## anonymous one year ago a,b,c, and d are positive integers such that a/b < c/d Which one is greater? a. a+c/b+d b. c/d

1. AaronAndyson

< means less-than > means greater-than

2. hybrik

Lets say A and B is 1 and C and D is >1

3. anonymous

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4. Michele_Laino

we have the subsequent implication: $\frac{a}{b} < \frac{c}{d} \Rightarrow \frac{a}{c} < \frac{b}{d}$

5. anonymous

Is that a rule?

6. Michele_Laino

no, I have multiplied your original inequality by b/c: $\Large \frac{a}{b} \times \frac{b}{c} < \frac{c}{d} \times \frac{b}{c} \Rightarrow \frac{a}{c} < \frac{b}{d}$

7. anonymous

okay whats the nexxt step

8. Michele_Laino

we can write the subsequent steps: $\Large \frac{{\frac{{a + c}}{{b + d}}}}{{\frac{c}{d}}} = \frac{{a + c}}{{b + d}} \times \frac{d}{c} = \frac{{\frac{{a + c}}{c}}}{{\frac{{b + d}}{d}}} = \frac{{\frac{a}{c} + 1}}{{\frac{b}{d} + 1}} < 1$

9. anonymous

this..... is....... super........ confusing can you use that actual numbers please....

10. Michele_Laino

since we have: $\Large \frac{a}{c} < \frac{b}{d}$ then we can write: $\Large \frac{a}{c} + 1 < \frac{b}{d} + 1$ and dividing bot sides by (b/d)+1, we get: $\Large \frac{{\frac{a}{c} + 1}}{{\frac{b}{d} + 1}} < 1$ am I right?

11. Michele_Laino

oops.. both*

12. anonymous

....i have absolutely no idea what all this is i dont understand why what i did up there is wrong...

13. anonymous

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14. Michele_Laino

please note that if I use numbers I'm not giving you a proof, since I'm giving you a check only

15. anonymous

ok

16. Michele_Laino

so the subsequent step: $\Large \frac{a}{b} < \frac{c}{d} \Rightarrow \frac{{\frac{a}{c} + 1}}{{\frac{b}{d} + 1}} < 1$

17. Michele_Laino

is right for you?

18. anonymous

yea

19. Michele_Laino

ok then from this inequality: $\Large \frac{{\frac{{a + c}}{{b + d}}}}{{\frac{c}{d}}} = \frac{{a + c}}{{b + d}} \times \frac{d}{c} = \frac{{\frac{{a + c}}{c}}}{{\frac{{b + d}}{d}}} = \frac{{\frac{a}{c} + 1}}{{\frac{b}{d} + 1}} < 1$

20. Michele_Laino

we can write this one: $\Large \frac{{\frac{{a + c}}{{b + d}}}}{{\frac{c}{d}}} = < 1$

21. Michele_Laino

oops.. $\Large \frac{{\frac{{a + c}}{{b + d}}}}{{\frac{c}{d}}} < 1$

22. anonymous

yea...

23. Michele_Laino

now I multiply both sides by c/d, so I can write: $\Large \frac{{a + c}}{{b + d}} < \frac{c}{d}$

24. anonymous

ok...

25. Michele_Laino

so, what can you conclude?

26. anonymous

I can conclude that if there is a question like this on my test, I'M DEFINITELY FAILING because I don't understand any of this. This was way too complicated.

27. Michele_Laino

please study all my steps carefully, and you will become an expert on this type of question

28. anonymous

so..... lost

29. Michele_Laino

I'm sorry, nevertheless my procedure above, is the unique way to solve questions like yours