Ch 3_Student_Edition.pdf - Algebraic Expressions and Properties 3 3 3.1 Algebraic Algeb l b Expressions 3.2 Writing Expressions 3.3 Properties of

# Ch 3_Student_Edition.pdf - Algebraic Expressions and...

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Algebraic Expressions and Properties 3.1 Algebraic Expressions 3.2 Writing Expressions 3.3 Properties of Addition and Multiplication 3.4 The Distributive Property 5 6 4 3 2 1 10 12 8 6 4 2 15 18 12 9 6 3 20 24 16 12 8 4 25 30 20 15 10 5 30 36 24 18 12 6 1 2 3 4 5 6 5 6 4 3 2 1 5 6 4 3 2 1 10 12 8 6 4 2 15 18 12 9 6 3 20 24 16 12 8 4 25 30 20 15 10 5 30 36 24 18 12 6 1 2 3 4 5 6 5 6 4 3 2 1 “Did you know that 5 3 6 5 6 3 5, but 5 4 6 Þ 6 4 5?” “Only certain operations like addition and multiplication preserve equality when you switch the numbers around.” “Descartes, evaluate this expression when x 5 2 to determine the number of cat treats you are going to eat today.” “Remember that you evaluate an algebraic expression by substituting the value of x into the expression.” 3.1 Algeb 3 l b 3
Interpreting Numerical Expressions Example 1 Write a sentence interpreting the expression 3 × (19,762 + 418). 3 × (19,762 + 418) is 3 times as large as 19,762 + 418. Example 2 Write a sentence interpreting the expression (316 + 43,449) + 5. (316 + 43,449) + 5 is 5 more than 316 + 43,449. Example 3 Write a sentence interpreting the expression (20,008 752) ÷ 2. (20,008 752) ÷ 2 is half as large as 20,008 752. Write a sentence interpreting the expression. 1. 3 × (372 + 20,967) 2. 2 × (432 + 346,322) 3. 4 × (6722 + 4086) 4. (115 + 36,372) + 6 5. (392 + 75,325) + 78 6. (352 + 46,795) + 100 7. (30,929 + 425) ÷ 2 8. (58,742 721) ÷ 2 9. (96,792 + 564) ÷ 3 Example 4 Simplify 4 2 ÷ 2 + 3(9 5). First: P arentheses 4 2 ÷ 2 + 3(9 5) = 4 2 ÷ 2 + 3 4 Second: E xponents = 16 ÷ 2 + 3 4 Third: M ultiplication and D ivision (from left to right) = 8 + 12 Fourth: A ddition and S ubtraction (from left to right) = 20 Simplify the expression. 10. 3 2 + 5(4 2) 11. 3 + 4 ÷ 2 12. 10 ÷ 5 3 13. 4(3 3 8) ÷ 2 14. 3 6 4 ÷ 2 15. 12 + 7 3 24 i 3 (19 762 418) x 0 1 2 4 4 + x 5 6 “Great! You’re up to x = 2. Let’s keep going.” What You Learned Before
110 Chapter 3 Algebraic Expressions and Properties Algebraic Expressions 3.1 Work with a partner. a. You babysit for 3 hours. You receive \$12. What is your hourly wage? Write the problem. Underline the important numbers and units you need to solve the problem. Read the problem carefully a second time. Circle the key word for the question. Write each important number or word, with its units, on a piece of paper. Write + , , × , ÷ , and = on five other pieces of paper. Arrange the pieces of paper to answer the key word question, “What is your hourly wage?” Evaluate the expression that represents the hourly wage. hourly wage = ÷ Write. = Evaluate. So, your hourly wage is \$ per hour. b. How can you use your hourly wage to find how much you will receive for any number of hours worked? ACTIVITY: Reading and Re-Reading 1 How can you write and evaluate an expression that represents a real-life problem? You babysit for 3 hours. You receive \$12. What is your hourly wage? hourly wage (\$ per hour) Algebraic Expressions In this lesson, you will use order of operations to evaluate algebraic expressions.
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