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shivraj

  • 2 years ago

4/x=-20/15 solve for x in the proportion

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  1. Hero
    • 2 years ago
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    Hint: Cross Mulitply

  2. monokerous
    • 2 years ago
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    cross multiply

  3. shivraj
    • 2 years ago
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    ok

  4. Hero
    • 2 years ago
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    @shivraj , why don't you post the result you get after cross multiplication.

  5. waterineyes
    • 2 years ago
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    Here we can do it by another simple method..

  6. Hero
    • 2 years ago
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    You mean a method other than cross multiplication?

  7. waterineyes
    • 2 years ago
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    Yes..

  8. waterineyes
    • 2 years ago
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    Let @shivraj solve first and at last I will tell the method..

  9. Hero
    • 2 years ago
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    Okay, so @waterineyes will probably simplify the right fraction before cross multiplying. But that's nothing new.

  10. waterineyes
    • 2 years ago
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    I will not use cross multiplication anywhere in my solution @Hero

  11. Hero
    • 2 years ago
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    So how will your method be "simpler"?

  12. waterineyes
    • 2 years ago
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    Can i show you??

  13. Hero
    • 2 years ago
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    I can see that the fraction will be reduced to 4x = -4/3

  14. Hero
    • 2 years ago
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    But now you still have to cross multiply. Doing anything else will just produce more steps.

  15. waterineyes
    • 2 years ago
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    I won't i said @Hero

  16. Hero
    • 2 years ago
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    err, I mean the fraction will be reduced to 4/x = -4/3 typo above

  17. waterineyes
    • 2 years ago
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    Yes: \[\frac{4}{x} = \frac{-4}{3} \implies \frac{4}{x} = \frac{4}{-3} \implies x = -3\]

  18. Hero
    • 2 years ago
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    Oh, I see what you did. Yeah, in that case, I guess you don't need to cross multiply. Nice trick.

  19. waterineyes
    • 2 years ago
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    That is what I am trying to say..

  20. Hero
    • 2 years ago
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    That's why the real first step is to actually simplify whenever possible

  21. waterineyes
    • 2 years ago
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    Yes...

  22. Hero
    • 2 years ago
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    Usually when I see a proportion, my first impulse is to cross multiply

  23. waterineyes
    • 2 years ago
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    Ha ha ha..

  24. Champs
    • 2 years ago
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    @waterineyes : Unknowingly you are cross multiplying the terms with 1. :) Still it's a good and simpler method. Well done.

  25. waterineyes
    • 2 years ago
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    See the way to look this problem is : If; \[\frac{x}{y} = \frac{x}{z}\] then y must be equal to z that is why they become equal.. That is the trick here.. @Champs

  26. waterineyes
    • 2 years ago
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    You are of course saying it mathematically but I am saying it logically...

  27. Hero
    • 2 years ago
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    What do you call that? The Denominator Equivalency Property?

  28. waterineyes
    • 2 years ago
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    Ha ha ha.. You can call that what you like..

  29. Hero
    • 2 years ago
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    Or perhaps the Denominator Equality Property

  30. monokerous
    • 2 years ago
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    I like it. :)

  31. Compassionate
    • 2 years ago
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    We see in this Problem that when a single fraction is equal to a single fraction, then the equation can be cleared by "cross-multiplying." If a c ---- = ---- b d , then ad = bc. -------------------------------------------------------- PROBLEM BELOW -------------------------------------------------------- x − 3 x − 5 ------ = ----- <=== SOLVE 3 2 Here is the cleared equation and its solution: 2(x − 3) = 3(x − 5) 2x − 6 = 3x − 15 2x − 3x = − 15 + 6 −x = −9 x = 9

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