Partial Quotients A Division Algorithm Created by Rina
Partial Quotients A Division Algorithm Created by Rina Iati, South Western School. Created District, Hanover, PA Western School by Rina Iati, South District
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 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 12 158 Subtract - 120 38 Subtract - 36 2 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, District PA 10 – 1 st guess 3 – 2 nd guess 13 Sum of guesses
Let’s try another one 36 7, 891 Subtract - 3, 600 4, 291 Subtract - 3, 600 691 - 360 331 - 324 7 Created by Rina Iati, South Western School District, Hanover, PA 100 – 1 st guess 100 – 2 nd guess 10 – 3 rd guess 9 – 4 th guess 219 R 7 Sum of guesses
Now do this one on your own. 43 Subtract 8, 572 - 4, 300 4272 -3870 402 - 301 101 - 86 15 Created by Rina Iati, South Western School District, Hanover, District. PA 100 – 1 st guess 90 – 2 nd guess 7 – 3 rd guess 2 – 4 th guess 199 R 15 Sum of guesses
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