1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 7.8 Translating English Phrases and Algebraic Expressions

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Translate English Phrases into algebraic expressions. o Translate algebraic expressions into English phrases.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Translating English Phrases into Algebraic Expressions a.

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Translating English Phrases into Algebraic Expressions (cont.) b.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Translating English Phrases into Algebraic Expressions (cont.) c.

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Translating English Phrases into Algebraic Expressions (cont.) d.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Translating English Phrases into Algebraic Expressions (cont.) e.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Translating English Phrases into Algebraic Expressions (cont.) f. g.

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Translating English Phrases into Algebraic Expressions Notes In Example 1b, the phrase “the sum of z and 3” was translated as z + 3. If the expression had been translated as 3 + z, there would have been no mathematical error because addition is commutative. That is, z + 3 = 3 + z. However, in part e, the phrase “3 less than the product of a number and 5” must be translated as it was because subtraction is not commutative. Thus

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Translating English Phrases into Algebraic Expressions Notes (cont.) “3 less than 5 times a number” means 5n − 3 while “5 times a number less than 3” means 3 − 5n and “3 less 5 times a number” means 3 − 5n. Therefore, be very careful when writing and/or interpreting expressions indicating subtraction. Be sure that the subtraction is in the order indicated by the wording in the problem. The same is true with expressions involving division.

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Write an English phrase that indicates the meaning of each algebraic expression. Algebraic Expression Possible English Phrase Example 2: Translating Algebraic Expressions to English Phrases the product of 5 and a number twice a number increased by 8 three times the difference between a number and 2

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Translating English Phrases to Algebraic Expressions Change each phrase into an equivalent algebraic expression. English Phrase Algebraic Expression

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. English Phrase Algebraic Expression Example 3: Translating English Phrases to Algebraic Expressions (cont.)

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems Change the following phrases to algebraic expressions. 1.7 less than a number 2. the quotient of y and 5 3.14 more than 3 times a number Change the following algebraic expressions into English phrases. (There may be more than one correct translation.) 4. 10 − x 5. 2(y – 3)6. 5n + 3n

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1. 2. 3. 3y + 14 4. 10 decreased by a number 5. twice the difference between a number and 3 6. 5 times a number plus 3 times the same number