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So now let's take a look at the unbundling process
when we're subtracting.
So suppose I have 5 feet 3 inches minus 1
foot 10 inches-- we can't really do subtraction
because I can't borrow 10 inches from 3 inches.
But remember that 1 foot is 12 inches.
So here's how we can write it.
We've lined up the feet in inches.
We have 5 feet 3 inches.
We're taking away 1 foot 10 inches-- can't
do the subtraction.
So I'm going to cross out the 5 feet, make it 4 feet.
So that will allow me the 1 foot to be unbundled as 12 inches.
This 12 inches then, I can move in this column here.
And the 12 inches plus the already existing 3 inches
will give me 15 inches total.
Now we can do our subtraction.
So 15 minus 10 is our 5.
4 minus 1 is the 3.
So you final answer is 3 feet 5 inches.
So if we couldn't subtract, we have to borrow.
And when we borrowed, we borrowed from the feet
because 1 foot is 12 inches, giving us
more inches to work with.
All right, let's do another example.
Let's say I have 5 weeks, 3 days, 5 hours,
23 minutes that I'm waiting for some event to take place.
And I'm doing a countdown.
I've already waited 4 weeks, 6 days, 19 hours, 53 minutes.
want to know how long I have to wait still.
So instead of having to write weeks,
days, hours, minutes, and words like
that I'm going to use variables.
So 5 weeks, 3 days, 5 hours, 23 minutes.
Take away 53 minutes from 23 minutes-- we can't do that.
There is not enough minutes.
But I can borrow an hour from the 5 hours,
make that a 4 hours and 60 minutes.
Then I'll have enough minutes to subtract.
So let's do that with all three of these quantities
and see what happens.
So I have my 23 minutes.
I'm going to take the 5 hours and write as 4 hours and the 1
hour-- I'm going to change it into minutes.
So 1 hour is 60 minutes.
Now I have 19 hours to take away from the 4 hours, which I don't
have enough of, so I'm going to break the days.
I'm going to write the 3 days as 2 days
plus one whole day, which is 24 hours.
Now I have enough hours.
Now I subtract days-- 6 days, but I only have 2.
So I'm going to break the weeks.
5 weeks to 4 weeks and the one week is 7 days.
So this 5 weeks got broken into 4 weeks and 7 days.
Now I can perform my subtraction.
So before I can do that, let's just combine and make sure
we have enough of the minutes, hours, and days.
So 4 weeks is 4 weeks.
7 days and 2 days-- again, adding like terms,
see how that's coming in here-- is 9 days.
24 hours and 4 hours is 28 hours.
16 minutes and 23 minutes is 83 minutes.
OK, so now let's do our subtraction.
So the 4 weeks minus 4 weeks, 9 days minus 6 days,
28 hours minus 19 hours, 83 minutes minus 53 minutes.
So when we do the subtraction, again
remember you can only add or subtract like terms.
So 4 minus 4, which will give me zero weeks.
9 minus 6 days will give me 3 days.
28 minus 19 hours will give me 9 hours.
83 minus 53 minutes is 30 minutes.
Another way to write 30 minutes is half hour,
so you could say 3 days and 9 and a half hours.
Or 3 days, 9 hours, and 30 minutes.
Another way we could have done it is this way.
And this is going to resemble very closely
to your decimal number system subtraction,
so pay very careful attention.
So we have weeks, days, hours, minutes, columns.
I cannot take away 53 minutes from 23 minutes.
I'm going to chuck the 5 hours to 4 hours.
Borrow the one hour, which is 60 minutes, and 60 plus 23 minutes
will give me 83 minutes.
So I have 83 minutes and I can do the subtraction.
But now here I have 4 hours minus 19 hours.
I cannot do, so I am going to borrow here.
So I'm going to make this 2 days.
I'm going to borrow 1 day which is 24 hours.
24 plus the original 4 hours, which gave me 28 hours.
Now I can do this subtraction.
Now I have 2 days, subtract 6 days, which I cannot do.
So I have to borrow one from there.
So we will take away the 5, make it 4 weeks.
1 week is 7 days.
7 plus the 2 days left over from before were 9 days.
Now I can do the subtraction of 9 minus 6.
So now everything is in place and we can do our subtraction.
So 83 minus 53 is 30.
28 minus 19 is 9.
9 minus 6 is 3.
4 minus 4 is 0.
So our final answer is 3 days, 9 hours, 30 minutes
or 3 days, 9 and a half hours.
Let's start with counting numbers and whole numbers.
Remember before when we were doing 7 apples minus 4 apples,
we said count down from 7.
So now we're going to have to count down from 53, 29 down.
So it'll be 53, 52, 51, 50, 49, 48, 47 and so on.
In fact, there's quite a lot of people
who use counting down technique to fall asleep.
And I clearly do not want you to fall asleep.
So this is not a very practical way to count down, is it?
So let's just start with how we did our addition.
We lined them up, do you remember that?
Our boxes are back.
All right, so 53 apples is 5 boxes
of 10 apples plus 3 loose apples.
And then we want to take away two boxes
of 10 apples and 9 loose apples.
Well, we can't really take away 9 loose apples--
we only have 3 here.
So we're going to open up one of our boxes
and make that 4 boxes.
And the 10 apples that were in the boxes,
we're going to take them out so that this number here
will become 13.
So we have 13 loose apples minus 9, which will give us 4.
And then 4 minus 2, which will give me 2.
So we have 2 boxes of 10 apples and 4 loose apples.
And this is exactly what the principle
of decimal subtraction is.
So let's take a look.
Let's take the same approach that we did to addition.
So write the numbers one underneath the other,
line up the decimal numbers.
If there are missing place values,
put zeros in their places.
So all place values are taken with a digit.
Let's start with the lowest place value and start there.
So we have 3 minus 6-- can't do it.
So we're going to borrow 10 from here and make that a 13.
13 minus 6 is 7.
Can't do 3 minus 5, so I have to borrow one from here.
Remember, borrowing one of these is
equivalent to 10 of the lower place values adjacent to it.
So borrowing one single is borrowing ten 10ths.
So now I have 13 10ths minus 5 10ths
which will give me 8 10ths.
And you do the same thing.
So 8 minus 7, which I can do.
7 minus 8, I cannot do.
We have 7 tens minus 8 tens, so I have to borrow one from here.
So that will make it 17 tens minus 8, which will give me 9.
And 5 hundreds minus 2 will give me 300.
And the decimal point will stay in the correct spot.
So 391.87 will be my final answer.
Pay very careful attention to the unbundling part.
Here's your video log.
For this third question, let's give you a hint.
One way to start thinking about these problems
is to concentrate on example.
So if you want to know a subtraction is commutative,
take some examples and play and see if this helps.
OK, one important note to make-- one example
is enough to disprove a mathematical statement
but it is not enough to prove a mathematical statement.
Keep that in mind when you're doing this number three.
So here are the other questions if you missed them.