The first numbers that we are introduced to from an early age are 1, 2, 3, 4 etc.
These are called the 'Natural numbers', and can be placed on a number line from 1
to infinity. The natural numbers, in order, are always 1 whole number larger or
smaller than the next.
When we add or subtract the natural numbers the answer is always a natural
number. If we use subtraction or division however, we would without any other
system, not always be able to obtain an answer within the natural number system.
The sum 8 minus 10 for example would be impossible therefore a new number
system is needed. Suggate (1998, p.40) uses temperatures below freezing as an
example. In this instance we record how many degrees below OÃÂ°c it is by counting
backwards from 0, to the left, using the 'negative' numbers. The integers are all
positive and negative whole numbers including 0 but the positive integers are also
When taking into account these numbers it is not always possible to calculate while
keeping the sum within the integer system. Therefore another system is needed. If
we take for example 1 cake which is whole and divide it into 4 parts. Each piece is
considered ÃÂ¼ of the original whole cake. Therefore there are 4 ÃÂ¼ pieces. These
fractions or 'rational numbers' tell us this by the bottom numbers - the denominator.
The number on top of the fraction is the numerator and tells us about how many
parts we are dealing with. With fractions there are different ways to write the same
amount, e.g. 2/4 is equal to ÃÂ½ . However we can also write fractions as decimals.
Therefore ÃÂ½ , half a whole number, can be expressed as 0.50 ( a half of 1)...