Fractions
The waterline on the glass indicates at first a glass half
full, then one third full and finally only one fourth full.
The previous topic showed that numbers in between whole numbers ( i.e. : 0,1,2,3, ...) can be
expressed as fractions or decimal numbers with digits after the decimal point.
Properly, a fraction is less than one whole ( in other words fraction means a part of a whole).
Thus, in the figure above the first glass (from left to right) is half full or 1/2 of one whole. The
second glass is one third full or 1/3 of one whole, and the third glass is one fourth full or 1/4 of
one whole. The fractions for the first, second and third glasses are 1/2, 1/3 and 1/4 respectively.
Obviously, for this case, we are expressing numbers in between 0 and 1 as fractions. These are
called Proper Fractions.
Improper Fractions.
Here, there is one full glass and another glass only
half way full.
Fractions can also be used to express numbers greater or equal to one.
The figure above is an example for representing numbers in between 1 and 2. There is a total of
one and a half glasses, or 1 + 1/2 = 2/2 + 1/2 glasses or 3/2 glasses. Here, the number one has
been written as 2/2 ( i.e: there are two halves in one whole) and has been added to 1/2 (one half) to
total 3 halves or 3/2. Both 2/2 and 3/2 are known as improper fractions, since they represent a
number greater than one. Note that improper fractions can be used to represent whole numbers as
well as numbers in between whole numbers.
Mixed Numbers.
The improper fraction 3/2 is really the combination of 1 whole (or 2/2) and 1/2 and it can be
alternatively written as 11/2 (one and one half). This is called a mixed number, since it consists of
a whole number and a proper fraction. Any improper fraction can be written as a mixed number.
Just try it! For instance: 5/2 (five halves- five half glasses) is equal to 2 full glasses and 1/2 glass
or 21/2 glasses!