Meaning of a Fraction
 

Meaning of a fraction:

Fractions are the method people use to describe pieces of a whole.

Things that are shredded.   The pieces are a fraction of the whole.

Things that are divided into pieces have been cut into pieces.  Each piece is a fraction of the whole.

Things that are listed can be consider part of the list.  They represent only a fractions of a list.

 

This pages talks about things that are shredded ....  Read the first few problems and answers.   Invent a rule that helps you know how to make fractions out of questions related to pieces of things.    Then, do the remaining problems to see if your rule always works.

................................................................................................................................

Shred a bar into 8 pieces.   Paste the bar back together.   Express how many pieces your have pasted back together as you go.

Given this bar, I will tear it along the marks below.

               

Here is 1 eighth of the bar

1  eighth

              

Here is 2 tenths of the bar pasted back together

2 eighths

            

Here is 3 tenths of the bar pasted back together

3 eighths

          

.... 

Here is 7 eighths of the bar pasted back together

7 eighths  

Here is 8 eighths of the bar.   It is whole (1 complete piece) again.

8 eighths ( 1 whole )

Below, we fill a glass with different amounts of lemonade ...   We assume that we could fill the glass full    (1 whole glass), then we describe how much lemonade we actually put in the glass.

         
         
         
         
         
         
2 sixths of a glass of lemonade 4 sixths of a glass of lemonade 1 sixths of a glass of lemonade 5 sixths of a glass of lemonade 6 sixths (1 whole)

Questions.   Can you guess how we came up with the names eighths, and  sixths?  

As a shorthand for writing things like 1 sixths, 3 eighths or 9 sixteenths we write:

1/6,   3/8,   9/16.

Have you ever poured a glass of orange juice (or other drink) ?    If you have, you have used fractions.   As you fill the glass, you have seen fractions of a 1 whole glass.    In the picture below, We have placed 16 lines behind a glass.   This "breaks" the glass up into 16 pieces.  As you pour juice into the glass, you get 1/16, 2/16, 3/16 and more juice until you stop pouring.

Notice  in the above picture of a glass, lines are marked behind the glass.   Since the glass tapers, this does not break the glass into 16 equal pieces.   It only approximates equal pieces.  

To see 1/4, 1/2 or 3/4 of a cup of juiced poured, click the appropriate button.

16 ths 8 ths 4 ths

 

 

Notice, the location for 1/4, 1/2 and 3/4 marks on the background.   Normally, we talk about glasses that are 1/4, 1/2 and 3/4 full.    If you break the glass up into 16ths, you will see the liquid at the lines for 4/16, 8/16 and 12/16.   If you break the glass up into 8ths, you will see the liquid at the lines for 2/8, 4/8 and 6/8.

 

Check Your Understanding 1

Given something that is shredded into the following number of pieces, what do you think they are ????

  1. 7 pieces            


  1. 16 pieces           


  1. 3 pieces            


  1. 5 pieces             


  1. 25 pieces           


  1. 10 pieces           

Check Your Understanding 2

  1. Which lizard has just bounced past 6/10 of the hurdles?       

  1. Which of the lizards has not yet passed 1/10 of the hurdles?  

  1. Which of the lizards will shortly pass 8/10 of the hurdles?     

More ...