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# A Deeper Analysis on the Natural Numbers

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 p40 uses temperatures below freezing as an example In this instance we record how many degrees below Oc 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 natural numbers -4-3-2-101234 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 of the original whole cake Therefore there are 4 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 eg 24 is equal to However we can also write fractions as decimals Therefore half a whole number can be expressed as 050 a half of 1 by using a

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