1. ORDER OF OPERATIONS 1. Multiplication & Division 2. Addition & Subtraction + - ÷

2. 1. Multiplication & Division Solve in the order they appear from left to right. 2. Addition & Subtraction Solve in the order they appear from left to right.

3. 1. Multiplication & Division Solve in the order they appear from left to right. 2. Addition & Subtraction Solve in the order they appear from left to right.

4. In the problem below: 5 + 6 3 - 4 Which operation is solved first? In the problem below: 5 + 6 3 - 4 Which operation is solved first?

5. Multiply first… and rewrite the rest of the problem. 5 + 6 3 - 4 5 + 18 - 4 Next? Multiply first… and rewrite the rest of the problem. 5 + 6 3 - 4 5 + 18 - 4 Next?

6. Add…and rewrite the rest of the problem. 5 + 6 3 - 4 5 + 18 - 4 23 - 4 Add…and rewrite the rest of the problem. 5 + 6 3 - 4 5 + 18 - 4 23 - 4

7. Last…subtract. 5 + 6 3 - 4 5 + 18 - 4 23 - 4 19 Last…subtract. 5 + 6 3 - 4 5 + 18 - 4 23 - 4 19

8. Let’s try another one! 24 ÷ 2 4 Which operation is solved first? Let’s try another one! 24 ÷ 2 4 Which operation is solved first?

9. Divide first. It appears first. Rewrite the rest of the problem. 24 ÷ 2 4 12 4 Divide first. It appears first. Rewrite the rest of the problem. 24 ÷ 2 4 12 4

10. Multiply and rewrite the rest of the problem. 24 ÷ 2 4 12 4 48 Multiply and rewrite the rest of the problem. 24 ÷ 2 4 12 4 48

11. Multiply and rewrite the rest of the problem. 24 ÷ 2 4 12 4 48 Notice….The problem will be in a triangular shape. Multiply and rewrite the rest of the problem. 24 ÷ 2 4 12 4 48 Notice….The problem will be in a triangular shape.

12. Solve this one. 18 + 4 ÷ 2 - 8 Solve this one. 18 + 4 ÷ 2 - 8

13. Divide first….even though it is in the middle of the problem. 18 + 4 ÷ 2 - 8 18 + 2 - 8

14. Next add…rewrite the rest of the problem. 18 + 4 ÷ 2 - 8 18 + 2 - 8 20 - 8

15. 18 + 4 ÷ 2 - 8 18 + 2 - 8 20 - 8 12

16. Try this with me….. 35 + 5 7 - 14 Try this with me….. 35 + 5 7 - 14

17. 35 + 5 7 - 14 35 + 35 - 14 35 + 5 7 - 14 35 + 35 - 14

18. 35 + 5 7 - 14 35 + 35 - 14 35 + 5 7 - 14 35 + 35 - 14

19. 35 + 5 7 - 14 35 + 35 - 14 70 - 14 35 + 5 7 - 14 35 + 35 - 14 70 - 14

20. 35 + 5 7 - 14 35 + 35 - 14 70 - 14 56 35 + 5 7 - 14 35 + 35 - 14 70 - 14 56

21. Get an answer to this one! 15 ÷ 3 + 20 5 5 + 20 5 5 + 100 105

22. Simplify these on topic paper! 1. 45 - 5 + 13 2. 20 ÷ 4 7 3. 10 - 24 ÷ 4 2 4. 4 3 + 25 ÷ 5 5. 6 + 8 ÷ 2 5

23. Solutions 1. 45 - 5 + 13 2. 20 ÷ 4 7 3. 10 - 24 ÷ 4 2 4. 4 3 + 25 ÷ 5 5. 6 + 8 ÷ 2 5

24. 1.45 - 5 + 13 40 + 13 53 1.45 - 5 + 13 40 + 13 53

25. 2.20 ÷ 4 7 5 7 35 2.20 ÷ 4 7 5 7 35

26. 3.10 - 24 ÷ 4 2 10 - 6 2 10 - 12 - 2 3.10 - 24 ÷ 4 2 10 - 6 2 10 - 12 - 2

27. 4.4 3 + 25 ÷ 5 12 + 25 ÷ 5 12 + 5 17 4.4 3 + 25 ÷ 5 12 + 25 ÷ 5 12 + 5 17

28. 5.6 + 8 ÷ 2 5 6 + 4 5 6 + 20 26 5.6 + 8 ÷ 2 5 6 + 4 5 6 + 20 26

29. Grouping Symbols ( parentheses ) [ brackets ] { braces }

30. ( ) parentheses Solve first…using order of operations rules inside. ( ) parentheses Solve first…using order of operations rules inside.

31. [ ] brackets Solve second … using order of operations rules inside.

32. { } braces Solve third…using order of operations rules inside.

33. Grouping symbols are nested inside each other and are worked from the inside to the outside. { [ ( ) ] } Grouping symbols are nested inside each other and are worked from the inside to the outside. { [ ( ) ] }

34. A number or grouping symbols next to grouping symbols indicates multiplication. 7(6 - 4) This means 7 times the (6 - 4) answer or 72 A number or grouping symbols next to grouping symbols indicates multiplication. 7(6 - 4) This means 7 times the (6 - 4) answer or 72

35. When several grouping symbols are in the same problem simplify ( ), then [ ], then { }. (1)[2]{3} Follow order of operations rules in the grouping symbols. 4{7 +6[5(3+9)-(8-2)]} 4{7+6[512-6]} ( ) are now removed. When several grouping symbols are in the same problem simplify ( ), then [ ], then { }. (1)[2]{3} Follow order of operations rules in the grouping symbols. 4{7 +6[5(3+9)-(8-2)]} 4{7+6[512-6]} ( ) are now removed.

36. Next simplify inside the brackets remembering to use order of operations. 4{7+6[5(3+9)-(8-2)]} 4{7+6[512-6]} 4{7+6[60-6]} 4{7+654} Next simplify inside the brackets remembering to use order of operations. 4{7+6[5(3+9)-(8-2)]} 4{7+6[512-6]} 4{7+6[60-6]} 4{7+654}

37. Simplify inside the braces remembering to use order of operations. 4{7+6[5(3+9)-(8-2)]} 4{7+6[512-6]} 4{7+6[60-6]} 4{7+654} 4{7+324} 4331 1324 Simplify inside the braces remembering to use order of operations. 4{7+6[5(3+9)-(8-2)]} 4{7+6[512-6]} 4{7+6[60-6]} 4{7+654} 4{7+324} 4331 1324

38. Last multiply to finish the problem. 4{7+6[5(3+9)-(8-2)]} 4{7+6[512-6]} 4{7+6[60-6]} 4{7+654} 4{7+324} 4331 1324 Last multiply to finish the problem. 4{7+6[5(3+9)-(8-2)]} 4{7+6[512-6]} 4{7+6[60-6]} 4{7+654} 4{7+324} 4331 1324

39. Simplify these on topic paper. SHOW ALL WORK!!! 1.8+7(5-1) 2.3(10-2)÷4 3.15-2[36-4(5+3)] 4.[3(6+5)-2(8-4)+2]5 5.20-1{3+3[2(4-3)+(7-5)]} Simplify these on topic paper. SHOW ALL WORK!!! 1.8+7(5-1) 2.3(10-2)÷4 3.15-2[36-4(5+3)] 4.[3(6+5)-2(8-4)+2]5 5.20-1{3+3[2(4-3)+(7-5)]}

40. Solution: 8+7(5-1) 8+74 8+28 36 Solution: 8+7(5-1) 8+74 8+28 36

41. Solution: 3(10-2)÷4 38÷4 24÷4 6 Solution: 3(10-2)÷4 38÷4 24÷4 6

42. Solution: 15-2[36-4(5+3)] 15-2[36-48] 15-2[36-32] 15-24 15-8 7 Solution: 15-2[36-4(5+3)] 15-2[36-48] 15-2[36-32] 15-24 15-8 7

43. Solution: [3(6+5)-2(8-4)+2]5 [311-24+2]5 [33-8+2]5 [25+2]5 275 135 Solution: [3(6+5)-2(8-4)+2]5 [311-24+2]5 [33-8+2]5 [25+2]5 275 135

44. Solution: 20-1{3+3[2(4-3)+(7-5)]} 20-1{3+3[21+2]} 20-1{3+3[2+2]} 20-1{3+34} 20-1{3+12} 20-115 20-15 5 Solution: 20-1{3+3[2(4-3)+(7-5)]} 20-1{3+3[21+2]} 20-1{3+3[2+2]} 20-1{3+34} 20-1{3+12} 20-115 20-15 5

45. Simplifying Exponents 4 2 4 is the base 2 is the exponent. It tells you how many times to take the base times itself. 4 2 = 4 4 = 16 4 2 4 is the base 2 is the exponent. It tells you how many times to take the base times itself. 4 2 = 4 4 = 16

46. Simplifying Exponents 4 2 4 is the base 2 is the exponent. It tells you how many times to take the base times itself. 4 2 = 4 4 = 16 4 2 4 is the base 2 is the exponent. It tells you how many times to take the base times itself. 4 2 = 4 4 = 16

47. When exponents are in order of operations problems they are usually simplified first. For example, in the problem 3 2 +5-4 3 2 is simplified first. When exponents are in order of operations problems they are usually simplified first. For example, in the problem 3 2 +5-4 3 2 is simplified first.

48. 3 2 +5-4 Simplify using order of operation rules. 33+5-4 9+5-4 14-4 10 3 2 +5-4 Simplify using order of operation rules. 33+5-4 9+5-4 14-4 10

49. If exponents are outside of grouping symbols, you must simplify the grouping symbols first. Then follow order of operations. 2+5(6-4) 3 2+5(2) 3 2+58 2+40 42 If exponents are outside of grouping symbols, you must simplify the grouping symbols first. Then follow order of operations. 2+5(6-4) 3 2+5(2) 3 2+58 2+40 42

50. If exponents are outside of grouping symbols, you must simplify the grouping symbols first. Then follow order of operations. The exponent will be simplified second. DO NOT MULTIPLY BY THE 5 BEFORE YOU SIMPLIFY THE EXPONENT. 2+5(6-4) 3 2+5(2) 3 2+58 2+40 42 If exponents are outside of grouping symbols, you must simplify the grouping symbols first. Then follow order of operations. The exponent will be simplified second. DO NOT MULTIPLY BY THE 5 BEFORE YOU SIMPLIFY THE EXPONENT. 2+5(6-4) 3 2+5(2) 3 2+58 2+40 42