Question

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

Answer 1

Hint: Cross Mulitply

Answer 2

cross multiply

Answer 3

ok

Answer 4

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

Answer 5

Here we can do it by another simple method..

Answer 6

You mean a method other than cross multiplication?

Answer 7

Yes..

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

So how will your method be "simpler"?

Answer 12

Can i show you??

Answer 13

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

Answer 14

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

Answer 15

I won't i said @Hero

Answer 16

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

Answer 17

Yes:

\[\frac{4}{x} = \frac{-4}{3} \implies \frac{4}{x} = \frac{4}{-3} \implies x = -3\]

Answer 18

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

Answer 19

That is what I am trying to say..

Answer 20

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

Answer 21

Yes...

Answer 22

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

Answer 23

Ha ha ha..

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

What do you call that? The Denominator Equivalency Property?

Answer 28

Ha ha ha..

You can call that what you like..

Answer 29

Or perhaps the Denominator Equality Property

Answer 30

I like it. :)

Answer 31

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