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