Rational numbers ............Maths, BCDP, Concepts, questions, examples

 Rational numbers (Q) 

A number is called a rational number if it can be expressed in form of p/q where p,  q are integers (q≠0).

Rational numbers set is represented by  Q

Eg- 

-3/5, 5/4, 6, 3/2, -13/46, 0, 16........

A important thing to remember while working with rational numbers is 

p/q, where p &q are integers, q≠0


Properties of rational numbers 

1) Closure -> result should belong to the group (here rational numbers) 

[Note- We should check a particular example by reversing the example ]

Addition -> Closed, Ex- 2+8=10, 8+2 =10 

Subtraction -> Closed, Ex- 2-8= -6, 8-2 = 6

Multiplication -> Closed, Ex- 2×8=16, 8×2=16

Division -> Not closed, Ex- 2/8= 1/4, 8/2= 4

           U can ask a question why does division is not closed,  

Any guesses, let me know in the comments below.


2) Commutative property 

Addition -> Commutative - a+b=b+a 

Subtraction -> Not commutative - a-b≠b-a 

Multiplication -> Commutative - a×b=b×a 

Division -> Not commutative - a/b≠b/a 


3) Associativity property 

•Addition -> Yes,

Ex- a+(b+c) = (a+b)+c 

2+(8+10) = (2+8)+10 

20

• Subtraction -> No   

Ex- a-(b-c)  ≠ (a-b) -c 

2-(8-10) ≠ (2-8)-10 

•Multiplication -> Yes 

Ex- a(b×c) = (a×b)c 

2(8×10) = (2×8)10

• Division -> No 


4) Distributivity property 

The property of multiplication over addition - 

a(b+c) = a×b+a×c 

Ex - 4/7×(-2/3+1/2) = 4/7×(-2/3)+4/7×1/2

= -2/3 

The property of multiplication over subtraction - 

a(b-c) = a×b - a×c 

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