Properties of Rational Numbers

In this ppt you will learn about the properties of Rational Numbers with examples . I have written all properties of Rational Numbers in Addition,Subtraction,Multiplication&Division.

1. Properties of rational numbers

2. Properties of Addition

3. Closure Property

4. If are rational numbers then is always a rational number .   Example :- =   ∴ rational numbers are closed under addition

5. Commutative Property

6. If are rational numbers then = .   Example :- =   ∴ Addition of rational numbers is commutative.

7. Associative Property

8. If are rational numbers then ( ) = ) .   Example :- ( ) = )   ∴ Addition of rational numbers is associative.

9. Additive Identity & Additive Inverse

10. Additive identity for rational number is 0 as + 0 =   Example :- + 0 =   ∴thus when we add 0 to rational number its answer is the number itself. Additive identity for rational number is 0 as + 0 =   Example :- + 0 =  

11. Additive inverse for rational number is (- )=0   Example :- + (- )=0   ∴thus for an rational number there exists its opposite (- ) such that there sum is zero, (- ) is additive inverse for .  

12. Properties of Subtraction

13. Closure Property

14. If are rational numbers then is always a rational number .   Example :- =   ∴ rational numbers are closed under subtraction.

15. Commutative Property

16. If are rational numbers then ≠ .   Example :- ≠   ∴ Subtraction of rational numbers is not commutative.

17. Associative Property

18. If are rational numbers then ( ) ≠ ) .   Example :- ( ) )   ∴Subtraction of rational numbers is not associative.

19. Properties of Multiplication

20. Closure Property

21. If are rational numbers then is always a rational number .   Example :- =   ∴ rational numbers are closed under multiplication

22. Commutative Property

23. If are rational numbers then = .   Example :- =   ∴ Multiplication of rational numbers is commutative.

24. Associative Property

25. If are rational numbers then ( ) = ) .   Example :- ( ) = )   ∴ Multiplication of rational numbers is associative.

26. Multiplicative Identity & Multiplicative Inverse

27. ∴thus when we multiply 1 to rational number its answer is the number itself. Multiplicative identity for rational number is 1 as 1 =   Example :- 1 =  

28. If is a rational number then =1   Example :- =1   ∴thus for an rational number there exists its opposite such that there product is 1, is additive inverse for .  

29. Properties of division

30. Closure Property

31. If are rational numbers then is always a rational number .   Example :- =   ∴ rational numbers are closed under Division.

32. Commutative Property

33. If are rational numbers then ≠ .   Example :- ≠   ∴ Division of rational numbers is not commutative.

34. Associative Property

35. If are rational numbers then ( ) ≠ ) .   Example :- ( ) )   ∴Division of rational numbers is not associative.

36. Distributive Property

37. If are rational numbers then   Example :-  

38. Thanks For Cooperating