This document discusses the partial quotients method for long division of whole numbers. It provides an example of dividing 177 by 8 using partial quotients. The divisor (8) is broken into "partial quotients" of 10, 10, and 2, which are multiplied and subtracted until the remainder is reached. The summary explains that different partial quotients could have been chosen, and picking ones closer to the final answer would solve it in fewer steps. It also shows an alternate way to solve the same problem using an initial partial quotient of 20.

1. Partial Quotients
• Fourth Grade Mathematics
File Name: NECP/Laptop T 12037/C:UsersNECPS4DesktopPartial Quotients MS PPT 1997
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2. Common Core Standard
CCSS.Math.Content.4.NBT.B.6
Find whole-number quotients and remainders with up to four-digit
dividends and one-digit divisors, using strategies based on place value,
the properties of operations, and/or the relationship between
multiplication and division. Illustrate and explain the calculation by
using equations, rectangular arrays, and/or area models.

3. 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
divisor.

4. 8 177
10
Ask - How many
[8s] 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 even a lower
number like 5.
A good tip is to start
with easy multiples,
like 10, 20, 50, or
100.

5. Multiply 10 * 8
8 177
80
10

6. Subtract 177 minus
80.
8 177
80
97
10

7. 8 177
80
97
10
10
Start the process
over again. Ask how many [8s] are
in 97?
Again, there are at
least 10.

8. Multiply 10 * 8.
8 177
80
97
80
10
10

9. Subtract 97 minus
80.
8 177
80
97
80
17
10
10

10. 8 177
80
97
80
17
10
10
2
Start the process
again. Ask - how
many [8s] are in 17.
There are at least
2.

11. Multiply 2 * 8.
8 177
80
97
80
17
16
10
10
2

12. 8 177
80
97
80
- 17
16
1
10
10
2
Subtract 17 minus
16.

13. 8 177
80
97
80
- 17
16
1
10
10
2
22
Since the 1 is less
than 8, you are
finished. Now add
up the partial
quotients - 10 plus
10 plus 2.

14. 22 R1
8 177
80
97
80
- 17
16
1
10
10
2
22
Write the answer
above with the
remainder.
You are finished.

15. 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.
Here, the student
starts with a partial
quotient of 20.

16. 8 177
20

17. Multiply 20 * 8
8 177
160
20

18. Subtract 177 minus
160.
8 177
160
17
20

19. 8 177
160
17
20
2
Start the process
over again. Ask how many [8s] are
in 17?
There are at least
2.

20. Multiply 2 * 8.
8 177
160
17
16
20
2

21. Subtract 17 minus
16.
8 177
160
17
16
1
20
2

22. 8 177
160
17
16
1
20
2
22
Since the 1 is less
than 8, you are
finished. Now add
up the partial
quotients - 20 plus
2.

23. 22 R1
8 177 20
160
17 2
16
1
22
Write the answer
above with the
remainder.
You are finished.