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Algebra menu. Order of operations. Formulae. Removing brackets. Factorising. Equations. Inequations. Smithycroft Mathematics. Algebra Menu. Presents. Order of operations. Hands up!. 3 + 5 x 2 ?. 13. B. O. M. D. A. S. A bit of order please!. Brackets. ( 3 + 4 ) x 3. = 7 x 3.

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1. Algebra menu Order of operations Formulae Removing brackets Factorising Equations Inequations

2. Smithycroft Mathematics Algebra Menu Presents Order of operations

3. Hands up! 3 + 5 x 2 ? 13

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

5. BOMDAS Practice • 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

6. Smithycroft Mathematics Algebra Menu Presents Formulae

7. e f means Algebra Short hand 3a means 3timesa btimesc bc means x² means xtimesx m/k means mdivided byk edivided byf

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

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

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

11. Now do Exercise 1 (HSDU Support Materials))

12. Smithycroft Mathematics Algebra Menu Presents Removing Brackets

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

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

15. Removing brackets (2) 5 8 5(8 - f) = 40

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

35. Smithycroft Mathematics Algebra Menu Presents Factorising

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

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

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

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

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

41. Factorising (2) ( ) ? 3 b b 3b 3b + bc =

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

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

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

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

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

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

48. Algebra Menu Now do Exercise 3 (HSDU Support Materials))

49. Smithycroft Mathematics Equations Algebra Menu Presents

50. x + 5 = 20

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