Fractions: Numerator, Denominator, Proper fraction, Improper fraction and Cancelling

When 2 is divided by 3, it may be written as    or 2/3 .  is called a fraction. The number above the line, i.e. 2, is called the numerator and the number below the line, i.e. 3, is called the denominator.

When the value of the numerator is less than the value of the denominator, the fraction is called a proper fraction; thus is a proper fraction. When the value of the numerator is greater than the denominator, the fraction is called an improper fraction. Thus
is an improper fraction and can also be expressed as a mixed number, that is, an integer and a proper fraction.
Thus the improper fraction is equal to the mixed number .
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When a fraction is simplified by dividing the numerator and denominator by the same number, the process is called cancelling. Cancelling by 0 is not permissible.

Example 1
Simplify

Solution

The lowest common multiple (i.e. LCM) of the two denominators is 3×7, i.e. 21.
Expressing each fraction so that their denominators are 21, gives: