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Partial quotients algorithm

Partial quotients algorithm

 
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Objective:

Demonstrate the mechanics of the partial quotients algorithm.

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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.

Questions and Answers

  • Answer 1
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    Sheila Stevens 11 months ago

    Why is it helpful to use partial quotients when dividing?

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    •  
      Judy Elkashif answered 8 months ago

      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.

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  • Answers 0
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    Shannon Bobbly 12 months ago

    Thank you

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  • Answer 1
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    Shannon Bobbly 12 months ago

    We'll what is partial-quotients algorithm

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    •  
      Dick Penus answered 7 days ago

      What you saw up there *******

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  • Answers 0
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    b g 12 months ago

    237=70+70+70+21+6

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  • 11 /247
    Answers 2
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    11 /247 — almost 2 years ago

    How do you do that?

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    •  
      Dick Penus answered 7 days ago

      I have a big penuse

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    •  
      Author
      Christopher Danielson answered almost 2 years 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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  • Answers 0
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    evan richardson almost 2 years ago

    ...

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  • Samantha
    Answers 0
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    Samantha — almost 2 years ago

    I totally get the videos thanks for help

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  • valorie
    Answer 1
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    valorie — about 2 years ago

    how to divid 43 by 581 whith partal puotients

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    •  
      Robin Mushrock answered almost 2 years ago

      13 r22

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  • Kilah Moore
    Answers 0
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    Kilah Moore — about 2 years ago

    What is 135/5

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  • Answers 4
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    Jasmine Hobson almost 4 years ago

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

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    •  
      Dick Penus answered 7 days ago

      I want to stick my penous up your butt Jasmine!

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    •  
      Dick Penus answered 7 days ago

      I want to **** with you!

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    •  
      Author
      Christopher Danielson answered almost 4 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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    •  
      Author
      Christopher Danielson answered almost 4 years ago

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

      Report
Academic Reviews
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