We want to use long division to find the quotient. We have a two digit number
divided by a one digit number. For this example instead of using the
traditional long division algorithym though we use a method called partial quotients. The first
step is to write the quotient in long division form, which is this form here.
These two division problems are equivalent where a is the dividend, b is the
divisor, and c is the quotient.
So we'll write seventy-six divided by four as seventy-six divided by four in this
form here. And for the partial quotients method,
we'll draw a vertical line to the right of our problem here.
We'll record the partial quotients on the right. Before we begin though, because the divisor is four,
it'll be helpful to list some products involving four, that we can easily
determine. For example we know that one times four
equals four.
Two times four equals eight.
Three times four equals twelve. Of course we
can continue, but let's just list two more. Let's list five times four equals twenty, and
ten times four equals forty.
Now going back over to our division problem. For the partial quotients method, we
begin by considering the entire dividend of seventy-six. We want to determine a certain
number of fours that we know for sure are in seventy-six. So looking back at our products,
because ten times four equals forty, and forty is less than seventy-six, we know there are
or at least ten fours in seventy-six. So we'll use ten as our first partial quotient. So we'll place
a ten on the right here. Now we multiply by the divisor. Ten times four is equal to
forty. So we place the forty below the seventy-six and now we subtract.
Seventy-six minus forty is equal to thirty-six.
Now we repeat the process. We want to determine a certain number of fours that
we know for sure are in thirty-six. Let's just say we don't remember that nine times four
equals thirty-six. Looking at our products here on the right, let's say we want to use the fact that
we know that five times four equals twenty. Because twenty is less than thirty-six, we know there's at least
five, fours in thirty-six. So five will be our next partial quotient. So we place a
five on the right. Multiply by the divisor. Five time four is equal to twenty. Place the twenty below the thirty-six and again
we subtract. Thirty-six minus twenty is equal to sixteen. And again we repeat the process. We want to determine
a certain number of fours that we know are in sixteen. Then again let's just say we didn't
remember that four times four is equal to sixteen, but we did remember that three times
four is equal to twelve. Because twelve is less than sixteen, we know there's at least three fours in
sixteen. Let's use three as our next
partial quotient. So place a three on the right. Three time four is equal to twelve. Place twelve
below the sixteen and subtract. Sixteen minus twelve is equal to four. We repeat the process because
this differences four, and so is the divisor, we can easily recognize there's
one four in four. So one is our last partial quotient. One time four equals four.
Once again we subtract. In this case the difference is zero, so our remainder is zero. Now we want to sum
the partial quotients on the right.
Ten plus five, plus three, plus one equals nineteen, which means our quotient is nineteen and we don't have a
remainder, and therefore, four is a factor of seventy-six.
So the nice thing about the partial quotients method is that we can use any
partial quotients that we can find based upon what we know about products
involving the divisor, or in this case products involving four. So there are many ways to
come up with this quotient, because we don't have to use these partial
quotients.
It's also true that because seventy-six divided by four equals nineteen. Nineteen times four equal seventy-six. Nineteen
copies, or nineteen groups of four is equal to seventy-six.
I hope you found this helpful.