How to check algebraic long division?

  • Context: High School 
  • Thread starter Thread starter Tyrion101
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Discussion Overview

The discussion revolves around strategies for verifying the correctness of algebraic long division results. Participants explore methods to check their answers before finalizing them, particularly focusing on the relationship between division and multiplication.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty with errors in multiplication, particularly with similar-looking numbers, and seeks a method to verify answers before submission.
  • Another participant suggests that since division is the inverse of multiplication, one can check the result by multiplying the quotient by the divisor and comparing it to the original dividend.
  • A later reply acknowledges the suggestion and expresses appreciation for the clarification.

Areas of Agreement / Disagreement

Participants appear to agree on the method of checking answers through multiplication, but the initial participant's specific challenges with multiplication errors remain unaddressed in terms of broader solutions.

Contextual Notes

Some participants note the need for conscious focus when multiplying terms, indicating that attention to detail is crucial in avoiding errors.

Tyrion101
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My errors all involve multiplying numbers that look the same, for instance if there is a 2 that I'm supposed to multiply by a 2a I'll put 2 a, and not think about it till I see I got the answer wrong. Is there a way I can do something to the answer to see if it is right before I submit it?
 
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Division is just multiplication backward. Multiplication is usually much easier and less error-prone. If I understand correctly, you're asking: "If I try to compute f/g and get answer h, how do I check whether it's correct?" If that's the question, then a quick check is to compute g*h and see whether you get f.
 
Tyrion101 said:
My errors all involve multiplying numbers that look the same, for instance if there is a 2 that I'm supposed to multiply by a 2a I'll put 2 a, and not think about it till I see I got the answer wrong.

Multiplying the individual terms requires a little bit of conscious focus. One must watch what one is doing.


Is there a way I can do something to the answer to see if it is right before I submit it?

Yes. Multiply the resulting quotient by the divisor. When you simplify this multiplication, to general form, it must match the dividend.
 
Don't know why it didn't occur to me, but that makes sense. Thanks.
 

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