1. Hangman Division (Partial Quotient)
Easy step by step directions to help with long division…..

2. Start by setting up the problem like this
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.
Discuss benchmark numbers…
X 1
X 10
X 100
177 8

3. Ask - How many [8s] are in 177? There are at least 10, so that will be the first partial quotient..
Write on the side
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800

4. Multiply 10 * 8 8
177 10 80
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800

5. Subtract 177 minus 80. 8
177 10 - 80 97
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800

6. Start the process over again. Ask - how many [8s] are in 97?
Again, there are at least 10. 8
177 10 - 80 97 10
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800

7. Multiply 10 * 8. 8
177 10 - 80 97 10 80
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800

8. Subtract 97 minus 80. 8
177 10 - 80 97 10 - 80
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800 17

9. Start the process again. Ask - how many [8s] are in 17
Start the process again. Ask - how many [8s] are in 17. There are at least 2. 8
177 10 - 80 97 10 - 80
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800 17 2

10. Multiply 2 * 8. 8
177 10 - 80 97 10 - 80
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800 17 2 16

11. Subtract 17 minus 16. 8
177 10 - 80 97 10 - 80
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800 17 2 - 16 1

12. Since the 1 is less than 8, you are finished
Since the 1 is less than 8, you are finished. Now add up the partial quotients - 10 plus 10 plus 2. 8
177 10 - 80 97 10 - 80
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800 17 2 - 16 22 1

13. Write the answer above with the remainder.
You are finished.
22 R1 8
177 10 - 80 97 10 - 80
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800 17 2 - 16 22 1

14. Let’s try another one…..
843 ÷ 4
Set up the problem

15. Ask - How many [4s] are in 843? There are at least 100, so that will be the first partial quotient..
Write on the side
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400

16. 843 4
- 400
100
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
443

17. 843 4
- 400
100
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
443
100
- 400 43
Start the process over again. Ask - how many [4s] are in 443?
There are at least 100 more.

18. 843 4
- 400
100
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
443
100
- 400 43 10
- 40 3
Start the process over again. Ask - how many [4s] are in 43?
There are at least 10 more.

19. 210 r 3
843 4
- 400
100
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
443
100
- 400 43 10
- 40 3
Since the 3 is less than 4, you are finished. Now add up the partial quotients = 210.

20. Hangman Division (Partial Quotient)