The partial quotients algorithm is an algorithm for dividing one whole number by another. Some important features of the algorithm are these:
In this packet, I will solve three problems:
This video demonstrates how to use the partial quotients algorithm with a one-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.
This video demonstrates how to handle a remainder in the partial quotients algorithm.
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.
It is helpful to use Partial Quotients when dividing because it breaks up the parts into manageable parts so that it can be easier to divide rather than long division.
You are asking how to 11÷247, right? This is an example of a larger class of problems in which the divisor (247) is greater than the dividend (11). The result will be a quotient less than 1 (i.e. a decimal).
I'll try to get a video up for this sometime soon.
In the meantime, the process is essentially the same. We have to ask, "What do I multiply 247 by to get 11?"
It's less than 0.1, since 0.1*247=24.7.
0.01 * 247 would be 2.47, so that's the right order of magnitude. I know that 2.47 is a bit less than 2.5 and that 2.5*4 is 10. So I would make my first guess 0.04.
I'll get a remainder, and go from there.
The principle is the same as for whole numbers, and it takes practice. But the algorithm continues to work, even to the right of the decimal point.
Christopher...do you realize this video does not complete the problem?
It has been fixed. Thanks for noticing! The document camera I was using was misbehaving and then I uploaded the wrong one. Glad I didn't swear at the end there.
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