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Order of operations Equations Formulae Removing brackets Factorising Inequations.

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Presentation on theme: "Order of operations Equations Formulae Removing brackets Factorising Inequations."— Presentation transcript:

1

2 Order of operations Equations Formulae Removing brackets Factorising Inequations

3 Presents Algebra Menu

4 Hands up! 3 + 5 x 2 ? 13

5 A bit of order please! Brackets Of Divide Multiply Add Subtract B O D M A S ( 3 + 4 ) x 3= 7 x 3= 21 ( 3 + 4 ) x 3 5 + ½ of 8= 5 + 4= 9 5 + ½ of 8 3 + 5 x 2= 3 + 10= 13 3 + 5 x 2 18 - 12 ÷ 3= 18 - 4= 14 18 - 12 ÷ 3 These are the very last things you do! BOMDAS

6 BOMDAS Practice (1) 3 + 7 x 6 (2) (3 + 7) x 6 (3) 32 – 24 ÷ 4 (4) 5 + 6 x 3 - 1 (5) 5 + 6 x (3 – 1) = 3 + 42 = 45 = 10 x 6 = 60 = 32 - 6 = 26 = 5 + 18 – 1 = 22 = 5 + 6 x 2 = 5 + 12 = 17

7 Presents Algebra Menu

8 Algebra Short hand 3a means 3 times a bc means b times c m/k means m divided by k x² means x times x efef means e divided by f

9 Formulae (1) Given that C = s + nr, calculate C when s=12, n=5 and r=8. C = s + nr BOMDAS C = 12 + 40 = 52 C = 12 +5x 85 x 8 M snr

10 p = 45 + 3 = 48 p = 5 x 9 + calculate p when a=5, s=9, d=18 and m=6. Given that p = as + dmdm p = as + dmdm 18 6 18 6 BOMDAS M D Formulae (2) as dmdm

11 s = 48 - 24 + 5 = 29 s = 3 x 4 x 4 - Given that s = 3t² - 6t + 5 calculate s when t=4. 6 x 4 BOMDAS M Formulae (3) s = 3t² - 6t + 5 + 5 3 x 4 x 4 6 x 4 3t² 6t

12 Now do Exercise 1 (HSDU Support Materials))

13 Presents Algebra Menu

14 Removing brackets (1) 3(b + 5) = 3b 3 b This means 3 times b

15 Removing brackets (1) 3(b + 5) = 3b + 15 3 5 + This means 3 times 5

16 Removing brackets (2) 5(8 - f) = 40 5 8

17 Removing brackets (2) 5(8 - f) = 40 - 5f 5 f - Tip: Draw lines to keep you right. 5(8 – f) = 40 - 5f

18 Now do Exercise 2 Question 1 (HSDU Support Materials)) Algebra Menu

19 Removing brackets (3) 4(3b + 2) = 12b 4 3b 4 x 3b= 4 x 3 x b= 12 x b= 12b

20 Removing brackets (3) 4(3b + 2) = 12b + 8 4 2 +

21 Removing brackets (4) 3(7a – 2b) = 21a 3 7a

22 Removing brackets (4) 3(7a – 2b) = 21a - 6b 3 2b -

23 Removing brackets (5) c(3c + b) = 3c² c 3c c x 3c= 3c x c= 3c²

24 Removing brackets (5) c(3c + b) = 3c² + bc c b + Tip: Remember to draw lines to keep you right. c(3c + b) = 3c² + bc

25 Removing brackets (6) 6(5e + 3f - 2) = 30e 6 5e

26 Removing brackets (6) 6(5e + 3f - 2) = 30e 6 3f + 18f

27 Removing brackets (6) 6(5e + 3f - 2) = 30e 6 2 + 18f- 12 Careful! Tip: Remember to draw lines to keep you right. 6(5e + 3f -2) = 30e + 18f- 12

28 Now do Exercise 2 Questions 2 & 3 (HSDU Support Materials)) Algebra Menu

29 Simplifying (1) 4(3a + 5) - 8 = 12a 4 3a

30 Simplifying (1) 4(3a + 5) - 8 = 12a 4 5 + 20 This is not inside the brackets So don’t multiply! - 8- 8

31 Simplifying (1) 4(3a + 5) - 8 = 12a + 20 - 8- 8 This can be tidied up = 12a + 12

32 Simplifying (2) 3b + 2(5b – 6) = 10b 2 5b 3b + This is not inside the brackets So don’t multiply!

33 Simplifying (2) 3b + 2(5b – 6) = 10b 2 6 3b + - 12 Careful!

34 Simplifying (2) 3b + 2(5b – 6) = 10b3b + - 12 This can be tidied up = 13b - 12

35 Now do Exercise 2 Questions 4, 5. (HSDU Support Materials)) Algebra Menu

36 Presents Algebra Menu

37 Factorising (1) 4a – 6b = 4 ? What’s the highest number that will divide into both 4 and 6? 6 This is called the highest common factor 2

38 ? Factorising (1) 4a – 6b = 4a 2 2a ( ) 2

39 ? Factorising (1) 4a – 6b = 6b 2 2a ( ) 3b - 2

40 Factorising (1) 4a – 6b = 2 2a ( ) 3b -

41 Factorising (2) 3b + bc = b ? What’s the highest common factor? b b This time it’s the letter b that they have in common.

42 ? Factorising (2) 3b + bc = 3b b 3 b ( )

43 ? Factorising (2) 3b + bc = bc b 3 c + b ( )

44 ? Factorising (2) 3b + bc = b 3 c + ( )

45 Factorising (3) 6f + 9gf = ? What’s the highest common factor? 3 3 divides into 6 and 9. 6 9 f Notice that the letter f is also common to both. 9gf 6f6f

46 Factorising (3) 6f + 9gf = 3 f ( ) ? 2 6f

47 Factorising (3) 6f + 9gf = 3 f ( ) 2 9gf ? 3g +

48 Factorising (3) 6f + 9gf = 3 f ( ) 2 3g +

49 Now do Exercise 3 (HSDU Support Materials)) Algebra Menu

50 Presents Algebra Menu

51 x + 5 = 20

52 x+5 20 (-5) x + 5 = 20

53 x 20 (-5) x + 5 = 20

54 x 15 x = 15 x + 5 = 20

55 (-5) (-5) x = 15 Example 1: x + 5 = 20

56 1)x + 8 = 122) a + 12 = 30 3)5 + x = 134)b + 7 = 42 (-8) x = 4 (-12) a = 18 (-5) x = 8 (-7) (-7) b = 35 Answers Exercise A

57 3x + 7 = 25

58 3x+7 25 (-7) 3x + 7 = 25

59 3x 25 3x + 7 = 25 (-7)

60 3x 18 3x = 18 3x + 7 = 25 ?

61 This means 3 times x equals 18 3 times 6 equals 18 So x must be 6 x = 6 3x = 18

62 3x + 7 = 25 (-7) (-7) 3x = 18 Example 2: x = 6

63 1) 2x + 7 = 23 2) 6a + 11 = 29 3) 5 +8y = 37 4) 9 + 3d = 42 (-7) (-7) 2x = 16 x = 8 (-11) (-11) 6a = 18 a = 3 (-5) (-5) 8y = 32 y = 4 (-9) (-9) 3d = 33 d = 11 Exercise B Answers

64 5x - 6 = 44

65 5x-6 44 (+6) 5x - 6 = 44

66 5x 44 5x - 6 = 44 (+6)

67 5x 50 5x = 50 5x - 6 = 44

68 (+6) (+6) 5x = 50 Example 3: x = 10

69 1) 5b - 8 = 122) 7a - 9 = 33 3) 6y - 6 = 304) 9z- 7 = 20 (+8) (+8) 5b = 20 b = 4 (+9) (+9) 7a = 42 a = 6 (+6) (+6) 6y = 36 y = 6 (+7) (+7) 9z = 27 z = 3 Exercise C Answers

70 Is there a shortcut?

71 5x - 6 = 44 Change side, change sign - 6

72 5x = 44 + 6 5x = 50 x = 10 Change side, change sign

73 5x - 6 = 44 5x = 44 + 6 5x = 50 Example 4: x = 10

74 3x + 7 = 25 Change side, change sign

75 3x = 25 - 7 3x = 18 x = 6 Change side, change sign

76 3x + 7 = 25 3x = 25 - 7 3x = 18 Example 5: x = 6

77 1) 2a + 7 = 23 2) 7x - 9 = 33 2a = 23 - 7 2a = 16 a = 8 7x = 33 + 9 7x = 42 x = 6 Exercise D Answers

78 6x = 9 + 2x Tricky one! 6x – 2x = 9 4x = 9 + 2x ?

79 4x = 9 Change side, change sign The 4 is multiplying the x, so when it changes side, it divides. 4

80 x = 9 ÷ 4 x = 2.25 4x = 9 Change side, change sign 4

81 5x + 2 = 3x + 6

82 5x+2 3x+6 (-2) 5x + 2 = 3x + 6

83 5x (-2) 3x+6

84 5x 3x+4 (-3x) 5x + 2 = 3x + 6

85 5x 4 (-3x)

86 2x 4 2x = 4 5x + 2 = 3x + 6 So x = 2

87 Change side, change sign 5x = 3x + 6 - 2 5x = 3x + 43x 5x –3x = 4 2x = 4 5x + 2 = 3x + 6 x = 2 + 2

88 Change side, change sign 3x + 6 + 4 = 8x 3x + 10 = 8x3x 10 = 8x – 3x 10 = 5x 3x + 6 = 8x - 4 x = 2 - 4 Most Xs are on the right. So this time: Xs on the right, numbers on the left! 3x 8x

89 3x + 6 = 8x - 4 6+4 = 8x – 3x Example 6: 10 = 5x x = 2 Try two changes together!

90 1) 5a + 7 = 2a + 22 2) 3x + 9 = 7x - 15 5a – 2a = 22 - 7 3a = 15 a = 5 9 + 15 = 7x – 3x 24 = 4x x = 6 Exercise E Answers

91 Presents Algebra Menu

92 is greater than 9 8 Inequations 9 8 >

93 is less than Inequations 5 9 < 5 9

94 Hint: The less than sign is almost L shaped. Remember is greater than is less than < ess than < <

95 Practice: fill in the correct sign (1) 7 10(2) 12 9 (3) 2 3(4) 5 0 (5) 3 -2(6) -6 -3 (7) -2 2(8) -1 0 (9) -4 -5(10) 3 3 < > < > > < < < > < Click here for number line

96 To drive, what age do you have to be? To get married in Scotland, what age do you have to be? To buy alcohol, what age do you have to be? Click on the picture to reveal the answer.

97 What speed should you drive at in town? Click on the picture to reveal the answer. How many passengers can a black taxi take?

98 is greater than or equal to ABCD Next question

99 is less than ABCD

100 is greater than ABCD

101 is less than or equal to ABCD Finish

102 3a + 8 < 26 Solving inequations + 8 3a < 18 a < 6 - 8 Use the same method as for equations!

103 3a + 8 < 26 3a < 26 - 8 3a < 18 Example: a < 6

104 Now do Exercise ? (HSDU Support Materials))

105 K Hughes 2003

106 Aged greater than or equal to 18

107 Aged greater than or equal to 17

108 Aged greater than or equal to 16

109 Speed less than or equal to 30 mph

110 Passengers less than or equal to 5

111 Number Line 01234567-2-3-4-5-6-7 positive numbersnegative numbers Negative Positive

112

113

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