1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 7.5 Order of Operations with Real Numbers

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Use the rules for order of operations to evaluate expressions.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Using the Rules for Order of Operations Rules for Order of Operations 1.Simplify within grouping symbols, such as parentheses ( ), brackets [ ], and braces { }, working from the innermost grouping outward. 2.Find any powers indicated by exponents. 3.Moving from left to right, perform any multiplications or divisions in the order they appear. 4.Moving from left to right, perform any additions or subtractions in the order they appear.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Notes Other grouping symbols are the absolute value bars (such as ), the fraction bar (as in ), and the square root symbol (such as ). Using the Rules for Order of Operations

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Notes Even though the mnemonic PEMDAS is helpful, remember that multiplication and division are performed as they appear, left to right. Also, addition and subtraction are performed as they appear, left to right. For example but Using the Rules for Order of Operations

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Order of Operations with Integers Use the rules for order of operations to evaluate each of the following expressions. Solution

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Order of Operations with Integers (cont.) Solution

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Order of Operations with Integers (cont.) Solution

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Order of Operations with Integers (cont.) Note: Because of the rules for order of operations at no time did we even subtract 9 − 2.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Completion Example 2: Order of Operations with Integers Evaluate the expression Solution

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Order of Operations with Fractions Use the rules for order of operations to evaluate each of the following expression.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Order of Operations with Fractions (cont.) Solution

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Order of Operations with Fractions (cont.) Solution exponents

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Order of Operations with Fractions (cont.) Divide, then multiply and reduce. Find the LCD. Add.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Use the rules for order of operations to evaluate each expression. 1. 2. 3. 4. 5.6.

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems (cont.) Simplify. 7.

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.38.62.  83.  27 4. 5.6. 7.