19 January 2014

Introduction to Rational Numbers

All numbers, including whole numbers, integers, fractions and decimal numbers, can be written in the numerator-denominator form.  A rational number is a number that can be written in the form p/q, where p and q are integers and q ≠ 0.    .

The denominator of a rational number can never be zero.  A rational number is positive if its numerator and denominator are both either positive integers or negative integers.   .  If either the numerator or the denominator of a rational number is a negative integer, then the rational number is called a negative rational number.   

The rational number zero is neither negative nor positive.  

On the number line:
    • Positive rational numbers are represented to the right of 0.
    • Negative rational numbers are represented to the left of 0.
By multiplying or dividing both the numerator and the denominator of a rational number by the same non-zero integer, we can get another rational number that is equivalent to the given rational number. 
A rational number is said to be in its standard form if its numerator and denominator have no common factor other than 1, and its denominator is a positive integer.  

To reduce a rational number to its standard form, divide its numerator and denominator by their Highest Common Factor (HCF).  To find the standard form of a rational number with a negative integer as the denominator, divide its numerator and denominator by their HCF with a minus sign.  

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