1. Partial Quotient
A Division Algorithm

2. Partial Quotients
The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. Students might begin with multiples of 10 – they’re easiest.
This method builds towards traditional long division. It removes difficulties and errors associated with simple structure mistakes of long division.
Based on EM resources

3. Partial Quotients 13 R2 158 - 120 38 - 36 2 12 10 – 1st guess
There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) 12
158
- 120
10 – 1st guess
Subtract
There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess 38
- 36
3 – 2nd guess
Subtract
Since 2 is less than 12, you can stop estimating. 2
The final result is the sum of the guesses ( = 13) plus what is left over (remainder of 2 ) 13
sum of guesses

4. Here is another one... 219 R7 7,891 - 3,600 4,291 - 3,600 691 - 360
There are at least ’s in 7,891 (100 x 36=3600). Record it as the first guess. 36
7,891
- 3,600
100 – 1st guess
There is at least 100 more 36’s. Record 100 as the next guess
Subtract
4,291
- 3,600
100 – 2nd guess
36 x 10 is 360. There are 10 more 36’s. Record 10 as the next guess.
Subtract
691
There is not another 10 group in x 9 is Record 9 as the 4th guess.
- 360
10 – 3rd guess
Subtract
331
Since 7 is less than 36, you can stop estimating.
- 324
9 – 4th guess
Subtract
The final result is the sum of the guesses ( ) plus what is left over (remainder of 7 ) 7
219
sum of guesses

5. Try this one on your own! 199 R 15 8,572 - 4,300 4272 - 387043
8,572
Let’s see if you’re right.
- 4,300
100 – 1st guess
Subtract
4272
- 3870
90 – 2nd guess
Subtract
Way to go!
402
- 301
7 – 3rd guess
Subtract
101
2 – 4th guess
Subtract 15
Sum of guesses