A proportion is simply 2 fractions that are equal to each other. 

Example: 

If the two fractions are equal, then the cross products are equal… 

2 x 6 = 3 x 4. 

We use this fact to solve word problems when we know three of the four terms in the proportion. 

Example: 

From      we know the cross products    3x and 5 times 9 must be equal 

Thus, 3x = 45.  solve this equation for x by dividing both sides by 3 tells us x must be 15.

So, x = 15.

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In a word problem you have to write your own proportion.  What you need to remember is there are several proportions that might be correct for a given problem.  You just need to be consistent when you set up the fractions.

Example 1:  A car uses 5 gallons of gas on a trip of 160 miles.  At the same mileage rate, how much gas will a 384-mile trip require?

Example 2:  Sveta earns $6500 commission in 20 weeks in her new sales position.  At that rate, how much will she earn in 1 year (52 weeks)?

Example 3:

A copy machine makes 224 copies in 5 minutes and 20 seconds. How many copies does it make per minute?

 Solution:

I’m going to put copies on top and time on the bottom.  There is a little problem with the time in this one.  I can’t use minutes AND seconds.  I have to use one or the other.  If I convert 5 minutes and 20 seconds to minutes that would be 5 and minutes.  Changing that to an improper fraction gives me .  Thus my fraction comparing copies to minutes would be:

This is pretty messy, but fortunately I can avoid the complex fraction if I convert the time to seconds instead of minutes.  5 minutes is 5 times 60 = 300 seconds plus the other 20 seconds gives me a total of 320 seconds. 

The other fraction in the proportion would be how many copies (let this be x) does it make per 1 minute (use 60 seconds) or

. 

The proportion is then 

Now use the cross products to get

320x = 224(60) 

320x = 13440 

x = 42 copies