## shivraj 3 years ago 4/x=-20/15 solve for x in the proportion

1. Hero

Hint: Cross Mulitply

2. monokerous

cross multiply

3. shivraj

ok

4. Hero

@shivraj , why don't you post the result you get after cross multiplication.

5. waterineyes

Here we can do it by another simple method..

6. Hero

You mean a method other than cross multiplication?

7. waterineyes

Yes..

8. waterineyes

Let @shivraj solve first and at last I will tell the method..

9. Hero

Okay, so @waterineyes will probably simplify the right fraction before cross multiplying. But that's nothing new.

10. waterineyes

I will not use cross multiplication anywhere in my solution @Hero

11. Hero

So how will your method be "simpler"?

12. waterineyes

Can i show you??

13. Hero

I can see that the fraction will be reduced to 4x = -4/3

14. Hero

But now you still have to cross multiply. Doing anything else will just produce more steps.

15. waterineyes

I won't i said @Hero

16. Hero

err, I mean the fraction will be reduced to 4/x = -4/3 typo above

17. waterineyes

Yes: $\frac{4}{x} = \frac{-4}{3} \implies \frac{4}{x} = \frac{4}{-3} \implies x = -3$

18. Hero

Oh, I see what you did. Yeah, in that case, I guess you don't need to cross multiply. Nice trick.

19. waterineyes

That is what I am trying to say..

20. Hero

That's why the real first step is to actually simplify whenever possible

21. waterineyes

Yes...

22. Hero

Usually when I see a proportion, my first impulse is to cross multiply

23. waterineyes

Ha ha ha..

24. Champs

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

25. waterineyes

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

You are of course saying it mathematically but I am saying it logically...

27. Hero

What do you call that? The Denominator Equivalency Property?

28. waterineyes

Ha ha ha.. You can call that what you like..

29. Hero

Or perhaps the Denominator Equality Property

30. monokerous

I like it. :)

31. Compassionate

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