2. Order of Operations

3. Suppose we have the following: 3 + 4  8 = What operations are present here: Addition and Multiplication What is your result?

4. Which answer is correct? As you can see we get different results by performing the operations of multiplication and division in different orders. Both can not be right -so which one is correct? 35 or 56

5. Deciding what order... It seems we need some rules telling us which operation we should perform first. Whenever an expression contains more than one operation. The operations must be performed in a specific order.

6. What Order? Step 1 -Step 1 - Parentheses Perform all operations inside groupings first. This includes Parenthesis, Brackets and Braces. ( ) [ ] { } If there are parenthesis inside brackets begin with the innermost and work outward using steps 2-4.

7. Order of Operations cont.. Step 2-Step 2- Simplify any numerical expressions containing exponents. Step 3-Step 3- Do multiplication and division as they occur from left to right. Step 4-Step 4- Do addition and subtraction as they occur from left to right.

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9. Why this order? Consider the following… An item is marked 3 for $12. You want to know how much you would pay for 2 of these items. 12  3  2 = Do you divide or multiply first...

10. If I give you four blue envelopes containing $5 each and one red envelope with a $10 bill. How much money do you have? If I give you one yellow envelope containing $10 and four green envelopes containing $5 each. How much money do you have? Consider the following: Did you come up with the same answer? How did you come up with your answers? Why did you multiply first?

11. Or how about this... You purchase a pair of boots for $30 and two shirts marked at $20 each with a tag for $5 off on each. You also return a pair of boots originally marked at $15 but purchased them with a $3 discount…How much do you owe? 30 + 2(20  5)  (15-3)=

12. Now that we know why…Lets try some... 12 + (6 + 4)= 12 + 10 = simplify parentheses first 12 +10 = 22 perform addition 3(5+1)  3 2 + 8  4 = Perform operations in ( ) 3(6)  3 2 + 8  4 = Simplify exponents 18  9 + 2 = Perform multiplication/division 9 + 2 = 11 Add or subtract as they occur

13. You try it... 30 + 4 ( 7  2) 2  5 30 + 4 ( 5) 2  5 30 + 4 (25)  5 30 + 100  5 30 + 20 50

14. Think about it.. Explain the difference between simplifying 6+9  3 & (6+9)  3 When using the order of operations under what conditions it it possible to get more than one correct answer?

15. Lets try the calculator To determine whether or not your calculator follows the rules for order of operations plug in …. 3 + 4  2 The result is 11, if your calculator shows 14 then it does not follow and you will have to adjust.

16. Quick review What is the correct order of operations? Parentheses Exponents Multiplication/Division from left to right Addition or Subtraction from left to right.

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