Partial Quotient 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

Partial Quotients 13 R2 158 - 120 38 - 36 2 12 10 – 1st guess 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 There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess 38 - 36 3 – 2nd guess Subtract Since 2 is less than 12, you can stop estimating. 2 The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 ) 13 sum of guesses

Here is another one... 219 R7 7,891 - 3,600 4,291 - 3,600 691 - 360 There are at least 100 36’s in 7,891 (100 x 36=3600). Record it as the first guess. 36 7,891 - 3,600 100 – 1st guess There is at least 100 more 36’s. Record 100 as the next guess Subtract 4,291 - 3,600 100 – 2nd guess 36 x 10 is 360. There are 10 more 36’s. Record 10 as the next guess. Subtract 691 There is not another 10 group in 331. 36 x 9 is 324. Record 9 as the 4th guess. - 360 10 – 3rd guess Subtract 331 Since 7 is less than 36, you can stop estimating. - 324 9 – 4th guess Subtract The final result is the sum of the guesses (100 + 100 + 10 + 9) plus what is left over (remainder of 7 ) 7 219 sum of guesses

Try this one on your own! 199 R 15 8,572 - 4,300 4272 - 3870 43 8,572 Let’s see if you’re right. - 4,300 100 – 1st guess Subtract 4272 - 3870 90 – 2nd guess Subtract Way to go! 402 - 301 7 – 3rd guess Subtract 101 - 86 2 – 4th guess Subtract 15 Sum of guesses 199