1. Copyright (c) 2010 Pearson Education, Inc. § 3.1 Translating English Phrases into Algebraic Expressions

2. Tobey & Slater, Beginning Algebra, 7e2 Translating Phrases into Expressions  multiplied by of product of times  less than decreased by smaller than fewer than shorter than difference of + greater than increased by more than added to sum of Represented by the Symbol: The English Phrase: Continued.

3. Tobey & Slater, Beginning Algebra, 7e3 Translating Phrases into Expressions ÷ divided by ratio of quotient of 33 triple 22 double Represented by the Symbol: The English Phrase: = is was has costs equals represents amount to

4. Tobey & Slater, Beginning Algebra, 7e4 Translating Phrases into Expressions Example: Write each English phrase as an algebraic expression. a.) Twelve more than a number x + 12 b.) Six less than one-third of the sum of a number and four

5. Tobey & Slater, Beginning Algebra, 7e5 “The necklace costs $45 more than the bracelet.” Comparing Quantities Let b + 45 = the cost of the necklace. Let b = the cost of the bracelet. $45 more than the bracelet An expression may be written for several quantities using the same variable. No explicit information about the bracelet. (independent variable)

6. Tobey & Slater, Beginning Algebra, 7e6 During the summer, Nancy read twice as many books as Andy. Marty read five more books than Andy. Expressions for Several Quantities Example: Use the letter A to write an algebraic expression for each quantity. Let 2A = the number of books Nancy read. Let A = the number of books Andy read. Twice as many as Andy Let 5 + A = the number of books Marty read. Five more than Andy

7. Tobey & Slater, Beginning Algebra, 7e7 Expressions for Several Quantities Example: Write an algebraic expression for each quantity. The first angle of a triangle is 20 degrees more than the third angle. The second angle is double the third angle. Let x + 20 = the first angle. Let x = the third angle. 20 degrees more than the third angle Let 2x = the second angle. Double the third angle x x + 20 2x2x

8. 1.Verbal Model – Ask Yourself what you need to know to solve the problem. Write a verbal model of what you need to know 2.Labels – Assign labels to each part of your verbal model. Assign variables to unknowns. 3.Algebraic Model – Use the labels to write an Algebraic Model based on your verbal model. 4.Solve – Solve the algebraic model and answer the original question. 5.Check – Check that your answer is reasonable. Solving “Real-Life” problems using Verbal Modeling