Draw Three Parts and Shade Two

Date: 04/12/2001 at 22:18:31
From: Need help in math
Subject: Fractions

I've been having problems understanding fractions and being 
embarrassed when I go to the board and draw three parts and shade two 
in, and have to tell the teacher the name of the fraction I've shaded. 
Can you help me?

Date: 04/13/2001 at 13:05:23
From: Doctor Peterson
Subject: Re: Fractions

Hi,

I'll give you a basic introduction to the idea of fractions. If you 
need more help, I hope you won't be embarrassed to show me your 
mistakes, so I can help you figure out what you are doing wrong and 
learn how to do it. You can probably also ask your teacher for some 
private help, so you don't have to make your mistakes in front of the 
class.

A fraction is just a way to say "I've broken something into some 
number of pieces, and chosen some of them." It has two parts:

     2  <--- the numerator
    ---
     3  <--- the denominator

The numerator is the "numberer" (that's what the word means in 
Latin). It tells how many pieces I've chosen.

The denominator is the "namer" (again, it's Latin). It tells what kind 
of pieces they are.

You make the pieces by cutting a whole into some number of parts. If 
you cut it into three parts, we call them thirds, and write "3" for 
the denominator. For most numbers, the word we use for the denominator 
is the same as the word we would use to say the order of things: 
first, second, third, fourth, fifth, and so on. In a few cases, 
though, we use special words. A "first" (only one part) is just called 
"the whole"; you haven't cut it at all if you've cut it into one 
piece. A "second" is called a "half"; cutting it in two means cutting 
it in half. A "fourth" can be called that, but is also often called a 
"quarter" (like the coin, which is a fourth of a dollar). Otherwise, 
we use the usual words.

So if you cut a pie into three equal parts and color in two of them, 
the fraction you have colored in is 2/3, or "two thirds." Each piece 
is a third, and you colored two of them.

If you cut each of a batch of pies into one piece each (that is, you 
leave them whole), and take five of them, you've taken 5/1, which we 
can just call five pies, since there are five pieces, each of them a 
whole pie.

If this doesn't clear everything up, please write back and tell me 
anything I need to know about what you do and don't understand. Show 
me some examples of questions you have answered wrong, or ask all the 
questions you want. I'll be happy to help.

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