A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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

  • This Question is Closed
  1. AaronAndyson
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    < means less-than > means greater-than

  2. hybrik
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1437751183877:dw|

  4. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is that a rule?

  6. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay whats the nexxt step

  8. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  10. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oops.. both*

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1437753458344:dw|

  14. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  16. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is right for you?

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea

  19. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  21. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea...

  23. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok...

  25. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so, what can you conclude?

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  28. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so..... lost

  29. Michele_Laino
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  30. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.