A Division Algorithm Partial Quotients The Partial Quotients

A Division Algorithm

Partial Quotients § The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. Students might begin with multiples of 10 – they’re easiest. This method builds towards traditional long division. It removes difficulties and errors associated with simple structure mistakes of long division. Based on EM resources

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 Since 2 is less than 12, you can stop estimating. 12 158 Subtract - 120 38 Subtract - 36 2 The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 ) 10 – 1 st guess 3 – 2 nd guess 13 sum of guesses

There at least 100 36’s in 7, 891 (100 x 36=3600). Record it as the first guess. 36 7, 891 There is at least 100 more 36’s. Subtract - 3, 600 Record 100 as the next guess 4, 291 36 x 10 is 360. There are 10 more 36’s. Subtract - 3, 600 Record 10 as the next guess. There is not another 10 group in 331. 691 36 x 9 is 324. Record 9 as the 4 guess. Subtract - 360 Since 7 is less than 36, you can 331 stop estimating. Subtract - 324 The final result is the sum of the guesses (100 + 10 + 9) plus what is left over 7 (remainder of 7 ) th 100 – 1 st guess 100 – 2 nd guess 10 – 3 rd guess 9 – 4 th guess 219 sum of guesses

Let’s see if you’re right. 43 8, 572 Subtract - 4, 300 4272 Subtract - 3870 402 - 301 Subtract 101 Subtract - 86 15 Sum of guesses 100 – 1 st guess 90 – 2 nd guess 7 – 3 rd guess 2 – 4 th guess 199