Figuring Ratios

Date: 08/07/97 at 21:16:01
From: Licia
Subject: Ratios

How do you figure the ratio of something?

I learned how in 6th grade, but the information was never used and so 
I forgot. I really don't know if Pre-Algebra uses ratios but I would 
just feel better if I knew. Can you please help me? 

Licia

Date: 08/08/97 at 08:36:29
From: Doctor Jerry
Subject: Re: Ratios

The word ratio means different things to different people. I suspect 
that different mathematics texts have slightly different meanings 
attached to the word "ratio."

A ratio is usually a quotient of two numbers, like 2/3. If you have a 
classroom with 12 girls and 18 boys, then the ratio of girls to boys 
is 12/18 = 2/3.  The ratio of boys to girls is 18/12 = 3/2.  

If you go into another classroom and someone tells you that the ratio 
of girls to boys is 3/7 and that there are 21 boys, you can figure out 
the number of girls.  The ratio is g/21 and we know that this is 3/7.  
So,

   g/21 = 3/7.
      g = 9

People say "the odds are 5:3 that a certain horse will win."  This 
terminology is related to ratios.  In particular, 5:3 is associated 
with the ratio 5/(5+3) = 5/8.  On average, the horse will win 5 out 
of every 8 races. 

When you calculate a ratio, the two things must have the same units.  
If you have a rectangular field that is 240 feet on one side and 
20 yards on the other, it is a mistake to take the ratio of 240/20 in 
an attempt to compare the two sides.  

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/