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

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The discussion centers on the conversion of the ratio r/h = 4/6 into r = 2h/3. Participants confirm that simplifying 4/6 results in 2/3, and multiplying both sides by h leads to r = (2/3)h. There is an emphasis on the importance of understanding basic arithmetic in relation to calculus problems, particularly in related rates scenarios. The conversation highlights that proper manipulation of ratios is crucial for solving these types of mathematical problems. Mastery of these fundamental concepts is deemed essential for success in calculus.
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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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