properties of rational numbers-sangh

properties of rational numbers-sangh

1. What are the properties of Rational Numbers? Learning Objective

2. To discuss the closure property To discuss commutative property To discuss associative property Learning Outcomes

3. Properties of Rational Numbers What does the term ‘ closure ’ mean?

4. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and .  

5. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get __.  

6. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get .  

7. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is/is not a rational number?  

8. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .  

9. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   We say that rational numbers are closed under addition , if for any two rational numbers a and b , a + b is also a rational number.

10. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and and check if these numbers are closed under subtraction.  

11. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   We say that rational numbers are closed under subtraction , if for any two rational numbers a and b , ____ is also a rational number.

12. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   We say that rational numbers are closed under subtraction , if for any two rational numbers a and b , a - b is also a rational number.

13. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and and check if these numbers are closed under multiplication.  

14. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   We say that rational numbers are closed under _____________ , if for any two rational numbers a and b , a x b is also a rational number.

15. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   We say that rational numbers are closed under multiplication , if for any two rational numbers a and b , a x b is also a rational number.

16. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and and check if these numbers are closed under division.  

17. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   We say that rational numbers are closed under division , if for any two rational numbers a and b , ______ is also a rational number.

18. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   We say that rational numbers are closed under division , if for any two rational numbers a and b , a ÷ b is also a rational number.

19. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   If the two rational numbers were a and , would the closure property still hold?

20. Properties of Rational Numbers The ‘ Closure ’ Property Let’s take two rational numbers , and . Now, we add them and get . is a rational number . Thus, we say that and are closed under addition .   If the two rational numbers were a and , would the closure property still hold? No! Because any number divided by 0 is not defined .

21. To discuss the closure property To discuss commutative property To discuss associative property Learning Outcomes How confident do you feel?

22. To discuss the closure property To discuss commutative property To discuss associative property Learning Outcomes How confident do you feel?

23. Properties of Rational Numbers What is the ‘ Commutative ’ Property?

24. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and .  

25. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . Let’s do + .  

26. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = .  

27. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . Now, let’s do + .  

28. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . We get, + = .  

29. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . We get, + = .   We say that addition is commutative for rational numbers if for any two rational numbers a and b , a + b = b + a .

30. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s check if subtraction is commutative for rational numbers using and .  

31. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . We get, + = .   We can say that subtraction is ______________ for rational numbers .

32. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . We get, + = .   We can say that subtraction is not commutative for rational numbers .

33. Properties of Rational Numbers The ‘ commutative ’ Property Let’s check if multiplication is commutative for rational numbers using and .  

34. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . We get, + = .   We can say that multiplication is _____________ for rational numbers .

35. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . We get, + = .   We can say that multiplication is commutative for rational numbers .

36. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s check if division is commutative for rational numbers using and .  

37. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . We get, + = .   We can say that division is _____________ for rational numbers .

38. Properties of Rational Numbers The ‘ Commutative ’ Property Let’s take two rational numbers , and . We get, + = . We get, + = .   We can say that division is not commutative for rational numbers .

39. To discuss the closure property To discuss commutative property To discuss associative property Learning Outcomes How confident do you feel?

40. To discuss the closure property To discuss commutative property To discuss associative property Learning Outcomes How confident do you feel?

41. Properties of Rational Numbers What is the ‘ Associative ’ Property?

42. Properties of Rational Numbers The ‘ Associative ’ Property We shall take three rational numbers , , and .  

43. Properties of Rational Numbers The ‘ Associative ’ Property We shall take three rational numbers , , and . Let’s do + ( + ).  

44. Properties of Rational Numbers The ‘ Associative ’ Property We shall take three rational numbers , , and . We get + ( + ) = .  

45. Properties of Rational Numbers The ‘ Associative ’ Property We shall take three rational numbers , , and . We get + ( + ) = . Now, let’s do ( + ) + .  

46. Properties of Rational Numbers The ‘ Associative ’ Property We shall take three rational numbers , , and . We get + ( + ) = . We get ( + ) + = .  

47. To discuss the closure property To discuss commutative property To discuss associative property Learning Outcomes How confident do you feel?

48. To discuss the closure property To discuss commutative property To discuss associative property Learning Outcomes How confident do you feel?

49. What are the properties of Rational Numbers? Learning Objective

50. Properties of Rational Numbers Learning Activity Check the closure , associative and commutative properties with natural numbers , whole numbers and integers .