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

[Julia Coggins]

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.

 

[cnh1995]

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.

 

[Julia Coggins]

Thank you, it does belong to the mathematics category, but I'm unsure how to change it

 

[cnh1995]

but I'm unsure how to change it

You can't change it once you've posted it. A mentor will fix it.

 

[Julia Coggins]

Ah I see. Once again, thank you, I suppose for some reason I struggled with an otherwise simple question.

 

[HallsofIvy]

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.