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 are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) 10 – 1st guess 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 – 2nd guess Subtract Since 2 is less than 12, you can stop estimating. 2 The final result is the sum of the guesses ( = 13) plus what is left over (remainder of 2 ) 13 sum of guesses

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

Let’s see if you’re right. 43 8, – 1st guess - 4,300 Subtract – 2 nd guess Subtract – 3 rd guess Subtract – 4th guess - 86 Subtract 15 Sum of guesses 199