Name Class Date Translating Between Words and Math Going Deeper Essential question: How do you write algebraic expressions? 2-2 1 CC.6.EE.2a EXPLORE Writing Expressions from Models video tutor Write a description in words for each situation. Then write an algebraic expression from the description. Use x as the variable. A Andrew has a bag containing an unknown number of counters. He reaches in and removes 5 counters. Description in Words Algebraic Expression B Mercedes folds a piece of paper in half. Description in Words Algebraic Expression REFLECT 1a. What are some words that can describe addition and subtraction? 1b. What are some words that can describe multiplication and division? 1c. Write three algebraic expressions that represent the phrase 5 times y. TRY THIS! 1d. 8 fewer than m 1e. the product of 10 and c Chapter 2 51 Lesson 2
Expressions can be written with constants and variables, or they may be described in words. When given an expression in words, it is important to be able to translate the words into algebra. There are several different ways to describe expressions with words. Operation Addition Subtraction Multiplication Division Words added to plus sum more than subtracted from minus difference less than take away taken from times multiplied by product groups of divided by divided into quotient 2 CC.6.EE.2a EXAMPLE Writing Algebraic Expressions A 5 subtracted from y The operation is. The algebraic expression is y 5. B The product of 9 and p The operation is. The algebraic expression is. TRY THIS! 2a. n times 7 2b. 4 minus y 2c. 13 added to x 2d. x divided by 9 2e. 9 divided by x 2f. c plus 3 REFLECT 2g. Error Analysis Erica wrote 5 added to y as 5 + y and 5 subtracted from y as 5 y. Why is the first expression correct but the second incorrect? When is order important in writing an expression? Chapter 2 52 Lesson 2
When solving real-world problems, you may need to identify the action taking place to know which operation to use. Action Put parts together Put equal parts together Find how much more or less Separate into equal parts Operation Addition Multiplication Subtraction Division 3 CC.6.EE.2 EXAMPLE Translating Words into Algebraic Expressions Center City is 10 miles farther from Sam s house than Westonville is. Write an algebraic expression to represent the distance from Sam s house to Center City. Let w represent the distance from Sam s house to Westonville. The distance from Sam s house to Center City is 10 miles more / less than w. So, to find the distance from Sam s house to Center City, put together and. Which operation represents this action? The distance from Sam s house to Center City can be represented by the expression. TRY THIS! 3a. Sonia worked 25 hours last week. She was paid the same amount of money per hour that she worked. Let h represent Sonia s hourly pay. Write an algebraic expression that represents Sonia s total pay last week. 3b. Noah is saving to buy a new laptop computer. He has saved $119 so far. Let c represent the cost of the laptop. Write an algebraic expression that represents the amount of money Noah still needs to save. REFLECT 3c. What If? Suppose Center City was 10 miles closer to Sam s house than Westerville. How would the expression you wrote in 3 change? 3d. Are the expressions w 10 and 10 w equivalent expressions? Explain. Chapter 2 53 Lesson 2
practice 1. n divided by 8 2. p multiplied by 4 3. 3 groups of w 4. the sum of 1 and q 5. the quotient of 13 and z 6. c added to 45 7. h less than 30 8. 47 subtracted from m Write a phrase in words for each algebraic expression. 9. m + 8 10. 42s 11. 12 v 12. t 29 13. 32 r 14. 9b 15. 20 16. k + 32 d 17. Kai s score on a test was 12 points greater than Julia s score. Let k represent Kai s score. Write an algebraic expression to represent Julia s score. 18. The town of Rayburn received 6 more inches of snow than the town of Greenville. Let g represent the amount of snow in Greenville. Write an algebraic expression to represent the amount of snow in Rayburn. 19. Abby baked 48 cookies and divided them evenly into bags. Let b represent the number of bags. Write an algebraic expression to represent the number of cookies in each bag. 20. Eli is driving at a speed of 55 miles per hour. Let h represent the number of hours that Eli drives at this speed. Write an algebraic expression to represent the number of miles that Eli travels during this time. 21. Explain the difference between b divided by 10 and b divided into 10. Chapter 2 54 Lesson 2
Name Class Date 2-2 Additional Practice 1. Terry s essay has 9 more pages than Stacey s essay. If s represents the number of pages in Stacey s essay, write an expression for the number of pages in Terry s essay. 2. Let z represent the number of students in a class. Write an expression for the number of students in 3 equal groups. Write each phrase as a numerical or algebraic expression. 3. 24 multiplied by 3 4. n multiplied by 14 5. w added to 64 6. the difference of 58 and 6 7. m subtracted from 100 8. the sum of 180 and 25 9. the product of 35 and x 10. the quotient of 63 and 9 11. 28 divided by p Write two phrases for each expression. 12. n 91 13. 35 r 14. 20 s 15. Charles is 3 years older than Paul. If y represents Paul s age, what expression represents Charles s age? 16. Maya bought some pizzas for $12 each. If p represents the number of pizzas she bought, what expression shows the total amount she spent? Chapter 2 55 Practice and Problem Solving
Problem Solving Write the correct answer. 1. Holly bought 10 comic books. She gave a few of them to Kyle. Let c represent the number of comic books she gave to Kyle. Write an expression for the number of comic books Holly has left. 3. The temperature dropped 5 F, and then it went up 3 F. Let t represent the beginning temperature. Write an expression to show the ending temperature. 2. Last week, Peter worked 40 hours for $15 an hour. Write a numerical expression for the total amount Peter earned last week. Write an algebraic expression to show how much Peter earns in h hours at that rate. 4. Teri baked 48 cookies and divided them evenly into bags. Let n represent the number of cookies Teri put in each bag. Write an expression for the number of bags she filled. Circle the letter of the correct answer. 5. Marisa purchased canned soft drinks for a family reunion. She purchased 1 case of 24 cans and several packages containing 6 cans each. If p represents the number of 6-can packages she purchased, which of the following expressions represents the total number of cans Marisa purchased for the reunion? A 24 + 6p B 24 6p C 6 + 24p D 6 24p 7. Mei bought several CDs for $12 each. Which of the following expressions could you use to find the total amount she spent on the CDs? A 12 + x B 12 x C 12x D 12 x 6. Becky has the addresses of many people listed in her e-mail address book. She forwarded a copy of an article to all but 5 of those people. If a represents the number of addresses, which of the following expressions represents how many people she sent the article to? F a + 5 G 5a H a 5 J a 5 8. Tony bought 2 packs of 50 plates and 1 pack of 30 plates. Which of the following expressions could you use to find the total number of plates Tony bought? F 2 + 50 + 30 G (2 50) + 30 H (2 30) + 50 J 2(30 + 50) Chapter 2 56 Practice and Problem Solving