A Division Algorithm
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
There are at least ten 12’s in 158
(10 x 12=120), but fewer than
twenty. (20 x 12 = 240)
There are more than three (3
x 12 = 36), but fewer than four
(4 x 12 = 48). Record 3 as the
next guess
Since 2 is less than 12, you can stop
estimating.
12
158
Subtract - 120
38
Subtract - 36
2
The final result is the sum of the guesses
(10 + 3 = 13) plus what is left over
(remainder of 2 )
10 – 1st guess
3 – 2nd
guess
13
sum of guesses
There are at least 100 36’s in 7,891
(100 x 36=3600). Record it as the
first guess.
36
7,891
There is at least 100 more 36’s.
Subtract - 3,600
Record 100 as the next guess
4,291
36 x 10 is 360. There are 10 more 36’s. Subtract - 3,600
Record 10 as the next guess.
There is not another 10 group in 331.
691
36 x 9 is 324. Record 9 as the 4
Subtract - 360
guess.
Since 7 is less than 36, you can
331
stop estimating.
Subtract - 324
The final result is the sum of the guesses
(100 + 100 + 10 + 9) plus what is left
7
over (remainder of 7 )
th
100 – 1st guess
100 – 2nd guess
10 – 3rd guess
9 – 4th guess
219
sum of guesses
Let’s see if
you’re right.
43
8,572
Subtract - 4,300
4272
Subtract - 3870
402
- 301
Subtract
101
Subtract
- 86
15
Sum of guesses
100 – 1st guess
90 – 2nd guess
7 – 3rd guess
2 – 4th guess
199