Working with Multi-Part Ratios

Date: 05/21/2007 at 20:38:06
From: Joshua
Subject: Ratios with three parts

I've been studying for the ACT test and can't seem to remember how to 
do ratios with three parts like 2:3:6.  I fully understand normal 
ratios like 1:4.  No need to cover the basics of ratios.  

In the three part ones I find it hard to understand how each of the
numbers relates to the other two, though.  Using my earlier example,
how does the 2 relate to the 3 and 6?  The 3 to the 2 and 6?  

If you could please give me a few examples of their uses along with
explanations of the problems I would be much obliged!

Respectfully, 

- Joshua

Date: 05/29/2007 at 22:29:16
From: Doctor Peterson
Subject: Re: ratios with three parts

Hi, Joshua.

The usual situation with this sort of ratio would involve dividing
something (say, an inheritance) among three people in the ratio 2:3:6.
Imagine taking the whole and dividing it up this way:

  +---+---+---+---+---+---+---+---+---+---+---+
  |   2   |     3     |           6           |
  +---+---+---+---+---+---+---+---+---+---+---+

That is, person A gets 2 parts, B gets 3, and C gets 6 (all the parts
being equal).

How many parts are there in all?  2 + 3 + 6 = 11.

What fraction of the whole does A get?  He gets 2 of the 11 parts, or
2/11.

What amount of a $99,000 inheritance does A get?  2/11 times 99,000 =
$18,000.

You can do the same thing with any number of parts, e.g. 1:2:5:3:6:7.
Just add the parts to get the total number of parts, and use that as
the denominator to find the fraction corresponding to each.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 05/31/2007 at 13:22:02
From: Joshua
Subject: Thank you (Ratios with three parts)

Dear Doctor Peterson,

Thank you for your speedy reply to my ratio question!  I understood
your example and explanation without any trouble.                      
                 
Gratefully,

- Joshua