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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