4=3 True or False? Check it out and guess where's the mistake

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Discussion Overview

The discussion revolves around a mathematical claim that suggests the equation 4=3 can be derived from manipulating the equation a+b=c. Participants explore the reasoning behind this claim, focusing on the error involved in dividing by zero, and share personal anecdotes related to similar mathematical tricks.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a manipulation of the equation a+b=c leading to the conclusion that 4=3, indicating a mistake will be revealed later.
  • Another participant identifies that the mistake arises from dividing by zero, as a+b-c equals zero when a+b=c.
  • Several participants agree that dividing by zero is not permissible and emphasize the importance of this principle in algebra.
  • A participant shares a personal experience of learning about this trick in school, referencing a humorous "11th Commandment" regarding division by zero.
  • Another participant discusses a related example involving the equation x^2=4x, highlighting that many students incorrectly divide by x without considering the implications of x being zero.

Areas of Agreement / Disagreement

Participants generally agree on the error of dividing by zero as the critical mistake in the presented argument. However, there is no consensus on the broader implications of the example involving x^2=4x, as one participant suggests a partial correctness in the students' reasoning.

Contextual Notes

The discussion highlights the importance of understanding the conditions under which division is valid, particularly in the context of algebraic manipulation. There are unresolved nuances regarding the implications of dividing by variables in different contexts.

Who May Find This Useful

This discussion may be of interest to students learning algebra, educators looking for examples of common misconceptions, and anyone interested in mathematical reasoning and error analysis.

kthouz
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Let say that a+b=c
this can be writtem as
4a-3a+4b-3b=4c-3c
by arranging
4a+4b-4c=3a+3b-3c
taking out the constants
4*(a+b-c)=3*(a+b-c)
So 4=3



The mistake is that ... I'll post it soon. i read this from a notebook of my little brother and i firstly agreed to it but by the time i found out why not! Test your knowledge too.
 
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You divide by zero in the last step.
 
Last edited:
what he said ^
 
kthouz said:
4*(a+b-c)=3*(a+b-c)
So 4=3

You can't divide by a+b-c since a+b=c (i.e. a+b-c=0)...
 
Cool! you got it!
the trick was to know that dividing by zero is impossible.
 
Last edited:
I remember my dad showed it to me when I was in 5th or 6t grade. It stumped me, and I showed it to my Math teacher at school who explained the 11th Commandment to me: "You shall never divide by Zero"
 
kthouz said:
Let say that a+b=c
this can be writtem as
4a-3a+4b-3b=4c-3c
by arranging
4a+4b-4c=3a+3b-3c
taking out the constants
4*(a+b-c)=3*(a+b-c)
So 4=3



The mistake is that ... I'll post it soon. i read this from a notebook of my little brother and i firstly agreed to it but by the time i found out why not! Test your knowledge too.

This is exactly why you never ever divide by a variable. It is horrendous algebra.


x^2=4x


What is x?

75% of students will divide by x and say x=4.
 
Well they're half-right.
 
gravenewworld said:
This is exactly why you never ever divide by a variable. It is horrendous algebra.


x^2=4x


What is x?

75% of students will divide by x and say x=4.

Then those 75% should always remember that you can only divide by something only if it is not equal to zero!
 

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