Use Sophia to knock out your gen-ed requirements quickly and affordably. Learn more

Partial quotients algorithm

Author: Christopher Danielson


The partial quotients algorithm is an algorithm for dividing one whole number by another. Some important features of the algorithm are these:

  • We pay attention to the values of the numbers throughout the process (not just the values of the digits),
  • Each step of the algorithm gets us closer to the quotient, but does not have to be perfect, and
  • We have to make a choice at each step; the more we do the algorithm, the better choices we can make.

In this packet, I will solve three problems: 

  1. A 2-digit divided by 1-digit problem,
  2. A 4-digit divided by 2-digit problem, and
  3. A problem with a remainder.

One-digit divisor

This video demonstrates how to use the partial quotients algorithm with a one-digit divisor.

Two-digit divisor

This video demonstrates a harder problem-division by a two-digit divisor. In this case, we have fewer memorized facts to rely on.

Division with a remainder

This video demonstrates how to handle a remainder in the partial quotients algorithm.

What next?

After you learn the basic mechanics of the partial quotients algorithm, you can practice it to get more efficient. This will mean coming up with strategies for finding partial quotients beyond 2, 10 and 100 (for example, if you know 100 groups of A, then 50 groups of A will be half of that total, and 25 groups of A will be half again). In contrast to the standard algorithm, it seems plausible that practice with the partial quotients algorithm could improve your mental math skills.

Then you can learn to use the partal quotients algorithm to find decimal quotients (instead of using remainders or fractions). This will be the subject of another packet.

Finally, you can use the algorithm to find quotients of polynomials. Again, this will be the subject of another Sophia packet.