1. Partial Quotients A Division Algorithm
Created by Rina Iati, South Western School District, Hanover, PA

2. The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. You might begin with multiples of 10 – they’re easiest.
13 R2
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 38
There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess
3 – 2nd guess
- 36
Subtract 2 13
Sum of guesses
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 )
Created by Rina Iati, South Western School District, Hanover, PA

3. Let’s try another one 219 R7 7,891 - 3,600 4,291 - 3,600 691 - 360 331
100 – 1st guess
Subtract
4,291
- 3,600
100 – 2nd guess
Subtract
691
- 360
10 – 3rd guess
331
- 324
9 – 4th guess 7
219 R7
Sum of guesses
Created by Rina Iati, South Western School District, Hanover, PA

4. Now do this one on your own.43
8,572
- 4,300
100 – 1st guess
Subtract
4272
-3870
90 – 2nd guess
Subtract
402
- 301
7 – 3rd guess
101
2 – 4th guess
199 R 15
Sum of guesses 15
Created by Rina Iati, South Western School District, Hanover, PA