Partial quotients algorithm

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Author:
Christopher Danielson (502)
Objective:

Demonstrate the mechanics of the partial quotients algorithm.

(more)

Overview

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.

11 /247 — 4 months ago

How do you do that?

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Christopher Danielson (502) answered 4 months ago

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.

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evan richardson (35) — 6 months ago

...

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Samantha — 7 months ago

I totally get the videos thanks for help

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valorie — 8 months ago

how to divid 43 by 581 whith partal puotients

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Robin Mushrock (0) answered 5 months ago

13 r22

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Kilah Moore — 8 months ago

What is 135/5

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Jasmine Hobson (35) — over 2 years ago

Christopher...do you realize this video does not complete the problem?

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Christopher Danielson (502) answered over 2 years ago

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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Christopher Danielson (502) answered over 2 years ago

I do now. I'll have to fix that up! Sorry.

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SOPHIA has reviewed the tutorial and found it academically sound.
Anthony Varela (394) - about over 1 year ago

"I really enjoyed this packet because not only can the partial-quotients method be more easily understood, but you explain it in a way that reminds us what division is, which can be lost in trying to internalize a process. By this, I mean statements like "If we are trying to distribute 96 things into boxes of 4, we can make 10 boxes with 40 things, and still have 56 left." This makes a bigger connection than "how many times does 4 go into 96?" which is what we usually hear when practicing long division."