1. Partial Quotients
A Division Algorithm

2. The Partial Quotients Algorithm uses a series of
“at least, but less than” estimates of how many b’s are in a.
Students often begin with multiples of 10 because they’re easiest.
13 R2
There are at least ten 12’s in 158 (10 x 12=120). Record 10 as the first estimate. 12
158
- 120
10 (10 x 12=120)
Subtract 38
There are at least three more (3 x 12 = 36). Record 3 as the next estimate.
3 (3 x 12=36)
- 36
Subtract 2
13 (groups of 12)
Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses ( = 13) plus what is left over (remainder of 2 )

3. Let’s try another one 219 R7 7,891 - 3,600 4,291 - 3,600 691 - 360 331
100 (100 x 36=3600)
Subtract
4,291
- 3,600
100 (100 x 36=3600)
Subtract
691
- 360
10 (10 x 36=360)
331
9 (9 x 36=324)
- 324 7
219 R7

4. Now do this one on your own.43
8,572
How did you do?
- 4,300
100 (100 x 43=4300)
Subtract
4272
-3870
90 (90 x 43=3870)
Subtract
402
Note: You may have chosen different estimates than these. That’s okay. Just remember to use nice numbers to work with and be sure your answer is correct.
- 301
7 (7 x 43=301)
101
2 (2 x 43=86) 15
199 R 15

5. And - students make fewer errors.
Partial Quotients
This method of dividing supports :
Estimation – students can use any estimate as long as they don’t go over
Multiplication of 10 and 100
Relationship between multiplication and division
And - students make fewer errors.