Mathematics Principles V11

Clive W. Humphris

FRACTIONS: Proper and Improper Fractions.  


Written fractions where there is a numerator (top) and a denominator (bottom) separated by a dividing line are a much easier way for us humans to visualise an amount that is part of a whole. There are two types of fraction, proper and improper. A proper fraction is a common fraction whose value is less than one unit i.e. the numerator is always less than the denominator. An improper fraction is a common fraction whose value is greater than one, this time the numerator is larger than the denominator.

The numerator shows how many units you have and the denominator how many units there are. For example 3/4, there are four parts to the whole and you have three of them or three-quarters. Mental subtraction will say that their must be one quarter elsewhere. A fraction is a division problem that needs to be converted into a decimal equivalent before it can be used mathematically.

An improper fraction can be expressed as a mixed number and a proper fraction has no whole number part. If it's a mixed number it will consist of both a whole number and a fractional part. To express a decimal number as a fraction, it is necessary to remove the decimal point. '1' followed by zeros are then placed below the dividing line for each digit above. The number of zeros included makes the number of digits below the dividing line equal the number above (plus one for decimal values of less than one).

To simplify the fraction find the lowest common multiple of both numbers. See the topic LCM for a full explanation. A fraction where the numerator and the denominator are the same will always simplify to 1. Some fractions cannot be simplified further if both the numerator and denominator cannot be divided by at least two.

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