Here's the question you clicked on:
shivraj
4/x=-20/15 solve for x in the proportion
@shivraj , why don't you post the result you get after cross multiplication.
Here we can do it by another simple method..
You mean a method other than cross multiplication?
Let @shivraj solve first and at last I will tell the method..
Okay, so @waterineyes will probably simplify the right fraction before cross multiplying. But that's nothing new.
I will not use cross multiplication anywhere in my solution @Hero
So how will your method be "simpler"?
I can see that the fraction will be reduced to 4x = -4/3
But now you still have to cross multiply. Doing anything else will just produce more steps.
I won't i said @Hero
err, I mean the fraction will be reduced to 4/x = -4/3 typo above
Yes: \[\frac{4}{x} = \frac{-4}{3} \implies \frac{4}{x} = \frac{4}{-3} \implies x = -3\]
Oh, I see what you did. Yeah, in that case, I guess you don't need to cross multiply. Nice trick.
That is what I am trying to say..
That's why the real first step is to actually simplify whenever possible
Usually when I see a proportion, my first impulse is to cross multiply
@waterineyes : Unknowingly you are cross multiplying the terms with 1. :) Still it's a good and simpler method. Well done.
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
You are of course saying it mathematically but I am saying it logically...
What do you call that? The Denominator Equivalency Property?
Ha ha ha.. You can call that what you like..
Or perhaps the Denominator Equality Property
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