## shivraj Group Title 4/x=-20/15 solve for x in the proportion 2 years ago 2 years ago

1. Hero Group Title

Hint: Cross Mulitply

2. monokerous Group Title

cross multiply

3. shivraj Group Title

ok

4. Hero Group Title

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

5. waterineyes Group Title

Here we can do it by another simple method..

6. Hero Group Title

You mean a method other than cross multiplication?

7. waterineyes Group Title

Yes..

8. waterineyes Group Title

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

9. Hero Group Title

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

10. waterineyes Group Title

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

11. Hero Group Title

So how will your method be "simpler"?

12. waterineyes Group Title

Can i show you??

13. Hero Group Title

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

14. Hero Group Title

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

15. waterineyes Group Title

I won't i said @Hero

16. Hero Group Title

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

17. waterineyes Group Title

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

18. Hero Group Title

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

19. waterineyes Group Title

That is what I am trying to say..

20. Hero Group Title

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

21. waterineyes Group Title

Yes...

22. Hero Group Title

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

23. waterineyes Group Title

Ha ha ha..

24. Champs Group Title

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

25. waterineyes Group Title

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 Group Title

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

27. Hero Group Title

What do you call that? The Denominator Equivalency Property?

28. waterineyes Group Title

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

29. Hero Group Title

Or perhaps the Denominator Equality Property

30. monokerous Group Title

I like it. :)

31. Compassionate Group Title

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