The partial quotients algorithm uses a series of estimates to divide one number by another. It works by taking multiples of the divisor and subtracting until the remainder is less than the divisor. The estimates are then summed to give the quotient, with any remaining remainder. For example, dividing 158 by 12 gives estimates of 10 and 3, for a sum of 13 as the quotient and a remainder of 2.

1. Partial Quotients A Division Algorithm

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 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 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 43 8,572