1 and then
4:02
four on the denominator now how do you
4:05
add mixed numbers here's where some
4:08
people either lose it right but I'm here
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to tell you that you're lucky that I
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don't have I don't demand one way of
4:15
doing things okay now I'm going to show
4:17
you how to do the difficult way first
4:19
and then we going to learn how to do the
4:20
simple way which I think is this one
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okay now when you have mixed fraction
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remember uh when we were talking about
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mixed fraction and multiplying them L
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start you can multiply them like this
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you couldn't do that but with when it
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comes like adding it is possible right
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so mix fraction what you can do is this
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you can add the outer numbers the whole
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numbers you can add those together and
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then add the fractions together you can
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separate them right that is doable here
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so that's a good news so for example I
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have two and 38 and I'm trying to add
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that to 3 and 78 so what I'm going to do
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is I'm going to add the whole numbers
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right which are here 2 and three I can
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add those 2 + 3 and then I can add the
5:08
fractions 38 and then 78 right so that
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gives me 2 + 3 that's 5 and then 3 + 7
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that's 10 I get 10 over 8 and I can turn
5:17
this into a mixed fraction of five and
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108 but yes can
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I right but the question is the question
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is
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because it's a mixed fraction I have to
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simplify the fraction correct so that
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gives me now 5 and 5 4 this is still not
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complete yet because this is still a
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mixed fraction right 5 4 is still a
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mixed fraction so I can turn 5 4 into a
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improper mix fraction again now I get
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what I can split
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this right so that gives me 5 4 is 4 4 +
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1 4 and 4 4 is 1 so now I can add 5 and
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1 I get six and this gives me 6 and 1/4
6:03
this could be complicated for some of
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you guys right you may not like this cuz
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they just too much stuff now you can do
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the the other way which is simply turn
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this into What improper fractions right
6:16
we're going to do 2 * 8 that's 16 16 + 2
6:20
that's 19 over 8 and then 3 * 8 that's
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24 24 + 7 that's 31 so we have 19 over 8
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over 31 over 8
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again the fraction have the same
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denominators I can add the top right so
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19 + 31 I get 50 that's 50 over 8 and I
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can simplify this what goes into 50 that
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goes into 8 those right I get 254 and
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you can turn this 254 into a mixed
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fraction or leave it like this all right
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yes is this just one problem yeah why is
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it so complex well like I say this is
7:00
one way of doing it you can do it this
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way or you can do it this way this is
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why I'm saying you better write notes
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because if you don't write it you don't
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remember and I'm sure no one not how
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many people are watching the videos that
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I sent how many people are watching it
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tell the truth here 1 2 3 single faces
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right one two three that's
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it here I don't listen
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to anyway it's there it's there for you
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yeah go ahead it's there for you right
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so now this is 254 you can turn 25
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yeah can you simplify like the equation
7:40
simplify like here simplify you can't
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simplify that you mean can you turn them
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into mixed
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fraction when we multiply we could um
7:52
like do a cross like it goes into 19
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what here do that cross yeah but eight
8:00
doesn't go into
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19 is that what you're saying
8:05
yeah yeah yeah eight does not go into 19
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I'm tired today say but say it was a
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number that eight could go into yeah
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then you can simplify that this doesn't
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make sense to me what why can't we why
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can't we just leave it how it is the
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next fraction I never say you can't I
8:26
say you can leave it as in for fraction
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no like when you do it you have to make
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it why can't you just keep it as a five
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and 108 cuz you have to simpli as five
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and 54
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right now the question is this instead
8:42
of complaining and say why can't we do
8:45
this you should say you know what let me
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suck it up and let me do it doesn't make
8:51
sense because here's the problem we have
8:53
learned to be too soft we don't like
8:56
when things are hard why because we
8:58
think we want want everything to be easy
9:00
no a baby doesn't stay baby forever he
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doesn't crawl and forever he walks and
9:07
you get you grow up you got to grow so
9:10
part of growing up right you got to do
9:13
hard things okay now again I give you
9:15
two options you don't have to do it this
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way you can do it this
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way that's fine then you pick what works
9:21
for you and then stick with it if this
9:23
works for you use that if this works for
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you use this you're lucky I'm not saying
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I want you to do this way because I'm
9:30
trying to be a jerk no I I give you two
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options so pick the one that you like
9:35
and then stick with it now next thing is
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we going to learn how to subtract mixed
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numbers now there's a thing here there's
9:42
a there is a not subtracting just mix
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fraction regular fractions again this is
9:48
straightforward right A C minus b c
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again when the fractions have the same
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denominators I can just subtract the top
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I do know how to too much right so 3 10
10:03
- 9 /
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10 I'm going to subtract the top is 3 -9
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which is -6 over 10 right and then I can
10:13
do what I can simplify the the fraction
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cuz what goes into six that goes into 10
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two so I'm left with3 5
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okay so we always have to simplify
10:24
fractions right going forward any
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fractions let me say it again
10:29
if you have a fraction and you don't
10:31
simplify it I'm always going to take
10:33
either quarter or half of the greater
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okay you got to make sure you simplify
10:39
your fractions it's part of in
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mathematics that's just the requirement
10:44
yeah quar of the problem a quar of if
10:48
it's one point I take away 25% so you
10:51
get 75% instead of one right so I want
10:54
you to learn how to simplify your
10:56
fractions some people are still living
10:58
fractions not simplified that's not
11:00
acceptable okay now now we're going to
11:03
learn how to subtract mixed numbers
11:06
there's a way that the book shows I
11:07
don't want to use that way because I
11:09
feel like you guys are going to be like
11:10
no no no no it's called regrouping right
11:13
but we're not going to do regrouping
11:15
because it might just be like too much
11:18
we're just going to go the simple way
11:19
and just do the turn them into improper
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fraction and subtract them so I have 3
11:24
and 1/4 and then - 1 34 how do was turns
11:28
into proper fractions what am I going to
11:32
get I have 3 and 1 over 4 what does that
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give
11:35
me 13 13 134 right what about that
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here 7 four right and now can I can I
11:46
subtract them of course they have the
11:49
same denominator so what do I do
11:51
subtract the top so 13 7
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is six six right 6 over four am I done
11:59
no what do I do simplif simplify so that
12:01
gives me two two where one over two two
12:06
where 3 two 3 over two right my bad guys
12:09
3 over two and then I can leave it like
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this or I can turn this into a mixed
12:12
fraction switch it what was that going
12:14
to give me a fraction rotate
12:17
it one and what one and three one and2
12:23
right or three 3 two you can leave it
12:26
like this or you can go here if you want
12:29
to be zealous you can go here if you
12:31
don't want to be zealous you can stay
12:33
here okay what does that mean zealous is
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you going to show that you know what
12:37
you're doing so go further all
12:41
right now let's do
12:45
hey isn't a zealot like somebody in the
12:48
Bible who kills Roman people no
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Zealot what
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that's you have Zealot and this is
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zealous zealot
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zealous is someone that's courageous
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that want to show something and Zealot
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is people in the Bible that were anti-
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Romans okay oh zealous jealous not
13:13
zealous we're not zealous
13:16
we you don't like Romans no we are rom
13:20
we hate
13:21
Romans what I thought you jealous for
13:25
people who hated Romans or are you
13:27
saying
13:39
you're not like fully Italian like
13:42
Italian was very
13:44
Italian I'm mostly
13:56
Italian Monkey when
14:02
[Music]
14:04
go ahead and work
14:08
this we have the work problem here
14:10
everybody work on
14:12
it has five and8 yard of ribbon if he
14:18
uses one and 78 yard how much does he
14:20
have left okay how much is left so go
14:23
ahead and try and figure that out so he
14:26
has 5 and
14:28
18 and then he uses 1 78 and I want you
14:31
to I want you to tell me how much does
14:32
he have left and show me how he did
14:48
it look way better if his hair was like
14:51
like this you know like in the front
14:54
there like so much better like that
15:01
like why does he keep his hair like
15:03
that he literally has like this one
15:06
section of
15:09
hair like shave it all how about you
15:13
guys quiet and do the work that I give
15:15
you to do I am be quiet that's
15:25
enough K you should just date timy huh T
15:29
who
15:31
Timmy ksas American Girl
15:35
doll okay I'm getting rid of those
15:38
things so
15:43
know look like eth w what did you all
15:46
get he did though we're not ready yet
15:50
this we barely
15:53
started you think that were're way too
15:56
fast we're not
15:59
AB what you
16:03
got I want to hear what you
16:06
got good what you got
16:14
good
16:16
yes you got it all right
16:27
good yeah
16:44
that you can't do like that you got to
16:47
turn
16:49
Perfection that's why you're getting
16:51
what you're
16:53
getting you have to turn them into
16:55
improper fraction first okay what you
16:58
got
16:59
um 34 all
17:01
right um
17:04
I that's good you can use improper
17:07
fractions or you can use mixed fractions
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right but i' rather just stick with the
17:12
improper fraction because it's
17:13
straightforward and it's easier to do
17:15
like
17:18
that so we have five right 5 and
17:24
18 that's how much she has and she uses
17:27
1 and 78 right we want to see how much
17:29
is left so obviously is a subtraction so
17:32
we're going to subtract this right and
17:35
I'm going to turn this into a improper
17:39
fraction that's 5 * 8 is 40 40 + 1 is 41
17:44
right 41 over 8 and then 1 and 8
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multiply is 8 8 + 7 is 15 right so - 15
17:55
D what
18:00
41 - 15 is 26 right 26 over 8 and then
18:05
like we said you do not stop here we
18:07
always have to do what we always have to
18:09
simplify so we get two goes into 26 and
18:12
two goes into 8 we get
18:14
134 and if you want again be jealous you
18:16
can turn this into a improper fraction
18:19
you get one and 34 right you can stop
18:23
here you still get the grade now I don't
18:25
require you to go to mix fraction I
18:27
don't require that you can leave it here
18:28
I'm I'm okay with it right so what you
18:30
want to go up here that's fine now we
18:33
going to learn how to add uh and
18:35
subtract algebraic expressions algebraic
18:37
fractions which is let let's say you
18:40
have a letter right you have a letter
18:41
and you have a variable so how would you
18:43
do that so these are called algebraic
18:49
fractions
18:53
alic
18:55
fractions so how do you deal with this
18:58
kind of stuff okay so say we have 2 a
19:02
over
19:05
10
19:07
right plus 4 a over 10 so how how do you
19:11
think you do this here 2 a 10 + 4 a 10
19:14
yeah so first we do 2 + 4 okay and that
19:20
is 6 Plus so be 6 a okay 6 a 10 and then
19:27
over 10 over 10 do I simplify simplify
19:31
right so what do I give you 3 over five
19:34
3 over 5 right so 3 a over five okay
19:37
this is very simple stuff so basically
19:39
you're just adding the numerators and
19:42
then you keep the denominator the same
19:44
and then you can simplify okay so that's
19:47
pretty much this section so now you can
19:49
start working on your homework right you
19:53
can start working on that so go ahead
19:55
page 151 through 15 so starting class
19:58
right now
19:59
oh my gosh Nora what did you do you do
20:02
my marker yeah nor what you what did you
20:05
do I just
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