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Properties of Rational Number


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HD 22:58 Animated video Lecture for Properties of Rational Number

Rational numbers :
Numbers that can be expressed in the form  p q , where p and q are integers and q ≠ 0, are known as rational numbers. The collection of rational numbers is denoted by Q.

These rational numbers satisfies various laws or properties that are listed below:

Rational numbers are closed under addition, subtraction and multiplication. If a, b are any two rational numbers, then and the sum, difference and product of these rational numbers is also a rational number, then we say that rational numbers satisfy the closure law.

     Type of Number
                                         Closed Under
   Whole Numbers                     X                   X
       Integers                                          X
  Rational Numbers                                          X

Rational numbers are commutative under addition and multiplication. If a, b are rational numbers, then:

Commutative law under addition: a + b = b + a.

Commutative law under multiplication: a x b = b x a.

     Type of Number
                       Commutative Under
  Whole Numbers                  X                 X
         Integers                  X                 X
  Rational Numbers                  X                 X

Rational numbers are associative under addition and multiplication. If a, b, c are rational numbers, then:

Associative law under addition: a + (b + c) = (a + b) + c

Associative law under multiplication: a(bc) = (ab)c

     Type of Numbers
                                       Rational Numbers
    Closure                    X                     X
   Commutative                    X                X
       Associative                    X                X

     •  0 is the additive identity for rational numbers.

     •  1 is the multiplicative identity for rational numbers.

     •  The additive inverse of a rational number  p q  is -  p q , and the additive inverse of - p q is p q.

     •  If  p q x  a b = 1, then a b  is the reciprocal or multiplicative inverse of p q , and vice versa.

     •  For all rational numbers, p, q and r,  p(q + r ) = pq + pr  and  p(q - r ) = pq - pr , is known as the distributive property.

Distribution property of multiplication over substraction
p(q - r) = pq - pr where p,q and r are rational numbers.

Distributive property of multiplication over addition
p(q + r) = pq + pr where p,q and r are rational numbers.


Questions & Answers

1 . please suggest a good poem for my hindi recitation competition
select a poem on world with trees and greenery and compare with world without it. i recited such a poem and got the first prize for it. you...
2 . Two rational numbers that lies between -2/3 and -2/5
If a and b are two rational numbers then (a + b)/2 is a rational number that lies between a and b.
Given rational numbers are (-2/3)...
3 . How can i delete my learnnext account
Hi Harshit 
Yes even I want to delete the learnNext account as it doesnot provide us full video of t...
4 . Give 5 rational number between -5/6 and 7/8
5 rational number between -5/6 and 7/8 are : Taking LCM of denominator and multiplying the numbers with LCM we get :
-20/24 and 21/2...
5 . Express in p/q form.
0.48 = 48 / 100 = (48 ÷ 4) / (100 ÷ 4) = 12 / 25
0.1357 = 1357 / 10000 

Therefore, 0.48 and 0.1357 in p...