Prove that A:B is greater than C:D?

In summary, the conversation discusses how to prove that the ratio A:B is greater than C:D based on given data and equations. It is suggested that this topic should be posted in a mathematics forum for further discussion.
  • #1
Julia Coggins
17
0
From "Road to Reality" chapter 3 part two. If three ratios are known: M:N, A:B, C:D. A:B is greater than C:D if: A added to itself M times exceeds B added to itself N times and D added to itself N times exceeds C added to itself M times. Show that the ratio A:B is greater than C:D.
 
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  • #2
I believe this should be posted in maths forum.
Based on the data,
A(M+1)>B(N+1) and D(N+1)>C(M+1)
So,
A/B>(N+1)/(M+1)...(1)
and
C/D<(N+1)/(M+1)...(2)
1 and 2 clearly prove A:B>C:D.
 
  • #3
Thank you, it does belong to the mathematics category, but I'm unsure how to change it
 
  • #4
Julia Coggins said:
but I'm unsure how to change it
You can't change it once you've posted it. A mentor will fix it.
 
  • #5
Ah I see. Once again, thank you, I suppose for some reason I struggled with an otherwise simple question.
 
  • #6
cnh1995 said:
I believe this should be posted in maths forum.
Based on the data,
A(M+1)>B(N+1) and D(N+1)>C(M+1)
So,
A/B>(N+1)/(M+1)...(1)
and
C/D<(N+1)/(M+1)...(2)
1 and 2 clearly prove A:B>C:D.
This is assuming all the numbers involved are positive.
 
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Likes member 587159 and cnh1995

FAQ: Prove that A:B is greater than C:D?

What does "A:B is greater than C:D" mean?

When comparing two ratios, A:B and C:D, the statement "A:B is greater than C:D" means that the value of A:B is larger than the value of C:D. In other words, the first ratio has a greater proportion than the second ratio.

How do you prove that A:B is greater than C:D?

To prove that A:B is greater than C:D, we can use cross-multiplication. This involves multiplying the numerator of the first ratio by the denominator of the second ratio and comparing it to the product of the denominator of the first ratio and the numerator of the second ratio. If the first product is greater than the second product, then A:B is greater than C:D.

Can A, B, C, and D be any numbers?

Yes, A, B, C, and D can be any numbers as long as they are not equal to zero. In ratio comparisons, the actual values of the numbers do not matter, only their relative proportions matter.

How can this ratio comparison be useful in scientific research?

Ratio comparisons, such as A:B and C:D, can be useful in scientific research for several reasons. They can help to determine the proportion of different substances in a mixture, analyze data in experiments, and compare the effectiveness of different treatments or interventions. They can also be used to make predictions and identify trends in data.

Are there any limitations to using ratio comparisons?

While ratio comparisons can be useful, they have limitations in certain situations. For example, they may not accurately represent the true proportions if the numbers being compared are very small or very large. Additionally, ratio comparisons may not account for other factors that could influence the results, such as sample size or variability. It is important to consider these limitations when using ratio comparisons in scientific research.

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