Groups and Units: Multiply or Divide?

Date: 04/15/2003 at 22:23:01
From: Sally 
Subject: Customary System

Doctor Math, I read one of your explanations about changing feet to 
yards, but I'm not very good at math, and half of my assignment is 
changing units to other units. I was wondering if you knew a way to 
explain it to me that is a little less confusing? 

Is it okay if i give you an example? Let's take 
38 inches = ______ ft ?

We have to do problems like 2 1/3 c = ______ fl oz, and I'm confused 
about whether to multiply or divide.

Date: 04/15/2003 at 23:34:01
From: Doctor Peterson
Subject: Re: Customary System

Hi, Sally.

Let's try this:

There are 12 inches in a foot, so every 12 inches make one foot. 
Picture your 38 inches as 38 objects, which we want to group in 12's:

    ************ ************ ************ **

How do you find how many groups of 12 you can get out of 38 objects? 
You DIVIDE 38 by 12, and you get 3 with a remainder of 2. That is, 38 
is 3 groups of 12, with 2 left over.

So our 38 inches is 3 groups of 12 inches (which we call feet), and 2 
extra inches left over. And that's our answer:

  38 inches = 3 feet 2 inches

The same sort of thing will work for cups and fluid ounces. Each cup 
is a group of 8 ounces. So 2 1/2 cups is 2 1/2 groups of 8 ounces:

    ******** ******** ****

The total number of ounces is 8 TIMES the number of cups; 8 times 2 
1/2 is 16 + 4, or 20. So

  2 1/2 cups = 20 fluid ounces

This is really what math is all about: we can change one idea, that 
of units of measure, into another idea, that of groups; and then the 
concepts of multiplication and division that work for groups can be 
used to figure out the units too.

Let me know if that helps. If you have any further questions, feel 
free to write back, and be as specific as you can about where you 
have trouble.

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