Partial Quotients

1
Partial Quotients

• A Division Algorithm

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The Partial Quotients Algorithm uses a series of
at least, but less than estimates of how many
bs in a. You might begin with multiples of 10
theyre easiest.
13 R2
There are at least ten 12s in 158 (10 x
12120), but fewer than twenty. (20 x 12 240)
10 1st guess
- 120
Subtract
38
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
- 36
Subtract
2
13 Sum of guesses
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 )
3
Lets try another one
219 R7
- 3,600
100 1st guess
Subtract
4,291
- 3,600
100 2nd guess
Subtract
691
10 3rd guess
- 360
331
- 324
9 4th guess
7
219 R7 Sum of guesses
4
Now do this one on your own.
199 R 15
- 4,300
100 1st guess
Subtract
4272
-3870
90 2nd guess
Subtract
402
7 3rd guess
- 301
101
- 86
2 4th guess
199 R 15 Sum of guesses
15