The partial quotients algorithm is a method for long division that estimates the number of times the divisor goes into the dividend. It works by making a series of "at least, but less than" guesses for the quotients and subtracting the estimated results until the remainder is less than the divisor.

1. Partial Quotients A Division Algorithm Created by Rina Iati, South Western School District, Hanover, PA

2. 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 than twenty. (20 x 12 = 240) 10 – 1st guess - 120 38 Subtract There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess 3 – 2 nd guess - 36 2 13 Sum of guesses Subtract 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 ) 13 R2 Created by Rina Iati, South Western School District, Hanover, PA 12 158

3. Let’s try another one 100 – 1st guess - 3,600 4,291 Subtract 100 – 2 nd guess - 3,600 7 219 R7 Sum of guesses Subtract 219 R7 691 10 – 3 rd guess - 360 331 9 – 4th guess - 324 Created by Rina Iati, South Western School District, Hanover, PA 36 7,891

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