Partial Quotients Division
8 177
Start by setting up the problem
like this.
It looks just like the traditional
long division method, except
for the long line that is drawn
to the right of the dividend.
Partial Quotients Division
8 177
10
Ask - How many [8s] or
groups of 8 are in 177?
There are at least 10,
so that will be the first
partial quotient.
Notice that you could
pick other partial
quotients here. You
could have started with
20, or a lower number
like 5.
A good tip is to start
with (easy) multiples of
2, 5, 10, 20, 50, or 100.
Partial Quotients Division
8 177
80
10
Multiply 10 x 8.
Partial Quotients Division
8 177
80
97
10
Subtract 80 from 177.
Partial Quotients Division
8 177
80
97
10
Repeat the process.
Ask - how many [8s] are in 97?
10
Again, there are at least 10.
Partial Quotients Division
8 177
80
97
80
10
10
Multiply 10 x 8.
Partial Quotients Division
8 177
80
97
80
17
10
10
Subtract 80 from 97.
Partial Quotients Division
8 177
80
97
80
10
17
2
Repeat the process.
Ask - how many [8s] are in 17.
10
There are at least 2.
Partial Quotients Division
8 177
80
97
80
10
17
16
2
10
Multiply 2 x 8.
Partial Quotients Division
8 177
80
97
80
10
- 17
16
1
2
10
Subtract 16 from 17.
Partial Quotients Division
8 177
80
97
80
10
- 17
16
1
+2
10
22
Since the difference is
less than 8, you are
finished dividing.
The 1 left over is the
remainder.
Now add up the partial
quotients … 10 plus 10
plus 2.
Partial Quotients Division
22 R1
8 177
80
97
80
10
Write the answer on top
with the remainder.
10
Now, you are done.
- 17
16
1
+2
22
Partial Quotients Division
8 177
Notice that you could have
done the problem differently by
picking different partial
quotients.
You could have completed the
problem in fewer steps by
picking partial quotients that
were closer to the answer.
Partial Quotients Division
8 177
20
Here, you’ll start with a partial
quotient of 20.
Partial Quotients Division
8 177
160
20
Multiply 20 x 8.
Partial Quotients Division
8 177
160
17
20
Subtract 160 from 177.
Partial Quotients Division
8 177
160
17
20
Repeat the process.
Ask - how many [8s] are in 17?
2
There are at least 2.
Partial Quotients Division
8 177
160
17
16
20
2
Multiply 2 x 8.
Partial Quotients Division
8 177
160
17
16
1
20
2
Subtract 16 from 17.
Partial Quotients Division
8 177
160
17
16
1
20
+2
Since the difference is less
than 8, you are finished
dividing.
There is a remainder of 1.
22
Now add up the partial
quotients … 20 plus 2.
Partial Quotients Division
22 R1
8 177
160
17
16
1
20
Write the answer on top
with the remainder.
+2
Now, you are done.
22