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. 13 R2 There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) 12 158 - 120 10 – 1st guess Subtract 38 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 Subtract 2 13 Sum of guesses 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 219 R7 7,891 - 3,600 4,291 - 3,600 691 - 360 331 100 – 1st guess Subtract 4,291 - 3,600 100 – 2nd guess Subtract 691 - 360 10 – 3rd guess 331 - 324 9 – 4th guess 7 219 R7 Sum of guesses Created by Rina Iati, South Western School District, Hanover, PA

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