Rational numbers class 8

Tis is based on mathematics chapter 1 covering all properties you can revise anything from it it is very knowledgeable. It also covers some class 7 topics too. All your topics will be cleared from it.

1. RATIONAL NUMBERS CHAPTER - 1

2. Rational numbers are numbers in the form of where, . For e.g.:   RATIONAL NUMBERS

3. DIFFERENCE BETWEEN FRACTION & RATIONAL NUMBER Rational Numbers Fractions RATIONAL NUMBERS = POSITIVE FRACTIONS + NEGETIVE FRACTIONS

4. NUMBER SYSTEM Rational Numbers Integers Whole Numbers Natural Numbers

5. PROPERTIES OF RATIONAL NUMBERS Communicative Associative Distributive Inverse Identity Closure

6. CLOSURE PROPERTY Closure property means that if we divide/ add/ subtract/ multiply a rational number the answer should always be a rational number if one of the case becomes wrong then the whole law is wrong.

7. Addition   Since by adding two rational numbers answer is also rational number . therefore , addition of rational numbers is closed.

8. Subtraction   Since by subtracting two rational numbers answer is also rational number. Therefore, subtraction of rational number is closed.

9. Multiplication   Since by multiplying two rational numbers answer is also rational number. Therefore, multiplication of rational number is closed.

10. Division   Division of rational number is not closed.

11. COMMUTATIVE PROPERTY Commutative property means, that by interchanging the position of rational numbers the answer should be same.  

12. Addition Since by interchanging the position of rational numbers the answer is same. Therefore, addition of rational numbers is commutative.

13. Subtraction Since, by interchanging the position of rational numbers the answer is not same. Therefore, subtraction of rational numbers is not commutative.

14. Multiplication Since by interchanging the position of rational numbers the answer is same. Therefore, multiplication of rational numbers is commutative.

15. Division Since by interchanging the position of rational numbers the answer is not same. Therefore, division of rational numbers is not commutative.

16. ASSOCIATIVE PROPERTY Associative property means that by interchanging the position of three rational numbers the answer should be same.  

17. Addition Since by interchanging the position of rational numbers the answer is same. Therefore, addition of rational numbers is associative.

18. Subtraction Since by interchanging the position of rational numbers the answer is same. Therefore, subtraction of rational numbers is associative.

19. Multiplication Since by interchanging the position of rational numbers the answer is same. Therefore, multiplication of rational numbers is associative.

20. = = Division Since by interchanging the position of rational numbers the answer is not same. Therefore, division of rational numbers is not associative.

21. DISTRIBUTIVE PROPERTY This property is only of multiplication and is taken over by addition or subtraction.

22. Multiplication over addition

23. Multiplication over subtraction

24. MULTIPLICATIVE IDENTITY Multiplicative identity means that if we will multiply any number by a number the answer will always be same. 1 is the multiplicative identity for rational numbers. As it will not change the identity of rational number or any integer. For example: a. b.  

25. ADDITIVE IDENTITY Additive identity means that if we add any number by a number the answer will always be same. Zero is called the identity for the addition of rational numbers. It is the additive identity for integers and whole numbers as well. For example: a. b.  

26. RECIPROCAL OF RATIONAL NUMBERS Reciprocal of rational numbers means upside down. NUMBER -2 RECIPROCAL –½

27. MULTIPLICATIVE INVERSE Upside down Number -4 Multiplicative inverse = -¼ Number -0 Multiplicative = 1/0 = n.d ( does not exist )

28. ADDITIVE INVERSE Opposite in sign Number =3 additive inverse = (-3 ) Number = -5 additive inverse = 5

29. REPRESENTATION OF RATIONAL NUMBERS ON NUMBER LINE -1 -2 -4 -3 -5 5 4 3 2 1

30. HOW TO FIND RATIONAL NUMVERS BETWEEN NUMBER LINE? Take out the equivalent fraction of the rational numbers and write the rational numbers lying between them.

31. a.   To find rational nos. in between rational numbers.

32. 151/200 , 152/200 , 153 /200 , 154 /200 , 155/200 , 156/200 , 157 /200  

33. PRACTICE TIME

34. Q1 . Is a rational number?   YES NO

35. YOU GOT IT!

36. Additive identity of 56 is: 2 56 4

37. YOU GOT IT!

38. Reciprocal of 6/7 is: -7/6 7/6 -6/7 6/-7

39. YOU GOT IT!

40. Which of the following is the Multiplicative identity for rational numbers? 1 None of these -1

41. YOU GOT IT!

42. Which of the following lies between 0 and -1? 4/3 -2/3 -3

43. YOU GOT IT!

44. Which of the following is additive inverse of 7/29? 29/7 7/29 -7/29 -29/7

45. YOU GOT IT!

46. Which of the following is multiplicative inverse of 15/31? 31/15 15/31 -15/31 -31/15

47. YOU GOT IT!

48. Which of the properties indicate give operation: a + b + c = c + b + a Associative Property Closure Property Commutative property Distributive property

49. YOU GOT IT!

50. NEED PRACTICE

51. THANK YOU