# Partial Quotients A 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 h by Adela Sanders

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```									                         Partial Quotients
A 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.

There are at least ten 12’s in
158 (10 x 12=120), but fewer                            12  158
than twenty. (20 x 12 = 240)                                       10 – 1st guess
Subtract - 120
There are more than three                                    38
(3 x 12 = 36), but fewer than                                       3 – 2nd guess
four (4 x 12 = 48). Record 3 as                   Subtract - 36
the next guess

2      13
Since 2 is less than 12, you can stop
estimating. The final result is the sum
Sum of guesses
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   7,891
Subtract - 3,600     100 – 1st guess
4,291
Subtract - 3,600    100 – 2nd guess
691
- 360    10 – 3rd guess
331
- 324    9 – 4th guess

7        219 R7
Created by Rina Iati, South Western School District, Hanover, PA         Sum of guesses
Now do this one on your
own.
43           8,572
Subtract          - 4,300    100 – 1st guess
4272
Subtract           -3870    90 – 2nd guess
402
- 301    7 – 3rd guess
101
- 86      2 – 4th guess
199 R 15
15
Sum of guesses
Created by Rina Iati, South Western School District, Hanover, PA

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