January 29, 2009

Making the fractions in a proportion

"How do you know how to make the fractions in a proportion?
When making them, how do you know where each number goes making the fraction, like which ones go on top of the fraction?"

Well, actually you can choose which quantity will go on top; the proportion WILL work either way!

But, sometimes people are used to always putting certain quantity on top and certain on the bottom. For example, if the question is about speed and the unit is "miles per hour", that tells you that miles go on top, and hours on bottom, because "per" means division (the fraction line).

However, you could still solve the proportion by putting hours in the numerator of the fractions and miles in the denominator, and the calculation will turn out alright.

Or, if the question is about "dollars per pound", then dollars go to the numerator and pounds in the denominator.

Let's look at this problem for example:

A car drives on constant speed. It can go 80 miles in 90 minutes. How long will it take for it to travel 100 miles?

You can make both fractions to be

miles
-----------
minutes

OR

minutes
------------
miles


Let's try the first way:

80 mi 100 mi
-------- = ---------
90 min x

To solve, cross multiply and you get 80x = 100 * 90, and then x = 900/8 = 112.5 minutes.

The other way it will be

90 min x
-------- = --------
80 mi 100 mi

To solve, cross multiply and you get 80x = 90 * 100

You see, the final equation ends up being the same, no matter which
quantities were on top of the fractions.

HOWEVER, one way is wrong: that is if you but "miles" on top in one
fraction, and "minutes" on top in the other... then you'll get it wrong:

90 min 100 mi
-------- = -------
80 mi x min

=> 90x = 100* 80 (WRONG)
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