Welcome to a video on dividing whole numbers.
The goal of the video is to perform long division
with whole numbers.
Let's start by taking a look
at a more straight forward example.
Here we have six divided by two.
We should be aware there are several ways
to represent division of whole numbers.
Remember a fraction bar also represents division.
Then for long division,
we'll set up our division problems in this way.
Division of whole numbers means we will take
a certain number of items and split them up into groups.
So six divided by two means we have six items
and we want to divide these into two groups.
So if we take a total of six and divide it into two groups,
now we can see that when we take six
and divide it into two groups,
each group will have one, two, three items.
Therefore six divided by two is equal to three.
The number being divided is called the dividend.
So in this problem six is the dividend.
The number we are dividing by is called the divisor.
So in this problem two is the divisor.
Then the answer is called the quotient.
So for this problem three is our quotient.
Now before we take a look at some more involved problems,
let's go back and take a look at the multiplication table.
A multiplication table can also help us
perform long division.
For example if I wanted to know what 56 divided by eight was
I could use this multiplication table.
The first thing I would do is find 56 in the table,
which we see here.
If we take 56 and divide by eight,
notice eight is in this column,
we can find the quotient
by determining the factor in this row.
So 56 divided by eight is equal to seven.
Notice there's another 56 in this table,
and it doesn't matter which 56 we use.
If we take 56 and divide by eight using this row
then this column will tell us our quotient which is seven.
This table can be very helpful
when we're first learning how to divide.
Let's go ahead and take a look at some examples
that require long division.
So here we have 515 divided by five.
Let's set this up in long division form.
Notice we're dividing by five,
what we're going to be doing is determining
how many fives there are in several different numbers
to determine how many fives there are in 515.
The way we do this is we start
with the left most digits of the dividend
and start asking how many fives are in those numbers.
What I mean by that is we start with this left most digit
of the dividend and ask, how many fives are there in five?
Well there's one five in five,
so we put a one above that five and now we multiply.
One times five would be five,
and we place that product below that digit.
Now we're going to subtract.
Well five minus five would be zero.
To create the next number,
there we're going to ask the same question,
we bring down the next digit, which would be the one.
Now we ask the same question,
how many fives are there in one?
There aren't any fives in one,
so there are zero fives in one.
A zero above the one, and now we multiply again.
Zero times five would be zero.
Now we subtract again, one minus zero would be one.
Notice we have one more digit to bring down
and it's the last digit, which is the five,
which creates the number 15.
Now we ask the question again.
How many fives are there in 15?
Well there are three fives in 15,
so we place a three above the five, and we multiply again.
Three times five would be 15,
and we subtract.
Notice our final difference is zero.
Since there are no more digits to bring down
this tells us our remainder.
Since the remainder is equal to zero,
that means five divides evenly into 515,
and the quotient is 103.
To relate this to multiplication,
if 515 divided by five equals 103,
then it must be true that 103 times five
must equal 515.
Let's go ahead and take a look at another example.
Here we have 231 divided by four.
Let's go ahead and set it up,
and we're going to follow the same procedure.
We're going to be asking how many fours there are
in a variety of numbers to determine
how many fours there are in 231.
We start with the left most digits of the dividend,
so we start with the two, there aren't any fours in two,
because it's too small.
So now we go to the next digit and consider 23.
How many fours are there in 23?
Well five times four would be 20, so let's try that.
We place the 20 below the 23 and we subtract.
As long as this result is less than four,
this five is correct.
23 minus 20 is three, which is less than four,
so that five is correct.
Now we bring down the next digit, which is the last digit,
which creates the number 31.
Now we ask that same question,
how many fours are there in 31?
Well four times seven would be 28,
four times eight would be 32 which is too big,
so let's use the seven.
Seven times four again is 28,
now we subtract, 31 minus 28 would be three,
which again is less than four so the seven is correct.
But now notice we do have a remainder of three.
We know it's a remainder
because there are no additional digits to bring down.
So to show there's a remainder when we divide 231 by four,
we put our three at the end here.
So this quotient would be 57 with a remainder of three.
To relate this quotient to multiplication,
what this means is that 57 times four,
plus the remainder of three,
would equal 231.
Now let's take a look at dividing
by a two digit whole number.
1,104 divided by 46.
Now we're dividing by a two digit number
and these can be a little bit more challenging.
We start with the left most digit of the dividend,
there aren't any 46s in one or 11,
so now we consider 110.
How many 46s are there in 110?
Now that's not an easy question,
but this is approximately 50,
and this is approximately 100,
and I know there's two 50s in 100, so let's try a two.
Now we're going to multiply the 46 by two,
two times six would be 12, carry the one,
two times four is eight, plus one, that would be nine.
Let's go ahead and subtract,
notice we have to borrow here.
10 minus two would be eight,
then we have ten minus nine, that would be one.
The result is 18, which is less than 46,
so this two is correct.
Let's bring down the next digit.
We have 184,
how many 46s are there in 184?
Again that's difficult to determine,
but we could think of this as 50
and think of this as maybe 200.
There are four 50s in 200, so let's try four.
Four times six, that would be 24,
carry the two, four times four is 16,
plus two, that's 18.
Now when we subtract the result is zero,
I forgot the subtraction sign here.
There are no additional digits to bring down
so this does divide evenly
because we have a remainder of zero.
So our quotient is 24,
which means 24
times 46
equals 1,104.
Let's go ahead and try one more.
Here we have 12,092 divided by 28.
We start working with the left digits of the dividend,
we start with one, that's not big enough,
12 not big enough,
then we consider 120.
How many 28s are there in 120?
Again not an easy question to answer,
so let's think of this as 30 and think of this as 120.
I know there are four 30s in 120, so let's try four.
Four times eight would be 32, carry the three,
four times two would be eight,
plus three that would be 11.
Now we'll subtract,
120 minus 112 that would be eight,
which is less than 28 so the four is correct.
Bring down the next digit which is a nine.
How many 28s in 89?
When I see this I think of,
how many 30s are there in 90?
That would be three, so let's try three.
Three times eight would be 24, now we're going to carry a two.
Three times two would be six, plus two, that's eight.
That looks good because the difference here would be five.
Bring down the last digit.
So our last question is how many 28s are there in 52?
Let's try one,
one times 28 would be 28,
we have to borrow here,
12 minus eight would be four,
four minus two is two.
24 is less than 28 so this one is correct,
we have a remainder of 24.
What that means is,
431
times 28
plus a remainder of 24
would equal 12,092.
Okay that's going to do it for this video,
I hope you found it helpful, thank you for watching.