1-2 Order of Operations and Evaluating Expressions Vocabulary Review To simplify a numerical expression means to replace it with its single numerical value. Circle the simplified form of each expression. 1. 2 3 4 432 64 9 24 1 12 18 362 16 7 4 5 10 19 2. 12 36 36 2 3. 16 4 7 1 Vocabulary Builder exponent POW er power Related Words: base, exponent 7 2 base Definition: A power is a number that can be expressed using a base and an exponent. Main Idea: Powers provide a shorthand way for showing repeated multiplication. Example: The diagram above shows a power, its base, and its exponent. You can read the expression as, “seven to the second power.” Use Your Vocabulary 4. Circle the expression that shows a base of 7 and an exponent of 3. 37 7(3) 3 7 73 5. Underline the correct word to complete the sentence. A(n) exponent / power is a number that can be expressed using a base and an exponent. 6. For each expression, underline the base, circle the exponent, and draw a box around the power. 25 Chapter 1 4x wz m7 6 Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. power (noun) Problem 1 Simplifying Powers Got It? What is the simplified form of 34 ? 7. Follow the steps to find the simplified form of the expression. 1 2 3 Identify the base and the exponent in the expression 3 4. base: exponent: Expand the expression to show the repeated multiplication indicated by the exponent. Ƃ Ƃ Ƃ 3 4 Write the simplified form of the expression 3 4. 3 4 Key Concept Order of Operations 1. Perform any operation(s) inside grouping symbols, such as parentheses ( ) and brackets [ ]. A fraction bar also acts as a grouping symbol. 2. Simplify powers. Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. 3. Multiply and divide in order from left to right. 4. Add and subtract in order from left to right. Problem 2 Simplifying a Numerical Expression Got It? What is the simplified form of 5 ? 7 2 42 4 2? 8. Circle the part of the expression that you should simplify first. 5 ? 7 2 42 4 2 9. Without simplifying the expression, explain how you know that subtraction will be the last operation. _______________________________________________________________________ _______________________________________________________________________ 10. Simplify 5 ? 7 2 42 4 2. Show and justify each step. 7 Lesson 1-2 Problem 3 Evaluating Algebraic Expressions Got It? What is the value of the expression when a 3 and b 4? 3b a2 11. 3b a2 3 2 12. 13. 14. Substitute 3 for a and 4 for b. 2 Multiply. Simplify the power. Subtract. Problem 4 Evaluating a Real-World Expression 1 the cost of the items Got It? The shipping cost for an order at an online store is 10 you order. What is an expression for the total cost of a given order? What are the total costs for orders of $43, $79, $95, and $103? 15. Complete the model. Define total cost of an order is the shipping costs: the cost of plus 1 Ƃ the cost of the items the items 10 Let c â the cost of the items. total cost Write â à Ƃ 16. Use the model to complete the table for each value of c. Cost of Items Chapter 1 Shipping Cost Total Cost of Order $43 1 Ƃ 10 $43 $4.30 $43 $4.30 $ $79 1 Ƃ 10 $79 $ $79 $7.90 $ $95 1 Ƃ 10 $95 $ $95 $ $103 1 Ƃ 10 $103 $ $103 $ 8 $104.50 $ Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. Relate Lesson Check t Do you UNDERSTAND? Error Analysis A student simplifies an expression as shown below. Find the error and simplify the expression correctly. ï 17. What operation did the student do first? Is this correct? Explain. _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ 18. What operation did the student do next? Is this correct? Explain. _______________________________________________________________________ _______________________________________________________________________ Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. 19. Now simplify the expression 23 8 2 32 correctly. Math Success Check off the vocabulary words that you understand. power exponent base simplify evaluate Rate how well you can evaluate expressions using the Order of Operations. Need to review 0 2 4 6 8 Now I get it! 10 9 Lesson 1-2

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