Rational Number


What are Rational Numbers?
Any number which can be expressed in the form p/q, where p and q are integers and q ≠ 0, is called a rational number.

Positive and Negative Rational Numbers
In the rational number p/q, p is called the numerator and q the denominator.
If the numerator and the denominator have the same sign, the rational number is said to be positive. If they have different signs, the rational number is said to be negative.
Positive rational number:-  6/7, 11/23, -5/-8, -2/-7
Negative rational number :- -12/17, -2/9, 7/-15, 6/-13

Standard Form of Rational Number
A rational number is said to be in the standard form if it is in the lowest form and its denominator is positive.
For example, the rational numbers 21/17, -7/3, -4/9 are in standard form. But the rational numbers 4/-5, 12/16, -8/12 are not in standard form

Absolute Value of Rational Numbers
The absolute value of a rational number is its numerical value without taking into consideration its sign, i.e, the magnitude of the rational number.
The absolute value of –p/q and p/q is the same and is written as
 │-p/q│ = p/q and │p/q│ = p/q

Properties of Rational Number.
Closure Property

1. Addition Rational Number :- Sum of two Rational number is always a Rational number 
Ex. 1/2 + 3/7 =  7 + 6   
                           14 
                    = 13/14 is also a rational number.
2. Subtraction of Rational Number :- Difference of two Rational number is always a Rational number
Ex. 9/11 - 3/5 = 45 - 33
                            55
                     = 12/55 is also a rational number.
3. Multiplication of Rational Number:- The Product of two Rational number is always a Rational number 
Ex. 3/17 x 15/19 = 45/323 is also a rational number.
4. Division of Rational Number :- As for any rational number a, a ÷ 0 is not defined, therefore not all rational numbers are closed under division. you can say that expect zero, all rational numbers are closed under division.
Ex. 5/7 ÷ 3/8 = 5/7 x 8/3 = 40/21 is also a rational number.
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