Slide 1 / 68. Order of Operations
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1 Slide 1 / 68 Order of Operations
2 Slide 2 / 68 Table of Contents Introduction to Order of Operations Simplify Using Order of Operations More Challenging Order of Operations
3 Slide 3 / 68 Introduction to Order of Operations Return to Table of Contents
4 Slide 4 / (8) The answer is 40 The answer is 19 Which is right? 19 is correct! Can you explain why?
5 Slide 5 / 68 What are operations? When there exists more than one value, operations can be any of the following: addition subtraction multiplication division exponentiation
6 Slide 6 / 68 What does "Order of Operations" mean? The Order of Operations is an agreed upon set of rules that tells us in what "order" to solve a problem.
7 Slide 7 / 68 What does P E M/D A/S stand for? The P stands for Parentheses: Usually represented by ( ). Other grouping symbols are [ ] and { }. Examples: (5 + 6); [5 + 6]; {5 + 6}/2 The E stands for Exponents: The small raised number next to the larger number. Exponents mean to the power (2nd, 3rd, 4th, etc.) Example: 2 3 means 2 to the third power or 2(2)(2) The M/D stands for Multiplication or Division: From left to right. Example: 4(3) or 12 3 The A/S stands for Addition or Subtraction: From left to right. Example: or 4-3
8 Slide 8 / 68 How can we remember PEMDAS? P E M D A S Please Excuse My Dear Aunt Sally
9 Slide 9 / 68 Identify the Operation: 6(7) (16-2) ( ) Parentheses Exponents Multiplication Division Addition Subtraction
10 Slide 10 / 68 Simplify Using Order of Operations Return to Table of Contents
11 Slide 11 / Move the box to find out if you are correct! 5 8 Incorrect Correct
12 Slide 12 / 68 Let's take a close look at that problem P Ask yourself, do I have any parentheses? E No M or D Whichever occurs 1st from left to right A or S Whichever occurs 1st from left to right
13 Slide 13 / 68 Move onto the next letter P E No Ask yourself, do I have any exponents? No M or D Whichever occurs 1st from left to right A or S Whichever occurs 1st from left to right
14 Slide 14 / 68 Move onto the next letters P No E No M or D Ask yourself, do I have any multiplication or division? Yes! Solve from Left to Right. A or S Whichever occurs 1st from left to right It helps if you underline the part of HINT the problem you are going to solve.
15 Slide 15 / 68 Move onto the next letters P No E No M or D Yes! Solve from Left to Right. A or S
16 Slide 16 / 68 Check to make sure there isn't any more multiplication or division P No E No M or D Yes. Is there anymore? No more. A or S
17 Slide 17 / 68 Move onto the next letters P No E No M or D Yes. No more. A or S Ask yourself, do I have any addition or subtraction? Yes! Solve from Left to Right.
18 Slide 18 / 68 We did it! P No E No M or D Yes. No more. A or S Yes.
19 Slide 19 / 68 Let's try another problem. 3(1 + 9) P E Do I have any parentheses? Yes - do the math in the parentheses first. M or D A or S
20 Slide 20 / 68 Remember to take it one step at a time. 3(1 + 9) 3(10) P Yes! Simplify the parentheses. E M or D A or S
21 Slide 21 / 68 Move onto the next letter. 3(1 + 9) 3(10) P Yes E Do I have any exponents? No. M or D A or S
22 Slide 22 / 68 Move onto the next letters. 3(1 + 9) 3(10) P Yes. Identify and solve. E No. M or D Do I have any multiplication or division? Yes. Solve from left to right. A or S
23 Slide 23 / 68 We did it! 3(1 + 9) 3(10) 30 P Yes. Identify and solve. E No. M or D Yes. Solve from left to right. A or S
24 Slide 24 / 68 Try these! (7)
25 Slide 25 / (9)
26 Slide 26 /
27 Slide 27 / 68 4 (4)(3) + 8
28 Slide 28 /
29 Slide 29 / (2)
30 Slide 30 / (3 2 )
31 Slide 31 / 68 Allison is having a birthday party and is allowed to invite her friends from school. Of her classmates, 7 girls and 5 boys are allowed to come. Each of Allison's party favors costs $4 to make. Write an expression to help Allison figure out how much money her party favors will cost. Try to use parentheses to write your expression. Evaluate your expression. (7 Expression + 5)4 Pull down to see (7 + the 5)4 step (12)4 by step solution 48 Make sure to label your $48 answer!
32 Slide 32 / 68 8 Rachel, Ted and Alice are going to the fair. Together, they were able to buy 75 tickets for rides. They used 15 of the tickets to ride the bumper cars. After the ride, they decided to split the remaining tickets equally. Use parentheses to write an expression that represents the number of tickets each friend will get. A B C
33 Slide 33 / 68 9 Erin and Elizabeth went shopping for family gifts. Together they spent the following: $10, $20, $8, $13 and $16. Write an expression to represent the amount that each of them would spend, if the total were to be split equally.
34 Slide 34 / Fifteen boys went to the pizza parlor and each ordered a slice for $2.00, a soda for $1.50 and garlic bread for $0.75. Write an expression to represent the total spent in the pizza parlor.
35 Slide 35 / Mary received a paycheck for $55. She paid the following debts: $7.50 each to three friends, a $5 video fee and $15 for a magazine subscription. Write an expression to represent the amount of money Mary has left.
36 Slide 36 / 68 Let's have a quick review of the basics! 8 (1+3) Ask yourself, are there any grouping symbols? Yes - so simplify 8 (1+3) Ask yourself, are there any exponents? Yes - so simplify
37 Slide 37 / Is there any multiplication or division? Yes - so simplify from left to right Is there anymore multiplication or division? Yes - so simplify from left to right Is there any addition or subtraction? Yes - so simplify from left to right
38 Slide 38 / 68 Let's try a big problem (2 + 2) + 8 Are there any grouping symbols? Simplify them (2 + 2) (4) + 8 Are there any exponents? Simplify them
39 Slide 39 / Is there any multiplication or division? Simplify from left to right Is there any addition or subtraction? Simplify from left to right
40 Slide 40 / 68
41 13 Slide 41 / 68
42 Slide 42 / 68 Let's try an even bigger problem. What happens if there is more than one set of grouping symbols? [ 6 - ( 2 8 ) + ( ) 7 ] 3 When there are more than 1 set of grouping symbols, start inside and work out following the Order of Operations. [ 6 - ( 2 8 ) + ( ) 7 ] 3 [ 6 - ( 16 ) + ( 16-9 ) 7 ] 3 [ 6 - ( 16 ) + ( 7 ) 7 ] 3
43 Slide 43 / 68 [ 6 - ( 16 ) + ( 7 ) 7 ] 3 [ 6 - ( 16 ) + 1 ] 3 [ ] 3 [ -9 ] 3-27
44 Slide 44 / [(-3)(2) + (-5)(4)]4-1
45 Slide 45 / [5 + 3] + 7
46 Slide 46 / [2-5]
47 Slide 47 / (15-7)
48 Slide 48 / 68 Here are a few examples of problems where you might see the new grouping symbols. 2.4 [ (12-6.2) 4 ] (9)(3) -2 { 15-4 [ ( ) - 5 ] - 3 } Let's simplify these!
49 Slide 49 / (2)(8) + 9
50 Slide 50 / [ (12-6.2) 4 ] Pull 16 4 (9)(3) Pull
51 19 [(2)(4)] 2-3(5 + 3) Slide 51 / 68
52 Slide 52 / Pull -2 { 15-4 [ ( ) - 5 ] - 3 } Pull
53 Slide 53 / 68 More Challenging Order of Operations Return to Table of Contents
54 Slide 54 / 68 The same Order of Operations rules apply when a problem contains negative numbers (-2 6) (-12)
55 Slide 55 / 68 The first step in Order of Operations actually includes all grouping symbols, not just parentheses. Can you think of any other types of grouping symbols? Brackets Braces Absolute Value Division or fraction bar
56 Slide 56 / 68 Order of Operations G = Grouping Symbols E = Exponents M = Multiplication D = Division A = Addition S = Subtraction
57 Slide 57 /
58 Slide 58 / (-2)
59 Slide 59 / (-3)(2)
60 23 3(4-5) - (-2) 3 Slide 60 / 68
61 24 4-3[8 - (5-7)] Slide 61 / 68
62 Slide 62 /
63 Slide 63 / 68
64 27 Slide 64 / 68
65 Slide 65 / 68
66 29 4(6-11) - (-4) 3 Slide 66 / 68
67 30 Slide 67 / 68
68 Slide 68 / 68
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