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How To Find The LCD & Add Or Subtract Unlike Fractions And Mixed Numbers
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Feb 19, 2025
In our last session, we learned how to add, subtract like fractions and mixed numbers. Now we'll get introduced to a new set of fractions, the ones that do not have the same denominator, we'll learn how to add and subtract them. Chapters: 00:00 Introduction 00:41 What is the LCD ( Lowest common denominator) 02:09 How To find the LCD using multiples 06:31 How to find the LCD using the L method 09:16 How To find the LCD using the factor tree 13:24 working on different examples
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0:00
did we do this last year no we we might
0:02
have done it in hey last
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one uh last last year you probably did
0:09
it in like whatever grade you were in
0:11
last year six right but again no I was
0:14
in second grade so for this chapter
0:17
right I'm going to teach you three
0:18
different ways of finding the lowest
0:20
common denominator or the lowest common
0:22
multiple right so now it's easier for
0:25
some some ways are easier for some
0:27
people and other ways are easier for
0:28
others so I'm going to teach you like
0:30
each way and then you going to pick the
0:33
one that best suit your needs all right
0:35
so
0:36
first uh introducing right what is the
0:40
lowest common denominator why do we use
0:42
it like last chapter right when we talk
0:45
about fraction can I go to bathroom not
0:48
yet you add fractions right when you
0:51
have fractions that have the same
0:52
denominator you can add them up together
0:53
right we talked about fractions like
0:55
this like if I have 1/4 right Plus 7 uh
1:01
+ 94 is easy to just add this because
1:04
they have the same denominator right
1:07
that gives me 104 yes
1:11
sir yeah you going to put it in there
1:13
right that's 10 10 over 4 okay but the
1:17
problem comes when you have fractions
1:20
like this
1:21
2/3 plus
1:24
12 now some people I remember my
1:27
previous years people see stuff like
1:29
this 23 + 1 over2 and I've seen people
1:32
write oh this is equal to 3 over 5 I say
1:35
how' you get that they go well I just
1:36
add the numerators and then add the
1:38
denominators this is not how you deal
1:41
with fractions that do not have the same
1:43
denominators they are called unlike
1:44
fractions okay so this is not how you do
1:46
it this is not a product so you can't do
1:49
that okay so what we need to find is the
1:52
lowest common denominator now how do you
1:54
find the common denominator good
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question now yes oh wait
2:00
oh no it was a rhetorical question Yeah
2:03
so basically to find a common
2:06
denominator when the fractions are small
2:08
like this are you guys paying attention
2:10
here I hope so right when the fractions
2:13
are small all you have to do is just
2:15
list their common multiples right their
2:17
multiples and then once you get to their
2:19
the common multiple you Circle that so
2:22
for example I have 2/3 right plus2 so I
2:27
start with three right the first
2:30
multiple of three is obviously what
2:32
three right three is a multiple of
2:35
itself right so three and then next
2:38
multiple of three is what 6 because 3 *
2:40
1 is equal to what 3 and then 3 * 2 is
2:43
equal to 6 and then 3 * 3 is nine right
2:47
now I can keep going but
2:50
for I want to keep my sanity I don't
2:52
want to go cuz I already know that it's
2:53
going to be six right I'm going to do
2:55
the same thing with two 2 * 1 is 2 2 * 4
2:59
2 is 4 and 2 * 3 is 6 so once I get here
3:03
I see that they have six in what common
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right so therefore I stop and I say my
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LCD my lowest common denominator or
3:13
lowest common multiple is six right so
3:16
that means each fraction now has to be
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transformed yes um could we do
3:23
like couldn't we just multiply um you
3:26
can do that but how how to get there is
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what I'm showing you you here right
3:31
later on when we get a little bit older
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we going to just do it quick because we
3:34
already know about now we need to know
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the basics you got have to crawl before
3:37
you walk right unless you started you
3:40
came out of your mother's room and you
3:41
started walking I've never heard of such
3:42
I
3:43
came so here we have 2/3 + 1 12 so now
3:47
that I know that my common denominator
3:49
is 6 how do I go from 3 to
3:53
6 yes multip by whatever number so that
3:57
three would be two two right but here's
3:59
the thing if I do something in the
4:01
denominator I have to repeat it where on
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the top top or the numerator right so if
4:07
I multiply 3 * 2 I have to also multiply
4:10
two by two right so it gives me 4 6 and
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I'm going to do the give me the second
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fraction how do I go from 2 to six I
4:19
times it by what three right now I have
4:22
4 six plus 36 can I add them up now yes
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because they have the same denominator
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it gives me what 7/ 6 and if you want to
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be zealous you can break this down into
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a mixed fraction okay so yes we also do
4:41
two what
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two4 well now cuz it's not going to Happ
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you if you get two four the denominators
4:48
are not the same you have to get the
4:49
same denominator oh right if the
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denominators are not the same you can't
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up yes any question you have a question
4:57
okay now let me ask another question
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right for this is easy okay so now what
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if I
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have uh two now let's say 7 over 20
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right + 5 over
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32
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right if I have this 20 and then 32 or
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let's say let let me do something easier
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maybe maybe
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um uh let's time something a little
5:27
easier there unless uh
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5 over 12 + 7 over 30 for example let's
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start with this two fractions here right
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and I want to add these two together now
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what is different between these and the
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last one what do you see that's
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different tell me what you see that's
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different here yeah double digits double
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digits right so now for yeah what am I
5:55
writing what are you writing not all
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this is notes right now here if you look
6:02
at it the fraction are double they are
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bigger number so for me to go out and
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then write the multiples it's going to
6:07
take me a long time I don't feel like
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doing that right cuz I'm going to go 12
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24 36 48 60 I don't want to do all of
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that you can but you don't have to let
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me show you another way that I've
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learned right see if you like that right
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so it's called using the L right so I'm
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going to go
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12 and then 30 I'm going to put them
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here right now I want to find a number
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that goes both into 12 and 30 give me
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one yeah five five does not go to 12 I
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mean six all right six right six goes
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into 12 how many times two six goes into
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30 how many times five right and then
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you go like this so now you go like this
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right now I want to find a number that
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goes into two and five the only number
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that goes into 2 five is what one right
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and therefore you're done you find your
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LCD now all you have to do is draw this
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L shape here and your LCD is 6 * 1 * 2 *
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5 I believe that gives you 6 * 2 is 12
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12 * 5 is 60 so LCD is equal to 60 is a
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very Rapid Way of finding the that looks
7:16
so complicated it looks complicated to
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something not
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complicated I get it I get it who likes
7:23
this sweet raise your hand if you like
7:25
it sure raise your hand all right put
7:29
your thumbs down if you hate it after
7:31
you say this is garbage thumbs down if
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you think it's garbage all right good so
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two people don't you like this all right
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I have a question yes
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um couldn't um six just be the lowest
7:46
common denominator no because six the
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six goes into 12 and 30 but you have to
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find the lowest common
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multiple lowest common multiple okay
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right so a number that they both go into
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no not number that can divide both a
8:00
number that they both go into that's
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called the L common multiple
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yeah okay does that make sense cuz of
8:07
the five and seven exactly because 12
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and 30 right now the five and seven in
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the numerator we are not worried about
8:12
it at all we are just looking at the
8:15
numerator the denominator 12 and 30 I
8:17
want to change the denominators so that
8:19
I can add the fractions that's my goal
8:21
is to get a common denominator yes they
8:24
both can be divided by six would that be
8:26
the lowest denominator no the both can
8:29
be divided by six but they both cannot
8:31
go into
8:32
six you have to find a number that they
8:34
both go into why do we need to find a
8:37
number if you don't find that you can't
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add the fraction here right it's called
8:41
the lowest common multiple or lowest
8:43
common denominator right so because if I
8:46
don't find that because six goes into 12
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that means nothing because I if I if I
8:51
put 5 over six I didn't really change
8:53
nothing right I didn't really do nothing
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so all I did was just I didn't do
8:57
anything at all this is absolutely wrong
9:00
right but I want to find a number that
9:02
if I multiply that number by this number
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and this number right I can still
9:06
simplify the fraction and get the same
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thing that's what I'm looking for right
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so if you like this way you can do it
9:11
this way there's another way to do it
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it's called using what the prime factors
9:16
or the three factors have you heard
9:18
about that the three factors factor
9:21
three right factor three I don't like
9:23
that way I feel like it's just too much
9:25
work but I'll show you anyway right so
9:28
if you like this
9:30
so I've had like almost like unanimously
9:32
everybody likes this the three Factor
9:34
everybody like the L stuff all right so
9:38
let's let's do the the factor three
9:40
right 12 and 30 so I'm going to break
9:43
down 12 and
9:44
30 so 12 and 12 is two and what 2 * what
9:49
2 * 6 right and six
9:52
is 3 * 2 right now I have that now I'm
9:56
going to do the same thing with 30 30 is
9:57
what 5 and 6 and 6 is 2 and three right
10:02
so now I have this so 12 is basically 2
10:06
* 2 * 3 and then
10:09
30 is 2 * 3 * 5 so the way you find the
10:15
common denominator is this you look at
10:17
what they have in common right what do
10:19
they have in common here let's write LCD
10:21
let me put
10:22
LCD so what do they have in
10:25
common two two and three right so I
10:28
start with so if they have two in common
10:30
I take the highest number the one with
10:33
the highest number so how many twos am I
10:34
going to take
10:35
them two right I always take the one
10:39
with the highest number because I'm
10:40
looking for the lowest common multiple
10:42
right so my LCD will start I'm going to
10:45
start with two I'm going to take two and
10:47
two so since I've taken them I'm going
10:48
to cross them out now what's the next
10:50
thing that they have in common three
10:52
three right I take the highest number
10:53
which is just three one time right so
10:57
times three and then what they have what
10:59
they whatever they don't have in common
11:00
you add it to it which is what five
11:03
right so my lowest common denominator is
11:05
2 * 2 which is 4 4 * 3 is 12 12 * 5 is
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16 so that's another way of doing this
11:11
oh I think I like the L method you like
11:12
this one better no l method right L is
11:16
better cuz L is like straight to the
11:17
point yeah you can right L is better
11:20
right if you like L do the L if you like
11:24
this do the three factors is that in our
11:26
book The L Factor the L fact is not in
11:28
your book do multip until we get it
11:31
right we're going to do a couple more so
11:33
that until we understand it now now this
11:35
is just the first portion right we just
11:38
found the LCD now I have let me go back
11:40
to my fraction so 5
11:42
12 right 5 over
11:46
12+ 7 over 30 right so how do I go from
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128
11:54
8:45 I said 845 right so how do I go
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from 12 to 60
12:00
times what five five right so I'm going
12:03
to multiply this by five and this by
12:06
five remember we always have to multiply
12:08
by five on both side right how do I go
12:10
from 30 to
12:11
60 two two right so now I get what
12:16
25 over 60 + 14 over 60 right and now
12:22
that they have the same denominator what
12:24
do I do I just add them up right that
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gives me what 39
12:29
over 60 right can you simplify that can
12:32
I simplify it of course what goes into 6
12:36
39 that goes into 60 uh three right so
12:40
three goes into 39 how many times 13 and
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three goes into
12:44
30 12 uh o 3 go 20 times so 13 over 20
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right so that's your final result right
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cuz now we got we have to learn how to
12:54
do what how to simplify fraction
12:57
yes yes all right now I let's let's do
13:01
some of the L-shaped stuff to try to
13:03
find some denominators real quick right
13:06
so now let me have let me show you this
13:09
example here what about here no let me
13:13
do it on the corner
13:16
here right what if I
13:19
have 5 over 6 + 7 over 8 would it be
13:23
easier to use the L or to use the
13:26
multiples what do you all think
13:29
multiples multipl multiples right so six
13:32
what's the multiple of six uh six plus
13:35
what else n no nine is not so that's
13:39
three um 12 what else 18 and then and
13:44
then 24 24 right and I can keep going
13:48
what about eight what's the first
13:49
multiple eight eight
13:55
16 21 24 24 and our St here right so my
14:00
lowest command Dieter
14:02
is 24 right now let's try the L shape
14:06
with this one see which one is faster
14:08
let's try so six
14:12
and 6 and 8 right let's start what goes
14:15
in the eight that goes in the six two
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right so two goes in six how many times
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time is it three right and three goes
14:23
into this is time for you to get a watch
14:26
right now what goes into three that goes
14:28
into one that
14:31
four one right and that's it is there
14:34
any other number no right so therefore
14:38
my lowest is 3 * 1 * 4 right 2 * 1 is 2
14:45
2 * 3 is 6 6 * 4 24 which one did you
14:50
like
14:52
better who like the this one better for
14:55
that problem yeah for this problem who
14:57
likees the L better I'm not going to say
15:00
all right so you you choose whichever
15:02
one works for you all right you have a
15:04
question yeah yeah how did you get the
15:06
one here yeah all right so did I get to
15:09
one I got so let me start here right is
15:12
it always going to be one yeah well once
15:14
you get to one that's when you know
15:15
you're done yeah all right one and done
15:17
say it to yourself one done right so so
15:21
two goes into six how many times three
15:23
times two goes into it four times right
15:26
I draw this line here right now
15:29
what's the smallest number that goes
15:31
into three they only one so therefore
15:33
I'm done when you get to the one you say
15:35
I'm done and then when you're done you
15:37
just draw your L and say okay that's it
15:41
okay so my my LCD is 2 * 1 * 3 * 4 which
15:46
is 24 right and now how do I go from 6
15:50
to 24 you want to go right go ahead yeah
15:53
how do I go from 6 to 24 four four times
15:57
right and now got to do it on top how do
16:00
I go from 8 to
16:01
24 three times right so now I have I
16:05
bring it back here 20 over
16:08
24 plus 21 over 24 right and I can add
16:12
them up I get 41 over 24 and that's my
16:17
final result right you see that yeah so
16:20
the L if he works for you then do it if
16:22
you 24 yeah that's
16:25
24 all right now we're going to learn
16:28
how subtract fractions right
16:31
so now that we did all of this can I
16:34
keep this here or can I raise this can I
16:36
raise that all right
16:39
sure sure sure
16:44
I so let's say I
16:46
have we're going to learn how to do uh
16:49
to subtract fractions as well actually
16:51
before we do that let's do this here
16:54
uh mixed numbers I got -3
16:59
over 10
17:01
right
17:04
plus -5 3 four so what's my first step
17:09
before I even solve this I find low one
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what do I have to do
17:16
firster FR improper fraction right all
17:19
right so this is still -3 10 right plus
17:24
now what does this give me this fraction
17:26
here what do I get
17:29
- 23 right 23 over 4 now how about
17:33
denominators so shall
17:35
we do the multiples or the L so what do
17:39
you think the lowest go ahead and find
17:41
the lowest Comm you got you guys do it I
17:43
want to know how you do it I've done it
17:45
three times now right you guys go ahead
17:47
and find the lowest
17:49
Comm and let me know what you
17:56
got you can use a multi
17:59
you can use the factor Tre you can use
18:02
the
18:02
[Music]
18:05
L find the Lord the nominator finding
18:08
the LCD first Abigail can you give me a
18:13
whiteboard yeah you could have just
18:15
called her
18:16
Abby she chose abig girl I just I
18:20
just stretched out it just like
18:25
depends sorry I didn't mean to CL you
18:27
said strch out
18:30
if you don't
18:32
mind get a watch 853 I mean I could read
18:36
the but like
18:39
why I already know how
18:42
to y' are lazy lazy bum cheeks yes
18:47
that's
18:48
right what' you get next it's like
18:52
851 20 like 8 what you got 20 all right
18:57
50 like two
19:01
what you got
19:04
[Music]
19:07
the what you got 20 all right
19:15
20 um I got
19:18
nothing what you got all right 20 good
19:21
yeah I got you use the
19:24
multiples multiples okay is it Comm or
19:29
come on c o o c o m m o
19:44
n all right so let's use both ways to
19:48
find it right so if I start with 10
19:52
right what's the first multiple of 10
19:54
obviously 20 no is always itself 10 and
19:58
then the next is 20 20 20 right now I
20:00
already know I already know these
20:01
numbers so I'm going to stop here for a
20:03
minute right I'm going to start with
20:04
four now what's four the first one is
20:07
obviously and then 8 12 12 18 16 20 20
20:15
right and then we got that 20 here right
20:18
so our come on denominator is 20 now
20:20
let's do it with the L I got 10 and I
20:23
got four right what goes into 10 that
20:26
goes into four two two right two goes
20:30
into 10 how many
20:31
times two goes into four twice right now
20:35
I'm here now one and what what's the
20:38
word one and done right one and done so
20:41
therefore my LCD is 2 * 1 * 5 * 2 which
20:46
is equal to 20 again the way you do is
20:49
up to you I don't impose the way I like
20:53
particular like the L better cuz I feel
20:55
like I get to the point faster than
20:58
anything else
20:59
right so now my lowest Comm is 20 so now
21:03
I can Times by
21:05
what two right two here and then what
21:09
five and five right 2 * -3 is -6 / 10 5
21:15
* -23 is probably 115 so plus-
21:20
115 over 20 and then you add them up you
21:23
get
21:24
-21 over 20 right that should be -21
21:28
over 20 okay why is 6
21:32
10 oh 6 over
21:36
20
21:38
right 121 over 20 all right so this is
21:42
how we going to do for subtraction for
21:44
addition so this is how you do it so now
21:47
I'm going to give you some sample work
21:49
to work
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