What Is a Ratio?

Date: 12/08/96 at 22:48:25
From: Mitchell Floyd
Subject: Math

I need to know what a ratio is and how to do it.  I have searched my 
whole math book. Do you think you can help me?  If so, thank you very 
much! Tell the doc I said "Hi!"

Date: 12/16/96 at 22:51:06
From: Doctor Reno
Subject: Re: Math

Hi, Mitchell!

While researching your question, I realized how confusing ratios can 
be for someone without too much experience in mathematics. Let's see 
if we can clear up the confusion!

Ratios are pairs of numbers and they are used to make comparisons. 
A ratio compares two numbers using a fraction. Ratios can be written 
three different ways:
 
(1) 2 to 3
(2) 2:3
(3) 2/3

They all mean the same thing.  Pretend I have a class of 25 students: 
10 students are boys and 15 are girls.  I can compare number of boys 
to girls using the ratio 10/15 (or 10:15; or 10 to 15). This ratio 
means the same thing as saying that for every ten boys in my class, I 
have 15 girls. You can "reduce" this fraction (remember, ratios are 
comparisons using fractions) to 2/3 by dividing both numerator and 
denominator by 5. 

Let's say some new kids move into the neighborhood and join my class. 
In order to keep the ratio of boys to girls the same, every time two 
boys join the class, three girls have to join as well. If more or less 
girls or boys than this join my class, the ratio of boys to girls in 
my class would change.

This idea of keeping the ratio the same can be important. Let's say 
I'm making brass in a factory. Brass is an mixture of copper and zinc. 
Different kinds and colors of brass result from changing the mix of 
the two metals.  One kind of brass has 7 parts of copper for every 3 
parts of zinc. This ratio is written as 7/3. Would a mix of 14 parts 
copper and 6 parts zinc make the same brass?  Well, this ratio would 
be written as 14/6. Using your knowledge of equivalent fractions, you 
can see that 7/3 = 14/6 (multiply the numerator and denominator of 7/3 
by 2 and you get 14/6).  So the brass is the same. If one day I didn't 
have enough zinc to make the ratio of copper and zinc the same as 7/3, 
I would be making a different kind of brass, and my customers might be 
very upset because the color would be differnt.

If anyone at your home bakes a lot, look at the recipes. Ratios in 
recipes are very important!  Use too much sugar or not enough eggs, 
and the goodies you cook won't be very  good! Nobody wants a chocolate 
chip cookie without enough chocolate chips!

I hope this helps you in your study of mathematics, Mitchell. If you 
have further questions, be sure to ask!


-Doctor Reno,  The Math Forum
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