We're asked to use long division
to find the quotient.
We have a four digit number divided by a two digit number.
For this example, instead of using
the traditional long division algorithm,
we'll be using a method of partial quotients.
The first step is to write the quotient
in long division form, which is this form here.
We can write this quotient as 2465 divided by 29.
We keep our work organized,
we'll draw a vertical line to the right
of our division problem here,
we'll record the partial quotients on the right side.
Before we begin though,
it's helpful to find products involving the divisor.
In this case, products involving 29.
For example, we know that one times 29 equals 29,
but because our dividend is in the thousands,
we do want to find larger products.
Because one times 29 equals 29,
we should be able to recognize that
10 times 29 would be equal to 290.
Then, from here, two times 29 would be equal
to 29 plus 29, or 58,
and therefore, 20 times 29 is equal to 580.
We still want to find at least one product
that's in the thousands, or a product
that's close to our dividend.
So let's see if we can determine five times 29.
Well, if we needed to, five times 29
is the same as 29 times five.
We would have 45, perform an exchange with the four,
five times two plus four is 14,
so five times 29 is equal to 145,
which means 50 times 29 would be equal to 1450.
I think these products will be all that we need
in order to find our quotient using partial quotients.
To begin the partial quotients method,
we consider the entire dividend,
and we need to determine a certain number of 29s
that we know for sure are in 2465.
Looking at our largest product,
because 1450 equals 50 times 29,
and 1450 is less than 2465,
this tells us there is at least 50 29s in 2465.
So, 50 will be our first partial quotient.
Record a 50 here on the right,
and now we'll multiply by the divisor.
50 times 29 equals 1450.
Now, we subtract.
By subtracting, we just removed 50 29s
from our dividend of 2465, but we still have 1015.
Now, we repeat the process.
We need to determine a certain number of 29s
that we know for sure are in 1015.
Looking at our products, because 580 is less than 1015,
and 580 is equal to 20 times 29,
we know there's at least 20 29s in 1015.
We'll use 20 as the next partial quotient.
20 times 29 equals 580, and we subtract.
By subtracting, we are removing 20 29s from 1015.
Subtracting, we have a five in the ones place value.
Here, we need to perform an exchange.
11 minus eight is three, and nine minus five is four,
so the difference is 435.
Repeating the process, we need to determine
a certain number of 29s that are in 435.
Well, because 10 times nine,
well, because 290 is less than 435,
and 290 is equal to 10 times 29,
we know there's at least 10 29s in 435.
Let's use 10 as our next partial quotient.
10 times 29 is 290.
We subtract,
and now we have 145.
We need to determine a certain number of 29s
that we know for sure are in 145.
Looking at our products, notice five times 29 equals 145,
and therefore, we know there's 5 29s in 145.
The next partial quotient will be five.
Again, five times 29 is 145, and we subtract.
Notice here, we have a difference of zero,
which means the remainder is zero,
and therefore, 29 divides evenly into 2465.
To find our quotient, we sum the partial quotients.
50 plus 20 plus 10 plus five equals 85,
so our quotient is 85.
This is one way to use the method
of partial quotients to find a quotient.
The nice thing about the method of partial quotients
is that we can use any partial quotients that we want
in order to find this quotient,
and the result would be the same.
I hope you found this helpful.