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Partial QuotientsA Division Algorithm
Created by Rina Iati, South Western School District, Hanover, PA
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.
12 158There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240)
10 – 1st guess
- 12038
Subtract
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
2 13 Sum of guesses
Subtract
Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 )Created by Rina Iati, South Western School District, Hanover, PA
Let’s try another one
36 7,891100 – 1st guess
- 3,6004,291
Subtract
100 – 2nd guess
- 3,600
7 219 R7 Sum of guesses
Subtract
69110 – 3rd guess
- 360 331
9 – 4th guess
- 324
Created by Rina Iati, South Western School District, Hanover, PA
Now do this one on your own.
43 8,572100 – 1st guess
- 4,3004272
Subtract
90 – 2nd guess
-3870
15199 R 15
Sum of guesses
Subtract
4027 – 3rd guess- 301
1012 – 4th guess
- 86
Created by Rina Iati, South Western School District, Hanover, PA