Class 6 - Maths (Integers).pptx

Powerpoint Presentation of Integers

1. MATHEMATICS Class VI Lecture # 7

2. MATHEMATICS Mathematics is the science of numbers and figures through logical reasoning.

3. The coldest continent on Earth is Antarctica where average temperature range from 5°C in summer to -80°C in winter. The highest temperature ever recorded in Antarctica was 15°C, while the lowest temperature ever recorded in Antarctica was -89.2°C.

4. In previous classes, we have learnt about whole numbers , decimals and fractions , such as , 9 , 5.8 and .  

5. Positive Numbers : Numbers that are greater than 0 are called ‘positive numbers’ . Such as 8, 9.8, .   1 2 3 4 5 6

6. Negative Numbers : Numbers that are less than 0 are called ‘negative numbers’ . Such as -100, -1.1, -   -1 -2 -3 -4 -5 -6

7. Use of Negative Numbers in the Real World Negative Numbers Are Used to Measure Temperature

8. Negative Numbers Are Used to Measure Under Sea Level 10 20 30 -10 -20 -30 -40 -50

9. Negative Numbers Are Used to Show Debt Let’s say your parents bought a car, but had to get a loan from the bank for Rs.50,000. How can we represent the amount of money your parents have as an integer? -Rs.50,000

10. I N TE G ERS

11. W h at is a n In t eger?

12. A n i n t e g er i s a po si t ive or neg a t i ve whol e nu m b er, i n cl u di ng 0 . … - 3 , - 2 , -1 , , 1 , 2 , 3… Note: 0 is neither a positive nor a negative integers.

13. If you don’t see a negative or positive sign in front of a number it is positive. Tip:

14. Exercise 2A

15. Answer:

16. Homework Practice Now (Page 27) Q.1. and Q.2. (in copy)

17. I N TE G ERS Lecture # 8

18. Le t ’ s R evi e w…

19. Wh a t i s a n in t e g er ?

20. A N S W E R A n i n t e g e r is a po s i t ive o r n e g a t i ve w hole nu m b e r, i n cl u di ng 0. Note: 0 is neither a positive nor a negative integers.

21. Ca n you g i v e a n e xamp l e of a n i nte g e r ?

22. A N S W E R • … - 3 , - 2 , - 1, 0 , 1, 2 , 3 …

23. Exercise 2A

24. Answer:

25. Number Line

26. Exercise 2A

27. Answer:

28. Exercise 2A

29. Answer:

30. Answer:

31. Answer:

32. Answer:

33. Homework Practice Now (Page 29) Q.1 and Q.2 (in copy)

34. The r e a r e “ 4 ” In t e g e r Op e r a t i o n s

35. 4 I n t e g er O pera t i o ns Ad d i t ion + S u b tr a c tion - M u l t ipl i c a tion x Di v i s ion ÷

36. R u l e # 1 f o r A ddi ng In t e g e r s (+) T he s u m of t w o p os iti v e i n t e g e r s i s alw a y s p os iti v e. 5 + 1 = 6

37. R u l e # 2 f o r A ddi ng In t e g e r s (+) T he s u m of t w o n e g a ti v e i n t e g e r s i s alw a y s n e g a ti v e. - 5 + ( -1) = -6

38. R u l e # 3 f o r A ddi ng In t e g e r s (+) T he s u m of a po s i t i v e a n d a n e g a ti v e i n t e g er c o u l d b e p os iti v e, n e g a ti v e , or z e ro.

39. R u l e # 3 for A d d i ng I n t e g e rs Con t in u e d W h e n y o u a d d a p o s i t i v e a n d n e g at i ve i n t e g e r , y ou ar e r e ally s u b tr a c t i n g . Th e n , y o u g i v e the an s w e r the s i g n o f th e g r e a t e r ab s olu te val u e . 5 + ( - 1) = -4 -5 + 1 = 4 -5 + (- 5 ) =

40. Let ’ s Pra ct i c e “ A d d i t io n” 1) 5 + 6 = • -3 + ( -2 ) = • -6 + 5 = • 8 + ( - 7 ) = • -9 + 9 =

41. Let ’ s C he c k 1) 5 + 6 = 11 • -3 + ( - 2 ) = -5 • -6 + 5 = -1 • 8 + ( - 7 ) = 1 • -9 + 9 =

42. R u l es f or S u b t ra c t i ng In t e g e r s (-) T o s u b t r a c t a n i n t e g e r, a d d it s opp os it e. Y ou w i ll n ee d t o c o r r ec t ly c h a n ge a l l s u b tr a c tion p r o b l e m s i n t o a ddi t i on p r o b lems!

43. H o w d o yo u ch a n ge a s u b tr a c t i o n p r o b lem into a n a d d iti o n p r o bl em?

44. T he r e a re t h ree s t e p s : K eep t he fir s t i n t e g er t he same. ( S am e ) Cha n g e t he s u b t ra ct ion s i g n i n t o a n a d dition s i g n . (Cha n g e) T a k e t h e o pp os it e of t h e n u m b e r t h a t i m m e d i a t ely f ol lo ws t h e n ewly p l a ced a d dition s i g n . (Cha n g e)

45. S am e , Ch a n g e , Ch a n g e E x amples:  5 – ( -2 ) = 5 + 2 = 7  -5 – 2 = -5 + ( - 2 ) = -7 Thi n k …

46. Let’s Pra ct i c e “ S u b t ra c t i on” 1) 5 – 2 = 2 ) -3 – 4 = 3 ) -1 – ( - 2 ) = 4 ) -5 – ( -3 ) = 5 ) 7 – ( -6 ) =

47. Let ’ s C he c k 1) 5 – 2 = 5 + ( - 2 ) = 3 2 ) -3 – 4 = -3 + ( - 4 ) = -7 3 ) -1 – ( - 2 ) = -1 + 2 = 1 4 ) -5 – ( - 3 ) = -5 + 3 = -2 5 ) 7 – ( - 6 ) = 7 + 6 = 13

48. R ules f o r M u l t i pl y i n g I n t e g ers ( x ) T he p r o d u c t of t w o i n t e g e r s w it h t he same s i g n s i s P O SI T I V E . T he p r o d u c t of t w o i n t e g e r s w it h dif f e re n t s i g n s i s NE G A T I V E .

49. R u l e s Sum m a r y for M u l t i p lica t i on P os i ti v e x Pos i t i v e = Pos iti v e N e ga t i v e x Ne g a ti v e = P os i t i v e P os i ti v e x Ne g a ti v e = N e ga t i v e N e ga t i v e x Pos iti v e = Ne g a t i v e

50. L e t ’s Pra c t i c e “ Mul t i p l i cat i o n ” 1) 6 x ( - 3 ) = 2 ) 3 x 3 = 3 ) -4 x 5 = 4 ) -6 x (- 2 ) = 5 ) -7 x (- 8 ) =

51. L e t ’s Check 1) 6 x ( - 3 ) = -18 2 ) 3 x 3 = 9 3 ) -4 x 5 = - 2 4 ) -6 x (- 2 ) = 12 5 ) -7 x (- 8 ) = 5 6

52. D id yo u know t h a t t h e rul e s f o r m ul t i p l ica ti o n a n d di v i s ion a re t he sa m e ?

53. G u e s s w h a t…. They a r e !

54. T h e r u l es f o r d i v i s i o n a r e e x a c t l y t h e s ame as t h ose f o r m ul t i p l i c a t i o n . • If w e we r e to t ak e t h e r u l e s f o r mu l t i p li c a t i o n a nd ch a n g e t h e m u l t i p li c a t i o n s i g n s to d i v i s i o n s i g n s , w e w o u l d h a v e a n a cc u r a t e s et o f r u l es f o r d i v i s i o n .

55. R ules f o r D i v idi ng In t e g e rs (÷) T he qu o t ient of t wo i n t e g e r s wi t h t he same s i g n s i s P O SI T I V E . T he qu o t ient of t wo i n t e g e r s wi t h dif f e re n t s i g n s i s NE G A T I V E .

56. R u l e s Sum m a r y for D i vi s ion P os i ti v e ÷ P os i t i v e = Pos iti v e N e ga t i v e ÷ Ne g a ti v e = P os it i v e P os i ti v e ÷ Ne g a ti v e = N e ga t i v e N e ga t i v e ÷ Pos it i v e = N e ga t i v e

57. Le t ’ s Pra c t i c e “ D i vi s i on ” 1) 18 ÷ ( - 2 ) = 2 ) -4 8 ÷ ( - 6 ) = 3 ) -2 7 ÷ 9 = 4 ) 6 4 ÷ 8 = 5 ) 3 ÷ ( - 5 ) =

58. Let ’ s C he c k 1) 18 ÷ ( - 2 ) = -9 2 ) - 4 8 ÷ ( - 6 ) = 8 3 ) - 2 7 ÷ 9 = -3 4 ) 6 4 ÷ 8 = 8 5 ) 3 ÷ ( - 5 ) = -6

59. W ha t a re t h e f o ur op er a t i o n s?

60. A N S W E R T h e f our o p e ratio n s a r e : ad d i t io n , s u b t r a c t i on , mul t ipli c a t i o n, a nd d iv i si o n.

61. H o w do y o u a d d int eg er s ?

62. A N S W E R T he s um of t w o p o s i t i v e i n t e g e r s i s a l w a y s pos i t i v e . T he s um of t w o n e g at i ve i nt e ge r s i s al w a y s n e g at i v e . W h e n y o u a d d a p o s i t i v e a n d n e g at i ve i n t e g e r , y ou ar e r e ally s u b tr a c t i n g . Th e n , y o u gi ve the a n s w e r the s i g n o f t h e g r eat e r a b sol u te val u e .

63. H o w do y o u s ubtr a ct in t e g er s ?

64. A N S W E R T o s u b t r a c t a n i n t e g e r, a d d it s opp os it e. S a m e , C ha n g e , Ch a n ge

65. H o w do y o u m ul t ip ly int eg er s ?

66. A N S W E R If t he s i g n s a r e t he same, you r a n s w er i s alw a ys po s iti v e . If t he s i g n s a r e di f fe re n t , y o u r a n s w er i s alw a ys n e ga t i v e.

67. H o w do y o u di v i d e int eg er s ?

68. A N S W E R I f the s i g n s a r e th e s a m e , yo u r a n s w e r i s a l w a y s pos i t i ve . I f the s i g n s a r e di f f e r e n t, y ou r a n s w e r i s a l w a y s n eg a t i v e . *M u l t i plic at io n a n d D i v i s i on Rul es a r e the s a m e !