Right, this is fifth grade, module 3, lesson 6.
We're going to continue using a...
continue subtracting fractions.
We're going to continue using that area model.
and the only thing that's different this lesson
is we're going to be subtracting where that first number is
gonna be somewhere between 1 & 2.
So it might look like something like 1 and one third
minus four fifths
because that first number here is gonna be between one and two
but it also might look like umm
well in this case it might look like four thirds
minus four fifths. So now it's a little harder to see
that it's between one and two... auh cause it's an improper fraction
but at least you know it's greater than one.
So these are the two kinds of problems
that we're gonna be subtracting in this lesson.
So we're gonna, this is a,
this problem is from the umm teacher notes alright,
so if you're a parent watching this video you won't find this in your student's work.
ahh but this is for the teachers and for the parents really
to give you an idea of what we're going to be doing
cause it's gonna look different than anything you might have experienced when you were a kid.
So... to model this, what we're gonna do is, we're gonna draw one and three fourths
alright and we need
two rectangles and I'm trying to make them identical
and because, so, this is our one
and then this is gonna be our three fourths
So that means, we have to cut it up into four pieces
There we go
and then shade in three of them
so one...
two...
three
now this
right here is a one whole
so technically, we should shade that one in as well.
So, I'm going to shade the whole thing in
so there we go
So there's our one and three fourths
now we're supposed to subtract four fifths.
alright
Now if I wanted to I would draw
another rectangle way over here
to show you what four fifths would like
and of course we would do it horizontally
one, two
three
four -five
and then I would shade in four fifths
So, let me shade in four fifths
one
two
three
four. There's my four fifths. Alright.
but we're gonna do a little bit of umm
shorthand here
ahh because a what we're gonna do is we're gonna quit
drawing this one
and we're just gonna do it
on top
of the original, that that first number
I can never remember if that's the minuend or the subtrend
but whatever we're gonna do the first number
alright so, I'm going to cut
each of our area rectangles into fifths.
there is fifths
and
one
two
three
four -five.
fifths.
Alright.
Now,
ahh
this first rectangle here
I'm going to cut it into fourths as well,
just so we can see what we're talking about.
there's a
fourths
So now you can see
that 1 and three fourths
we could think of it
as
being let's see. Let's count
now we've got
20 pieces here
and then I'm gonna count; 21, 22, 23, 24, 25
26, 27, 28 29
30
31, 32, 33, 34, 35.
So we could think of this as
thirty-five twentieths.
and we're gonna subtract four fifths
well if you think of what
four fifths is gonna look like
it's gonna be four of these strips
right here.
so, four fifths
means, we're gonna subtract out
one
two
three
four
five
six
seven
eight
nine
ten
eleven
twelve
thirteen
fourteen
fifthteen
sixteen
So we're gonna subtract out
sixteen-twentieths
and in doing that
we end up with ...
oh goodness. I don't know what the answer is.
(laughing)
ahh nineteen.
nineteen
twentieths
Now how did we know that it's nineteen-twentieths?
Well we can count the remaining
ahh we could count
say, "Ok there's one, two
three
four
and then
five, six
seven, eight, nine
ten, eleven, twelve
thirteen, fourteen
fifteen, sixteen, seventeen, eighteen, nineteen."
So those are nineteen-twentieths
ok, so that's one way we could have done it.
Now another way we could have a modeled this
umm I'll re-write this down here.
except I want to do this in black, ok
So I'm gonna do one and three-fourths
minus
four-fifths. and I'm gonna scroll
ok, Now we're gonna start
by drawing those umm
area rectangles again
So there's our one
and two
and then try to make 'em identical
and at ...I'm gonna draw them in fourths
because, cut them into fourths, cause the fraction says fourths
So even though this is one whole
and this is the three fourths
I'm going to cut everything into fourths
So one, two, three, four
One, two, three, four
and so now I'm gonna shade in
here's my whole, I mean three fourths right here
There's my three fourths
and then here's my one whole
Now another way
that we can show what's going on
is ok so if we're going to subtract our four fifths right?
so I need to cut everything into fifths,
So one, two, three, four, five
and then one, two, three, four, five
alright so now, we can see that
umm...
one and three fourths
becomes one and
if we counted those
it would be twentieths
So it would be 1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 14, 15 -15 … twentieths
and were gonna subtract out four fifths
and what does four fifths look like?
Well four fifths is gonna look like
umm it's going to have a denominator of 20
So it's going to be sixteen twentieths
alright so we're going to subtract out sixteen twentieths
So, one way we could do it
is you could
take this one and fifteen twentieths
I'm gonna write it down here
one and fifteen twentieths take away sixteen twentieths
So another way you could do it
is we know we're supposed to take away
sixteen … so I'm gonna
these sixteen, well if I take away fifteen of them
that makes
this go away
but then we're left with just one twentieth
remaining that we still have to subtract out
So now we have one whole
take away one twentieth
and that equals nineteen twentieths
so that's another way we could have subtracted this problem
So the point is
there's a lot of different ways to subtract
these two fractions and I've shown you
right now only two ways
and in the future problems
I'm going to see if I can kind of mix it up
and show you even more ways
that you can think of how to subtract these two
pro- ah subtract fractions
alright so we're gonna continue using the area model
to subtract our fractions
cause that's it says to do umm
now three halves right here
three halves that's gonna look like
there's two halves
and there's one more half
so here's two halves
which is one whole
and then here's one more half
so there
right here
is our three halves
and it says to take away
five sixths
so since we're going to take away five sixths
what that means is we need to
umm cut them into six pieces
oh my goodness. So we're gonna go this way
and we're gonna cut it into six pieces
there's six equal size pieces
and then we're gonna cut this in to sixths
alright
now...five sixths
we can see is right here
so five sixths
is woah
five sixths
is right here
five sixths
So, if we want to take away those five sixths
we could just cross 'em off.
One,
two,
three,
four,
five
alright so I just took away five sixths
and so what do we have left over?
well we have to count
so we're gonna count. There's one,
two
and then
three,
four,
five,
six,
seven,
eight
So there's our eight
and what is it? What's the denominator?
It's gonna be eight twelfths
So, I can write that down
but let me, I'm gonna write that down right here
but what did we do?
Well we took our
umm
one whole, which is right here
and we took this
and -this one and a half
this three halves
and we changed it to let's see
we got twelve pieces over here
plus six more pieces here
so that eighteen
so we got eighteen twelfths
and we took away
let's see
there was
one, two,
three, four, five, six
seven, eight, nine ten
so we took away
ten twelfths
so we took away ten twelfths
and that gives us eight twelfths
and because we know how to
umm simplify fractions, that's four times two
and this is four times three
so that is equal to two thirds
So our final answer is two thirds.
So that's one way to do this problem.
There's others,
but I'm showing you just one.
So in this problem same idea
We're going to use a rectangular model.
and the first thing we're going to do
is we're going to draw
one and two fifths
and there's our one whole
and two fifths
So I'm going to cut everything into fifths
and now we're going to shade it in.
so
two fifths is right here
one...
two
and then this whole
we're gonna shade in
this whole thing
So there is our one whole
and two fifths
Now, because we're going to subtract three fourths
That means we need to cut
ahh, going the horizontal way
We're going to cut it into fourths.
So, one, two
three, four
and then, one
two
three, four and three fourths
is this much right here
and so if we wanted to
We can change this to
let's see, ahh one whole
and
eight twentieths
so, cause if we wanted to count this
we could see this is still one whole
but this becomes
eight twentieths
and then we're gonna subtract out three fourths
but three fourths is this much right here
alright
and
three fourths
is gonna be; 3- 1, 2, 3-1, 2, 3 4, 5,
is gonna be 15
So it's gonna be fifteen twentieths
and if we're gonna cross out those three fourths
So let's do it.
1, 2, 3, 4, 5.
and 1, 2, 3 ,4, 5.
So I just crossed off three fourths
and so really, if you wanted to think of it this way
you could think of, and I'm gonna zoom in here
I'm gonna zoom in and change
this to twenty twentieths
plus eight twentieths
and when we take the twenty twentieths
and we subtract the fifteen twentieths
That's gonna give us
five twentieths left over.
and so that's gonna give us
five twentieths
plus
over here
our eight twentieths still sittin' there
and because here's out five twentieths
and I'm gonna make this green
So here's out five twentieths
Plus our eight twentieths left over
and so the answer
is whatever five plus eight is
So five plus eight
is thirteen twentieths
So that's another way to get our answer.
So the answer here is thirteen twentieths
and the last problem for this slide, this video is
umm a word problem of course.
OK, so Jackson had one and three eights fertilizer
He uses some fertilizer on his flower bed
and now he has two thirds left over
How much fertilizer was used in the flower bed?
So we're going to draw a tape diagram to make sure we understand what's going on
He had one and three eights
that's our total
now he used some
we don't know how much he used.
but we know
that he has
two thirds left over
two thirds of a kilogram left over
I'm not trying to draw this so that it's all proportional and stuff
an I'm just drawing it to make sure I understand the problem
and I can see that the problem is definitely a subtraction problem
So, we have one and three eights minus
two thirds.
So now it's time for us to draw our model
So, here's my one
and two
so there's my two area rectangles
and here's this one's going to represent the one
this is going to represent the three eights
So we're going to cut those into eights.
So first I'm going to cut 'em into quarters.
Then I'm gonna cut 'em into eighths
First I'm gonna cut it into quarters
and then I'm gonna cut it into eighths
and then we are going to shade those in.
and so
shading three eighths over here is pretty easy
1, 2, 3 eighths
and now over here, I'm just gonna shade in the whole thing
and I'm gonna kind of fast
alright
So there's our one whole
and our three eighths
Now, in order to subtract two thirds
Of course we're gonna use my red
and we're gonna cut it
into thirds.
Boom
Boom.
and now,
Here's my two thirds
Where here, so I can get rid of those
cause I'm supposed to subtract them.
1, 2, 3, 4, 5, 6, 7, 8
So really what I'm doing
is I took my one whole
which turned into
twenty four twenty-fourths
and then I still have that three eighths
but now I'm going to subtract out two thirds
Now two thirds
is sixteen twenty-fourths
Cause that's how many I chopped off over here.
and so twenty four
minus the sixteen
so twenty four twenty-fourths
minus the sixteen twenty-fourths
leaves me
with eight twenty-fourths
right here
Plus I still have the nine twenty-fourths
sitting over here.
so my answer
is seventeen twenty-fourths.
That's how much was used
in the flowerbed, is seventeen twenty-fourths
kilograms
woo, This was a long video
ahh, but that was
grade five, module three, lesson six
using the area model to subtract fractions.