1. Order of Operations Section 1.3

2. Agenda Warm-up Exercise Warm-up Exercise –Practice Listening Skills Learning Session on “Order of Operations” Learning Session on “Order of Operations” Early start on homework Early start on homework

3. What is “order of operations”? It is the order in which we do the operations in a mathematical equation It is the order in which we do the operations in a mathematical equation Example: 3 + 4 · 5 Example: 3 + 4 · 5 –What would be answer if we do addition first: (3 + 4) · 5 = (3 + 4) · 5 = 35 35 –What would be answer if we do multiplication first: 3 + (4 · 5) = 3 + (4 · 5) = 23 23 –Which answer is the “standard” answer using standard order of operations? 23 (multiplication, then addition) 23 (multiplication, then addition)

4. Standard Order of Operations First do operations that occur within symbols of grouping “() etc.”. First do operations that occur within symbols of grouping “() etc.”. Then evaluate powers. Then evaluate powers. Then do multiplications and divisions from left to right. Then do multiplications and divisions from left to right. Finally do additions and subtractions from left to right. Finally do additions and subtractions from left to right.

5. 18 – 9 2 · 3 2 - 9 2 · 9 - 9 Free Example 1 First evaluate powers Then do multiplication and division = 9 Finally do addition and subtraction

6. Free Example 2 5 + 8 · 3 + 2 5 + 8 · 3 + 2 5 + 24 + 2 5 + 24 + 2 29 + 2 29 + 2 31 31

7. Student Example 1 15 – 2 · 2 15 – 2 · 2 15 – 4 15 – 4 11 11

8. Student Example 2 10 · (3 + 1) – 16 10 · (3 + 1) – 16 10 · 4 – 16 10 · 4 – 16 40 – 16 40 – 16 24 24

9. Student Example 3 13 + (3 · 2) 2 – 8 13 + (3 · 2) 2 – 8 13 + 6 2 – 8 13 + 6 2 – 8 13 + 36 – 8 13 + 36 – 8 49 – 8 49 – 8 41 41

10. Student Example 4 X 3 – 4x + 9, when x = 4 X 3 – 4x + 9, when x = 4 4 3 – 4·4 + 9 4 3 – 4·4 + 9 64 - 4·4 + 9 64 - 4·4 + 9 64 – 16 + 9 64 – 16 + 9 48 + 9 48 + 9 57 57