Similar triangles. How does 4/6 turn into 2h/3 ?

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Homework Help Overview

The discussion revolves around the relationship between the variables r and h, expressed as a ratio of 4/6, and how this simplifies to r = 2h/3. The context is related rates in calculus.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the simplification of the ratio 4/6 to 2/3 and question the arithmetic involved in manipulating the equation. Some express confusion about the multiplication process and its effect on the variables.

Discussion Status

Several participants have offered insights into the simplification process, with some affirming the equivalence of the fractions and others questioning the arithmetic steps. There is no explicit consensus, but the discussion is actively exploring the mathematical reasoning behind the transformation.

Contextual Notes

Participants are working under the assumption that basic arithmetic skills are understood, given the context of related rates and calculus. There is an underlying concern about the implications of any arithmetic misunderstandings in more complex calculus problems.

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Homework Statement



r/h = 4/6

This turns into: r = 2h/3

How, can someone please refresh me? I am doing a related rates problem, and I for this! :(


Homework Equations





The Attempt at a Solution

 
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Isn't 4/6 = 2/3 ? (Everything is written in basis 10).
 
nukeman said:

Homework Statement



r/h = 4/6

This turns into: r = 2h/3

How, can someone please refresh me? I am doing a related rates problem, and I for this! :(


Homework Equations





The Attempt at a Solution


r/h = 4/6 = 2/3

Now multiply both sides of this equation by h.
 
4/6 * x = 2x/3x ?

Why is just 2x/3 ?
 
The multiplication affects only the numerator. Think about it as (6/4)x5 = (6:4)x 5 = 6:4x5 = 6x5:4 = 30:4 = 7.5
 
Last edited:
If you are doing things involving "related rates" and Calculus, I think we have right to assume that you can do arithmetic! 4/6= (2*2)/(2*3)= 2/3!
 
HallsofIvy said:
If you are doing things involving "related rates" and Calculus, I think we have right to assume that you can do arithmetic! 4/6= (2*2)/(2*3)= 2/3!
And if this assumption by us is incorrect, then you are going to have a very difficult time in calculus.
 

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