Fractions Comparison
 

Reaching this page, it's time for you to get a "gut" level feeling about the relation between fractions.   On this page, you will begin to understand the size relationship between fractions.    With this page, you will begin to understand the which fractions are bigger (greater than) and smaller (less than) when comparisons are done between fractions.    

Look at a few of the pictures below, and the associated answers.   Use the answers of the first few problems to come up with a feel for answering the questions.   Then, go on to complete the page and make sure your feel works.   Later, we will look at a formal method for comparing fractions, but, a gut level feeling is what is used in real life.

 

Below, you see a standard set of measuring cups.    These are used by folks that need to measure liquids.

 

Measuring cups are named by the amount of liquid, relative to a national standard, that can be held by the cup.  The picture below shows cups and the line of fractions below (in BLACK) represent the name given to each cup.   

         1 cup                        3/4 cup                2/3 cup              1/2 cup              1/3 cup           1/4 cup

       Do you see a relation between the fractions and pictures above?  

1       , 3/4   
 
3/4   , 2/3    
 
2/3   ,     1
 
1/2    , 3/4  
 
1/3    , 1/4  
 
1/4    , 2/3
 

 

Below, you see a standard set of sockets for a socket wrench.     These are used by folks that work on cars, planes, trucks and hundreds of other things that use nuts and bolts (or screws).

 

Sockets are named by the size of nut that can be removed with the socket.    Normally, nuts are labeled by the fraction of an inch that it measures across its surface.   The picture below shows the sockets and the line of fractions below (in BLACK) represent the name given to each socket.   If you were working with a friend, and wanted the friend to hand you a socket, you would use one of names (in BLACK) below.

           5/16"    3/8"   7/16"   1/2"    9/16"       5/8"       11/16"     3/4"          13/16"         7/8"

   5/16      6/16   7/16    8/16    9/16        10/16       11/16     12/16          13/16         14/16

Do you see a relation between the fractions and the names of the sockets above?  

                     
5/16    
3/8        (6/16)
7/16    
1/2         (8/16)
9/16    
 
5/8        (10/16)
 
11/16   
 
3/4        (12/16)
13/16  
7/8        (14/16)

 

Below, you see a standard set of auger bits.     These are used by folks that work with wood.   These bits are special because they permit the drilling of rather large holes in wood.

 

Auger bits are named by the size of size hole it will create.    Normally, holes are labeled by the fraction of an inch that it measures across.   The picture below shows the auger bit and the line of fractions below (in BLACK) represent the name given to each bit.   If you were working with a friend, and wanted the friend to hand you a auger bit, you would use one of names (in BLACK) below.

 

    

 

1/4"      3/8"      1/2"          5/8"              3/4"                   7/8"

2/8       3/8       4/8           5/8                6/8                     7/8

Do you see a relation between the fraction and the name of the auger bit above?  
1/4       (2/8)

 
3/8     

 
1/2       (4/8)

 
5/8    

 
3/4       (6/8)

 
7/8     

 

Notice one of the auger bits is missing.    You can tell that the auger bit is missing by noticing the gap left in the picture.   However, there is another way to notice the gap.   If no space had been left to indicate that a auger bit was missing, you could still figure out that a bit was missing.    

You will notice that for the bits shown, there are the following fractions in blue ....

2/8,    3/8,    4/8,    5/8,    7/8

The 6/8 is missing from the sequence.. This implies that 3/4 is missing. (How could you get the number 3/4 from the number 6/8???      )

 

Below, you see a standard set of drill bits.     These, or similar drill bits, are used by folks that want to drill a typical hole.   Drills with specially hardened tips may be used to drill concrete, wood, metal, plastic, fiber glass or other materials.

                    

                                     12/64      8/64      6/64       4/64
                                                       10/64       7/64      5/64

In the photo above, we  find 5 drill bits between 3/16 and 1/16.    Considering we would expect to count 1/16 ... 2/16 ... 3/16,  how is it possible for there to be 5 drill bits between 1/16 and 3/16?

Using the information above, can you find at least 2 drill bits that would fit between 3/16 and 1/16 that are NOT shown in the set above.   

 

 

Below, you see a set of wrenches.  These are used by folks that want to remove nuts from screws.   
  13/64    ???     15/64    16/64      20/64   22/64    24/64

7/32      ???        1/4        8/32     11/32       3/8         7/16