A farmer grows 531 tomatoes and is able to sell 176 of them
in three days, so is able to sell 176 of them in three days.
Given that his supply of tomatoes decreases by 176,
how many tomatoes does he have remaining
at the end of three days?
So he starts with 531 tomatoes.
Let me give myself a little bit more space to work with.
He starts with 531 tomatoes, and he's able to sell 176.
So he's essentially going to subtract the 176 that he's
selling if we want to figure out how many he's left with.
So we're going to subtract 176.
That's how many he sells in three days.
And they're asking us, how much does
he have left at the end of three days?
We just have to subtract those 176 from the amount
that he grew.
So it turns into this straight-up subtraction
problem, so let's see if we can do it.
So if we go straight to the ones place
right over here-- and actually, let
me do it in parallel, because I think
that might be interesting over here.
I'm going to do it the way you traditionally do it
here on the left, and then I'm going
to show you what's happening over here on the right.
So 531 is the same thing as 500 plus 30 plus 1.
And if you subtract 176, that's the same thing
as subtracting 100, subtracting another 70,
and subtracting another 6.
And I wrote it this way, because the 5 in 531
is the same thing as 500.
The 3 in 531 is in the tens place,
so it's really representing 30.
The 1 in 531 is in the ones place, so it represents 1.
And now it'll be a little bit clearer
what we're doing when we're borrowing or regrouping
on this problem right over here.
And so let's start off with the ones place.
1 is less than 6.
It'd be great if we can regroup some of the value
from the rest of the places so we could go straight
to the tens place.
The tens place, we can borrow or regroup 10 from it.
So if we take 10 from here, this becomes 20.
We're going to take that 10 and add it to the 1,
so this will become 11.
We just added 10.
We moved over 10 from the tens place to the ones place.
If you look at it over here, you could say, look,
we're taking 10 from the 30.
That becomes a 20, and then the 1 becomes an 11.
The way when I was first in school, people would say you
would borrow 1 from the 3.
And you'd kind of just stick that 1 right over here.
But what you're really doing is you're taking a 10 from a 30
and making it into a 20, and you're adding that 10 to the 1
and getting 11.
But either way, you'll end up with 11 in the ones place.
And now you can subtract.
11 minus 6 is 5.
Now we go over to the tens place.
In the tens place we now have 2 minus 7,
which is really representing 20 minus 7.
Well, that 70 is bigger than 20, so we
want to add some more to the tens place.
Well, we could go to the hundreds place
to find some more value to regroup.
So let's see if we can do that.
We have 500 here.
What happens if we take 100 from that?
So we're just left with 400 here.
And we take that 100, and we put it in the tens place.
So instead of 20, we now have 120.
If you look at it on this problem,
since we're using the places here,
we're going to take 100 from the 500 and have 400.
And then we're going to take that 100
that we took and put it to the tens place.
Well, 100 is 10 tens.
So we're going to add 10 to this,
so this is going to become a 12.
Once again, the more mechanical or rote way
of thinking about it is that, oh, you took 1 away from the 4.
And you stick that 1 onto the front of the 2.
But you're really taking 100 from the 500 to make it 400
and then adding that 100 to the 20 here and making it 120.
But you write it here as a 12 because it's 12 tens.
You're in the tens place.
Let me write it down.
This is the ones place.
This is the tens place, and this is the hundreds place.
So now that our number on top in the tens place
is bigger than our number on the bottom, we can subtract.
So we get 120 minus 70.
That is 50, or 12 minus 7 is 5.
But that 5 is in the tens place, so it's really representing 50.
Let me circle it with the same color
so you recognize that this 5 is representing 50.
Then finally, we're in the hundreds place.
400 minus 100 is 300.
4 minus 1 is 3, but this 3 represents 300.
This 5 represents 50.
This 5 represents 5, and so we're done.
We get 355.
The farmer is left with 355 tomatoes
at the end of three days, or 300 plus 50 plus 5 tomatoes.