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(2) 1-1. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____. NAME ______________________________________________ DATE______________ PERIOD _____. 1-1. Word Problem Practice. Enrichment. Toothpick Triangles. BLOCKS For Exercises 5–7, use the following information. A toy manufacturer produces a set of blocks that can be used by children to build play structures. The product packaging team is analyzing different arrangements for packaging their blocks. One idea they have is to arrange the blocks in the shape of a cube, with b blocks along one edge.. Figure 2. Figure 3. 3; 5; 7. b. 2. How many toothpicks does it take to make up the perimeter of each image?. 3; 4; 5. b. 10. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. 7. The team finally decides that their favorite package arrangement is to take 2 layers of blocks off the top of a cube measuring b blocks along one edge. Write an expression representing the number of blocks left behind after the top two layers are removed. b 3 2b 2 or (b 2) b 2. 2. Chapter 1. 6. The packaging team decides to take one layer of blocks off the top of this package. Write an expression representing the number of blocks in the top layer of the package. b 2. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 4. TIDES The difference between high and low tides along the Maine coast in November is 19 feet on Monday and x feet on Tuesday. Write an expression to show the average rise and fall of the tide 19 x for Monday and Tuesday. . 3. Sketch the next three figures in the pattern.. b3. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 6136 or about 198 shows per year y. 5. Write an expression representing the total number of blocks packaged in a cube measuring b blocks on one edge.. Figure 4. (Lesson 1-1). A4. 3. THEATER Howard Hughes, Professor Emeritus of Texas Wesleyan College, reportedly attended a record 6136 theatrical shows. Write an expression to represent the average number of theater shows attended if he accumulated the record over y years. Use the expression to find the average number of shows Mr. Hughes attended per year if he went to the theater for 31 years.. Figure 5. Figure 6. 4. Continue the pattern to complete the table. Image Number. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Number of toothpicks. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21. Number of toothpicks in Perimeter. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 5. Let the variable n represent the figure number. Write an expression that can be used to find the number of toothpicks needed to create figure n. 2n 1 6. Let the variable n represent the figure number. Write an expression that can be used to find the number of toothpicks in the perimeter of figure n. n 2. Chapter 1. 11. Glencoe Algebra 1. Page A4. 1. How many toothpicks does it take to create each figure? b. 10:26 AM. Figure 1. Lesson 1-1. Variable expressions can be used to represent patterns and help solve problems. Consider the problem of creating triangles out of toothpicks shown below.. Answers. 2. TECHNOLOGY There are 1024 bytes in a kilobyte. Write an expression that describes the number of bytes in a computer chip with n kilobytes. 1024 n or 1024n. 5/10/06. Variables and Expressions 1. SOLAR SYSTEM It takes Earth about 365 days to orbit the sun. It takes Uranus about 85 times as long. Write a numerical expression to describe the number of days it takes Uranus to orbit the sun. 365 85.
(3) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. NAME ______________________________________________ DATE______________ PERIOD _____. 1-2 1-2. Lesson Reading Guide Order of Operations. Study Guide and Intervention. Evaluate Rational Expressions. Numerical expressions often contain more than one operation. To evaluate them, use the rules for order of operations shown below.. Read the introduction to Lesson 1-2 in your textbook.. Order of Operations. represents the number of hours over 100 used by Nicole in a given month.. Step Step Step Step. Example 1. Read the Lesson. 1 2 3 4. Evaluate expressions inside grouping symbols. Evaluate all powers. Do all multiplication and/or division from left to right. Do all addition and/or subtraction from left to right.. parentheses, brackets, braces, and fraction bars. Multiply 2 and 4. Add 7 and 8. Subtract 4 from 15.. b. 3(2) 4(2 6) 3(2) 4(2 6) 3(2) 4(8) 6 32. 2. What does evaluate powers mean? Use an example to explain.. Sample answer: To evaluate a power means to find the value of the power. To evaluate 43, find the value of 4 4 4.. 38. 3 23 4 3 38 3 23 42 3 42 3. Add 2 and 6.. 19 3 4 62. e. multiplication 51 729 9. f. evaluate powers 2. Remember What You Learned. Glencoe Algebra 1. 4. The sentence Please Excuse My Dear Aunt Sally (PEMDAS) is often used to remember the order of operations. The letter P represents parentheses and other grouping symbols. Write what each of the other letters in PEMDAS means when using the order of operations.. E—exponents (powers), M—multiply, D—divide, A—add, S—subtract. 12. Answers. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. d. 69 57 3 16 4 division. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. c. 17 3 6 multiplication. Find 4 squared. Add 2 and 16. Multiply 3 and 18.. Multiply left to right. Add 6 and 32.. Evaluate power in numerator.. 11 42 3. Add 3 and 8 in the numerator.. 11 16 3. Evaluate power in denominator.. 11 48. . Multiply.. Exercises Evaluate each expression. 1. (8 4) 2 8. 2. (12 4) 6 96. 3. 10 2 3 16. 4. 10 8 1 18. 5. 15 12 4 12. 6. 3. 7. 12(20 17) 3 6 18. 8. 24 3 2 32 7. 9. 82 (2 8) 2 6. 4(52) 4 3 4(4 5 2). 16. 1. Chapter 1. 8(2) 4 84. 4 32 12 1. 12. 6. 2 42 82 (5 2) 2. 15. 2 35. 52 3 1 20(3) 2(3) 3. 18. 3. 10. 32 3 22 7 20 5 27 11. 1 13. 250 [5(3 7 4)] 2. 15 60 30 5. 14. 2 17. . 13. 4 32 3 2. 82 22 (2 8) 4. Glencoe Algebra 1. (Lesson 1-2). A5. b. 26 8 14 subtraction. Divide 12 by 3.. b. 2. 3. Read the order of operations on page 11 in your textbook. For each of the following expressions, write addition, subtraction, multiplication, division, or evaluate powers to tell what operation to use first when evaluating the expression. a. 400 5[12 9] addition. Evaluate each expression.. a. 3[2 (12 3)2] 3[2 (12 3)2] 3(2 42) 3(2 16) 3(18) 54. Answers. a. 7 2 4 4 7244784 15 4 11. 1. The first step in evaluating an expression is to evaluate inside grouping symbols. List four types of grouping symbols found in algebraic expressions.. Example 2. Evaluate each expression.. Page A5. 4.95 represents the 0.99 represents the cost of each additional hour after 100 hours, and (117 100) In the expression 4.95 0.99(117 100),. regular monthly cost of internet service,. Chapter 1. 10:26 AM. Order of Operations. Get Ready for the Lesson. Lesson 1-2. 1-2. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(4) 1-2. Study Guide and Intervention. NAME ______________________________________________ DATE______________ PERIOD _____. 1-2 1-2. (continued). Order of Operations. Skills Practice. 5/10/06. Order of Operations Evaluate each expression.. Evaluate Algebraic Expressions. Algebraic expressions may contain more than one operation. Algebraic expressions can be evaluated if the values of the variables are known. First, replace the variables with their values. Then use the order of operations to calculate the value of the resulting numerical expression.. 2. (9 2) 3 21. 3. 4 6 3 22. 4. 28 5 4 8. 5. 12 2 2 16. 6. (3 5) 5 1 41. 7. 9 4(3 1) 25. 8. 2 3 5 4 21. Evaluate x3 5( y 3) if x 2 and y 12. 23 5(12 3) 8 5(12 3) 8 5(9) 8 45 53. Replace x with 2 and y with 12. Evaluate 23. Subtract 3 from 12. Multiply 5 and 9. Add 8 and 45.. The solution is 53.. 4 5. 3 5. 4. x3 y z2 27. 5. 6a 8b 9 . 6. 23 (a b) 21 . 8. 2xyz 5 53. 9. x(2y 3z) 36. 10. (10x)2 100a 480. z2 y2 7 4 x. 7 8. 25ab y xz. 16. 1 . 2. Chapter 1. 冢 yz 冣. . 1. 2. 13 16. 5a2b 16. 3 5. 21 12. a2 2b 1 25 (z y)2 1 x 2. 15. . 3 5. 18. (z x)2 ax 5 . 17. 25 y. 6 xz y 2z 11. 20. . 14. 冢 z y x 冣 冢 y z x 冣. 1 24. 21. 1 . Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. 冢 xz 冣. 3xy 4 11. 7x. 14. 6xz 5xy 78. 13. 2. 19. . 3 5. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. y2 9. 7. 2 x 4. 3. x y2 11. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 2. 3x 5 1. 11. 14 7 5 32 1. 12. 6 3 7 23 22. 13. 4[30 (10 2) 3] 24. 14. 5 [30 (6 1)2] 10. 15. 2[12 (5 2)2] 42. 16. [8 2 (3 9)] [8 2 3] 6. Evaluate each expression if x 6, y 8, and z 3. 17. xy z 51. 18. yz x 18. 19. 2x 3y z 33. 20. 2(x z) y 10. 21. 5z ( y x) 17. 22. 5x ( y 2z) 16. 23. x2 y2 10z 70. 24. z3 ( y2 4x) 67. y xz 2. 25. 13. Chapter 1. 3y x2 z. 26. 20. 15. Glencoe Algebra 1. (Lesson 1-2). A6. 1. x 7 9. 10. 10 2 6 4 26. Lesson 1-2. Exercises Evaluate each expression if x 2, y 3, z 4, a , and b .. 9. 30 5 4 2 12. Answers. x3 5( y 3) . Page A6. 1. (5 4) 7 63. 10:26 AM. Example. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(5) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. NAME ______________________________________________ DATE______________ PERIOD _____. 1-2 1-2. Practice Order of Operations 2. 9 (3 4) 63. 3. 5 7 4 33. 4. 12 5 6 2 5. 5. 7 9 4(6 7) 11. 6. 8 (2 2) 7 14. 7. 4(3 5) 5 4 12. 8. 22 11 9 32 9. 9. 62 3 7 9 48. 10. 3[10 (27 9)] 21. 11. 2[52 (36 6)] 62. 12. 162 [6(7 4)2] 3. 52 4 5 4 2 5(4). 5t 100; 1400 students. 7 32 1 4 2 2. (2 5)2 4 3 5. 14. 26 2. 15. 2. 17. b2 2a c2 89. 18. 2c(a b) 168. 19. 4a 2b . 20. (a2 4b) c 8. 21. c2 (2b a) 96. 50. 2s 671; 8749 ft. 2c3 ab 4. 22. 39. 23. 5. 2(a b)2 9 24. 5c 10. b2 2c2 25. acb. Ann Carlyle is planning a business trip for which she needs to rent a car. The car rental company charges $36 per day plus $0.50 per mile over 100 miles. Suppose Ms. Carlyle rents the car for 5 days and drives 180 miles. 26. Write an expression for how much it will cost Ms. Carlyle to rent the car.. 5(36) 0.5(180 100) 27. Evaluate the expression to determine how much Ms. Carlyle must pay the car rental company. $220.00. GEOMETRY For Exercises 28 and 29, use the following information.. Glencoe Algebra 1. The length of a rectangle is 3n 2 and its width is n 1. The perimeter of the rectangle is twice the sum of its length and its width.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. CAR RENTAL For Exercises 26 and 27, use the following information.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 7. 3. TRANSPORTATION The Plaid Taxi Cab Company charges $1.75 per passenger plus $3.45 per mile for trips less than 10 miles. Write and evaluate an expression to find the cost for Max to take a Plaid taxi 8 miles to the airport.. 6–8, use the following information. During a long weekend, Devon paid a total of x dollars for a rental car so he could visit his family. He rented the car for 4 days at a rate of $36 per day. There was an additional charge of $0.20 per mile after the first 200 miles driven. 6. Write an algebraic expression to represent the amount Devon paid for additional mileage only. x – (36 4). $1.75 $3.45m; $29.35. 7. Write an algebraic expression to represent the number of miles over 200 miles that Devon drove the rented car.. 4. GEOMETRY The area of a circle is related to the radius of the circle such that the product of the square of the radius and a number gives the area. Write and evaluate an expression for the area of a circular pizza below. Approximate as 3.14.. x – (36 4) 0.20. 8. How many miles did Devon drive overall if he paid a total of $174 for the car rental? 350 mi. r 2; 153.86 in2. 7 in.. 28. Write an expression that represents the perimeter of the rectangle.. 2[(3n 2) (n 1)] 29. Find the perimeter of the rectangle when n 4 inches. 34 in. Chapter 1. 16. Answers. Glencoe Algebra 1. Chapter 1. 17. Glencoe Algebra 1. (Lesson 1-2). A7. bc2 a c. c2. CONSUMER SPENDING For Exercises. Answers. 2. GEOGRAPHY Guadalupe Peak in Texas has an altitude that is 671 feet more than double the altitude of Mount Sunflower in Kansas. Write and evaluate an expression for the altitude of Guadalupe Peak if Mount Sunflower has an altitude of 4039 feet.. Evaluate each expression if a 12, b 9, and c 4. 16. a2 b c2 137. 5. BIOLOGY Lavania is studying the growth of a population of fruit flies in her laboratory. She notices that the number of fruit flies in her experiment is five times as large after any six-day period. She observes 20 fruit flies on October 1. Write and evaluate an expression to predict the population of fruit flies Lavania will observe on October 31. 20 55; 62,500 flies. Page A7. 1. (15 5) 2 20. 1. SCHOOLS Jefferson High School has 100 less than 5 times as many students as Taft High School. Write and evaluate an expression to find the number of students at Jefferson High School if Taft High School has 300 students.. 10:26 AM. Order of Operations. Evaluate each expression.. 13. 1. Word Problem Practice. Lesson 1-2. 1-2. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(6) NAME ______________________________________________ DATE______________ PERIOD _____. 1-2 1-2. Enrichment. Graphing Calculator Activity. The Four Digits Problem. Answers will vary. Sample answers are given.. (4 3) (2 1). 19 3(2 4) 1. 3. (4 3) (2 1). 20 . 4. (4 2) (3 1). 5. (4 2) (3 1). 6. 4312. 8 9. 4 2 (3 1). 10 . 4321. 21 (4 3). 37 . 31 2 4. 21 . (4 3) (2 1). 38 . 42 (3 1). 22 . 21 (4 3). 39 . 42 (3 1). 40 . 41 (3 2). 41 . 43 (2 1). 42 . 43 (2 1). 23 31 (4 2) 24 . (2 4) (3 1). 25 (2 3) (4 1) 24 (3 1) 26 . 43 42 13. 27 . 3 (4 1). 44 . 43 (2 1). 28 . 21 3 4. 45 . 43 (2 1). 29 . 2(4 +1) 3. 46 . 43 (2 1). 2. 11 (4 3) (2 1) 12 (4 3) (2 1) 13 (4 3) (2 1) 14 (4 3) (2 1). 30 (2 3) (4 1) 34 (2 1) 31 . 47 . 31 42. 48 . 4 (3 1) 2. 15 . 2(3 4) 1. 32 . 42 (3 1). 49 . 41 23. 16 . (4 2) (3 1). 33 . 21 (3 4). 50 . 41 32. 17 . 3(2 4) 1. 34 . 2 (14 3). Example 2. 4y 5x. Evaluate xy if x 4 and y 12.. Evaluate the expression and display the answer as a fraction. ALPHA [:] 12 STO ALPHA [Y] ALPHA [:] Keystrokes: 4 STO ( 4 ALPHA [Y] ) ) ALPHA [Y] — ( 5 MATH 1 ENTER . Exercises Evaluate each expression if a = 4, b = 6, x = 8, and y = 12. For Exercises 4-6, express answers as fractions. 1. bx ay b. 40. a2. b 4. 2 2 x b. 11 14. 2. a[ x (y a)2]. 3. a3 (y b)2 x2. 2a(x b) 5. . b 3 a b 5b 6. . 68. 92 3. xy 9b. 2 3. 22 7. [ (. ). 2. ]. y a(x 1). Answers will vary. Using a calculator is a good way to check your solutions.. Chapter 1. 18. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. Does a calculator help in solving these types of puzzles? Give reasons for your opinion.. You can also use a colon, which is the ALPHA function above the decimal key, to chain commands together. This process is called concatenation. Using the colon in Example 1, the keystrokes become 8 STO ALPHA [A] ALPHA [:] ALPHA [A] x 2 — 4 ALPHA [A] + 6 ENTER .. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 3(4 1) 2 4321. 34 (2 1). Chapter 1. 19. Glencoe Algebra 1. (Lesson 1-2). A8. 7. 36 . Answers. 2. 35 2(4 +1) 3. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. (2 3) (4 1). Page A8. Example 1 Evaluate a2 4a 6 if a 8. Store 8 as the value for a. Keystrokes: 8 STO ALPHA [A] ENTER Enter the expression and press ENTER to evaluate. Keystrokes: ALPHA [A] x 2 — 4 ALPHA [A] + 6 ENTER. Express each number as a combination of the digits 1, 2, 3, and 4. 18 . Key. 10:26 AM. One well-known mathematic problem is to write expressions for consecutive numbers beginning with 1. On this page, you will use the digits 1, 2, 3, and 4. Each digit is used only once. You may use addition, subtraction, multiplication (not division), exponents, and parentheses in any way you wish. Also, you can use two digits to make one number, such as 12 or 34.. 1 (3 1) (4 2). STO. 5/10/06. Using The. When evaluating algebraic expressions, it is sometimes helpful to use the store key STO on the calculator, especially to check solutions.. Lesson 1-2. 1-2. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(7) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. NAME ______________________________________________ DATE______________ PERIOD _____. 1-3 1-3. Lesson Reading Guide. Study Guide and Intervention. Open Sentences. Solve Equations. How is the open sentence different from the expression 15.50 5n?. The open sentence has two expressions joined by the symbol.. Example 1 Find the solution set of 3a 12 39 if the replacement set is {6, 7, 8, 9, 10}.. Read the Lesson 1. How can you tell whether a mathematical sentence is or is not an open sentence?. An open sentence must contain one or more variables.. Replace a in 3a 12 39 with each value in the replacement set.. 2. How would you read each inequality symbol in words? Words. is less than. is greater than is less than or equal to. is greater than or equal to. a. Describe how you would find the solutions of the equation.. Replace n with each member of the replacement set. The members of the replacement set that make the equation true are the solutions. b. Describe how you would find the solutions of the inequality.. Replace n with each member of the replacement set. The members of the replacement set that make the inequality true are the solutions. c. Explain how the solution set for the equation is different from the solution set for the inequality.. The solution set for the equation contains only one number, 3. The solution set for the inequality contains the four numbers 0, 1, 2, and 3.. Glencoe Algebra 1. Remember What You Learned 4. Look up the word solution in a dictionary. What is one meaning that relates to the way we use the word in algebra?. Sample answer: answer to a problem 20. Answers. 8 b Simplify. 9. false false. 8 9. The solution is .. true false. Glencoe Algebra 1. Exercises Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 3. Consider the equation 3n 6 15 and the inequality 3n 6 15. Suppose the replacement set is {0, 1, 2, 3, 4, 5}.. Chapter 1. 2(4) b Add in the numerator; subtract in the denominator. 3(3). false. 1. . 1. Find the solution of each equation if the replacement sets are X , , 1, 2, 3 4 2 and Y {2, 4, 6, 8}. 1 2. 5 2. 1. x {2}. 2. x 8 11 {3}. 3. y 2 6 {8}. 4. x2 1 8 {3}. 5. y2 2 34 {6}. 6. x2 5 5 . 12 . 7. 2(x 3) 7 . 1 4. 9 4. 8. ( y 1)2 {2}. 1 16. 14 . 9. y2 y 20 {4}. Solve each equation. 10. a 23 1 7 1 4. 5 8. 7 8. 11. n 62 42 20 18 3 23. 12. w 62 32 324 15 6 27 24. 13. k . 14. p 3. 15. s 3. 16. 18.4 3.2 m 15.2. 17. k 9.8 5.7 15.5. 18. c 3 2 5 . Chapter 1. 21. 1 2. 1 4. 3 4. Glencoe Algebra 1. (Lesson 1-3). A9. . 2(3 1) b Original equation 3(7 4). Since a 9 makes the equation 3a 12 39 true, the solution is 9. The solution set is {9}.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 2(3 1) 3(7 4). Solve b.. Answers. 3(6) 12 39 → 30
(8) 39 3(7) 12 39 → 33
(9) 39 3(8) 12 39 → 36
(10) 39 3(9) 12 39 → 39 39 3(10) 12 39 → 42
(11) 39. Example 2. Page A9. A mathematical sentence with one or more variables is called an open sentence. Open sentences are solved by finding replacements for the variables that result in true sentences. The set of numbers from which replacements for a variable may be chosen is called the replacement set. The set of all replacements for the variable that result in true statements is called the solution set for the variable. A sentence that contains an equal sign, , is called an equation.. Read the introduction to Lesson 1-3 in your textbook.. Inequality Symbol. 10:26 AM. Open Sentences. Get Ready for the Lesson. Lesson 1-3. 1-3. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(12) Study Guide and Intervention. NAME ______________________________________________ DATE______________ PERIOD _____. 1-3 1-3. (continued). Open Sentences. → → → → →. 4 10 7 10 10 10 13 10 16 10. false false false true true. Since replacing a with 7 or 8 makes the inequality 3a 8 10 true, the solution set is {7, 8}. Exercises Find the solution set for each inequality if the replacement set is X {0, 1, 2, 3, 4, 5, 6, 7}. 2. x 3 6. {3, 4, 5, 6, 7}. 3. 3x 18. {0, 1, 2, 3, 4, 5, 6, 7}. {7}. x 5. 2 5. 3x 6. 2 8. 7. 3x 4 5. 8. 3(8 x) 1 6. 9. 4(x 3) 20. {4, 5, 6, 7}. no numbers. {4, 5, 6, 7}. {7}. {0, 1, 2, 3, 4, 5} {2, 3, 4, 5, 6, 7}. Find the solution set for each inequality if the replacement sets are. 14. . 1 2. X , , 1, 2, 3, 5, 8 and Y {2, 4, 6, 8, 10}. 10. x 3 5. 11. y 3 6. {3, 5, 8}. {2, 4, 6, 8, 10}. x 2. 13. 4. 16. 4x 1 4. 1 19. 3x 2 4. 1 1 , 4 2. Chapter 1. . 15. 2. {8, 10}. {2, 4}. 17. 3x 3 12. 18. 2( y 1) 18. 20. 3y 2 8. 1 21. (6 2x) 2 3 2. {3, 5, 8}. {2}. {8, 10}. {2, 3, 5, 8} 22. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. {1, 2, 3, 5, 8}. {6, 8, 10} 2y 5. 14. 2. 14, 12, 1, 2, 3, 5. . y 4. 12. 8y 3 51. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. x 4. 1 3. 4. 3b 15 48 11. 5. 4b 12 28 10. 6. 3 0 12. 36 b. Find the solution of each equation using the given replacement set. 1 2. 5 4. 冦 12. 3 4. 5 4. 冧. 3 4. 2 3. 1 4. 5 6. 冦 23. 3 5 4 4 4 3. 冧. 13 9. 冦 49. 5 2 7 9 3 9. 冧. 7 9. 8. x ; , , , . 7. x ; , , 1, . 4 3. 9. (x 2) ; , , , . 10. 0.8(x 5) 5.2; {1.2, 1.3, 1.4, 1.5} 1.5. Solve each equation. 11. 10.4 6.8 x 3.6. 12. y 20.1 11.9 8.2 6 18 31 25. 46 15 3 28. 14. c 4. 2(4) 4 3(3 1). 16. n 1. 13. a 1. 15. b 2. 6(7 2) 3(8) 6. Find the solution set for each inequality using the given replacement set. 17. a 7 13; {3, 4, 5, 6, 7} {3, 4, 5}. 18. 9 y 17; {7, 8, 9, 10, 11} {7}. 19. x 2 2; {2, 3, 4, 5, 6, 7} {2, 3, 4}. 20. 2x 12; {0, 2, 4, 6, 8, 10} {8, 10}. 21. 4b 1 12; {0, 3, 6, 9, 12, 15}. 22. 2c 5 11; {8, 9, 10, 11, 12, 13} {8}. {3, 6, 9, 12, 15} y 2. 23. 5; {4, 6, 8, 10, 12} {10, 12} Chapter 1. x 3. 24. 2; {3, 4, 5, 6, 7, 8} {7, 8}. 23. Glencoe Algebra 1. (Lesson 1-3). A10. 1. x 2 4. 3. 7a 21 56 5. Answers. 873946 Alg1 CH01 EP3. ?. 10 ?. 10 ?. 10 ?. 10 ?. 10. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 8 8 8 8 8. 2. 4a 8 16 6. Page A10. . 1. 5a 9 26 7. 10:26 AM. Find the solution set for 3a 8 10 if the replacement set is {4, 5, 6, 7, 8}.. Replace a in 3a 8 10 with each value in the replacement set. 3(4) 3(5) 3(6) 3(7) 3(8). 5/10/06. Open Sentences Find the solution of each equation if the replacement sets are A {4, 5, 6, 7, 8} and B {9, 10, 11, 12, 13}.. Solve Inequalities An open sentence that contains the symbol , , , or is called an inequality. Inequalities can be solved the same way that equations are solved. Example. Skills Practice. Lesson 1-3. 1-3. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(13) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. NAME ______________________________________________ DATE______________ PERIOD _____. 1-3 1-3. Practice. Word Problem Practice. Open Sentences. . . 4. 7b 8 16.5 3.5. 5. 120 28a 78 . 3 2. 3. 6a 18 27 . 3 2. 28 b. 6. 9 16 4. Find the solution of each equation using the given replacement set. 7 8. 17 12. 冦 12. 13 7 5 2 24 12 8 3. 冧. 13 24. 3 4. 冦 12. 1 2. 1 2. 冧. 1 2. 10. 12(x 4) 76.8 ; {2, 2.4, 2.8, 3.2, 3.6} 2.4. Solve each equation. 11. x 18.3 4.8 13.5 97 25 41 23. 14. k 4. 12. w 20.2 8.95 11.25 4(22 4) 3(6) 6. 37 9 18 11. 13. d 4 5(22) 4(3) 4(2 4). 15. y 3. 16. p 2 3. 17. a 7 10; {2, 3, 4, 5, 6, 7}. 18. 3y 42; {10, 12, 14, 16, 18}. {2}. {14, 16, 18} 20. 4b 4 3; {1.2, 1.4, 1.6, 1.8, 2.0}. {0.5, 1, 1.5} 3y 21. 2; {0, 2, 4, 6, 8, 10} 5. {0, 2}. {1.8, 2.0}. 冦. 1 1 3 1 5 3 22. 4a 3; , , , , , 8 4 8 2 8 4. 3 4. 冧 . 23. TEACHING A teacher has 15 weeks in which to teach six chapters. Write and then solve an equation that represents the number of lessons the teacher must teach per week if 6(8.5) there is an average of 8.5 lessons per chapter. . n. Nutrition Facts Serving Size 1 cup (228g) Servings Per Container 2 Amount Per Serving. Calories 250. Calories from Fat 110 % Daily Value *. Total Fat 12g Saturated Fat 3g. 27. VEHICLES For Exercises 5 and 6, use the following information. Recently developed hybrid cars contain both an electric and a gasoline engine. Hybrid car batteries store extra energy, such as the energy produced by braking. Since the car can use this stored energy to power the car, the hybrid uses less gasoline per mile than cars powered only by gasoline. Suppose a new hybrid car is rated to drive 45 miles per gallon of gasoline.. 18 % 15 %. 5. It costs $40 to fill the gasoline tank with gas that costs $2.50 per gallon. Write and solve an equation to find the distance the hybrid car can go using one tank of gas.. Trans Fat 3g. ; 3.4 15. LONG DISTANCE For Exercises 24 and 25, use the following information. Gabriel talks an average of 20 minutes per long-distance call. During one month, he makes eight in-state long-distance calls averaging $2.00 each. A 20-minute state-to-state call costs Gabriel $1.50. His long-distance budget for the month is $20.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 19. 4x 2 5; {0.5, 1, 1.5, 2, 2.5}. 2. FOOD Part of the Nutrition Facts label from a box of macaroni and cheese is shown below.. 1161 g 202 ; 8686 gal. Cholesterol 30mg. 10 %. 40 (45) m; 720 mi 2.50. Write and solve an inequality to determine how many servings of this item that Alisa can have for lunch if she is restricted no more than 45 grams of cholesterol.. 45 c ; 1.5 servings or less 30. 3. CRAFTS You need at least 30 yards of yarn to crochet a small scarf. Cheryl bought a 100-yard ball of yarn and has already used 10 yards. Write and solve an inequality to find how many scarves she can crochet. 100 – 10 30s;. 6. Write and solve an equation to find the cost of gasoline per mile for this hybrid car. Round to the nearest cent.. 2.50 c; 6¢ per mi 45. 3 scarves. Glencoe Algebra 1. 24. Write an inequality that represents the number of 20 minute state-to-state calls Gabriel can make this month. 8(2) 1.5s 20 25. What is the maximum number of 20-minute state-to-state calls that Gabriel can make this month? 2 Chapter 1. 24. Answers. Glencoe Algebra 1. Chapter 1. 25. Glencoe Algebra 1. (Lesson 1-3). A11. Find the solution set for each inequality using the given replacement set.. 12 c 3; 9:00 AM. g gal in pool. Answers. 9. 1.4(x 3) 5.32; {0.4, 0.6, 0.8, 1.0, 1.2}. 0.8. 27 8. 8. (x 2) ; , 1, 1 , 2, 2 2 . 7. x ; , , , , . 4. POOLS There are approximately 202 gallons per cubic yard of water. Write and solve an equation for the number of gallons of water that fill a pool with a volume of 1161 cubic feet. (Hint: There are 27 cubic feet per cubic yard.). Page A11. 2. 4b 8 6 3.5. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 1 2. 1 2. 1. a 1 . 873946 Alg1 CH01 EP3. and B {3, 3.5, 4, 4.5, 5}.. 1. TIME There are 6 time zones in the United States. The eastern part of the U.S., including New York City, is in the Eastern Time Zone. The central part of the U.S., including Dallas, is in the Central Time Zone, which is one hour behind Eastern Time. San Diego is in the Pacific Time Zone, which is 3 hours behind Eastern Time. Write and solve an equation to determine what time it is in California if it is noon in New York.. 10:26 AM. Open Sentences. 1 3 Find the solution of each equation if the replacement sets are A 0, , 1, , 2 2 2. Lesson 1-3. 1-3. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(14) 1-3. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____. NAME ______________________________________________ DATE______________ PERIOD _____. 1-3 1-3. Enrichment. Spreadsheet Activity. Solution Sets. 5/10/06. Solving Open Sentences A spreadsheet is a tool for working with and analyzing numerical data. The data is entered into a table in which each row is numbered and each column is labeled by a letter. You can use a spreadsheet to find solutions of open sentences.. Consider the following open sentence. It is the name of a month between March and July.. 1. It is the name of a state beginning with the letter A.. {Alabama, Alaska, Arizona, Arkansas}. Step 2 The second column contains the formula for the left side of the open sentence. To enter a formula, enter an equals sign followed by the formula. Use the name of the cell containing each replacement value to evaluate the formula for that value. For example, in cell B2, the formula contains A2 in place of x.. 2. It is a primary color.. {red, yellow, blue} 3. Its capital is Harrisburg. {Pennsylvania}. Vermont, Massachusetts, Rhode Island, Connecticut}. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 6. It is the name of a month that contains the letter r.. {Jan, Feb, Mar, Apr, Sept, Oct, Nov, Dec} 7. During the 1990s, she was the wife of a U.S. President.. {Barbara Bush, Hillary Clinton} 8. It is an even number between 1 and 13. {2, 4, 6, 8, 10,12} 9. 31 72 k {41} 10. It is the square of 2, 3, or 4.{4, 9, 16} Write an open sentence for each solution set. 11. {A, E, I, O, U} It is a vowel.. The solution set contains the values for which the open sentence is true. The solution set is {7, 8, 9, 10}.. 13. {June, July, August} It is a summer month.. 1 2 3 4 5 6 7 8. x. A. B. 7 8 9 10 11 12. Sheet 1. A. C. 4(x - 3) < 31 =B2<31 =B3<31 =B4<31 =B5<31 =B6<31 =B7<31. 4(x - 3) =4*(A2-3) =4*(A3-3) =4*(A4-3) =4*(A5-3) =4*(A6-3) =4*(A7-3) Sheet 2. Sheet 3. B. 7 8 9 10 11 12. 4(x - 3). Sheet 1. Sheet 2. C. 4(x - 3) < 31 TRUE TRUE TRUE TRUE FALSE FALSE. 16 20 24 28 32 36. Sheet 3. Exercises Use a spreadsheet to find the solution of each equation or inequality using the given replacement set. 1. x 7.5 18.3; {8.8, 9.8, 10.8, 11.8}. 2. 6(x + 2) 18; {0, 1, 2, 3, 4, 5}. 3. 4x 1 17; {0, 1, 2, 3, 4, 5}. 4. 4.9 x 2.2; {2.6, 2.7, 2.8, 2.9, 3.0}. 5. 2.7x 18; {6.1, 6.3, 6.5, 6.7, 6.9}. 6. 12x 8 22; {2.1, 2.2, 2.3, 2.4, 2.5, 2.6}. {10.8} {4}. {6.7, 6.9}. {1}. {2.6, 2.7}. {2.1, 2.2, 2.3, 2.4, 2.5, 2.6}. 14. {Atlantic, Pacific, Indian, Arctic} It is an ocean. Chapter 1. 26. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. 12. {1, 3, 5, 7, 9} It is an odd number between 0 and 10.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 5. x 4 10 {6}. Step 3 The third column determines whether the open sentence is true or false for the value in the replacement set. These formulas will return TRUE or FALSE.. x. Chapter 1. 27. Glencoe Algebra 1. (Lesson 1-3). A12. 4. It is a New England state. {Maine, New Hampshire,. 1 2 3 4 5 6 7 8. Lesson 1-3. Step 1 Use the first column of the spreadsheet for the replacement set. Enter the numbers using the formula bar. Click on a cell of the spreadsheet, type the number and press ENTER.. Page A12. Write the solution set for each open sentence.. 10:26 AM. Example Use a spreadsheet to find the solution set for 4(x 3) 31 if the replacement set is {7, 8, 9, 10, 11, 12}. You can solve the open sentence by replacing x with each value in the replacement set.. Answers. You know that a replacement for the variable It must be found in order to determine if the sentence is true or false. If It is replaced by either April, May, or June, the sentence is true. The set {April, May, June} is called the solution set of the open sentence given above. This set includes all replacements for the variable that make the sentence true..
(15) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 1-4. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____. NAME ______________________________________________ DATE______________ PERIOD _____. 1-4 1-4. Lesson Reading Guide. Study Guide and Intervention. Identity and Equality Properties. 10:27 AM. Identity and Equality Properties Identity and Equality Properties. Get Ready for the Lesson. The identity and equality properties in the chart below can help you solve algebraic equations and evaluate mathematical expressions.. Read the introduction to Lesson 1-4 in your textbook.. 1. Write the Roman numeral of the sentence that best matches each term. 5 7. V III. b. multiplicative identity. II. 18 18. VIII. d. Multiplicative Inverse Property. I. g. Transitive Property h. Substitution Property. II. V. 6 0 6. IV. VI. If 2 4 5 1 and 5 1 6, then 2 4 6.. VI. VII. If n 2, then 5n 5 2.. VII. VIII. 4 0 0. Remember What You Learned 2. The prefix trans- means “across” or “through.” Explain how this can help you remember the meaning of the Transitive Property of Equality.. Glencoe Algebra 1. Sample answer: The Transitive Property of Equality tells you that when a b and b c, you can go from a through b to get to c.. a b a b For every number , a, b
(16) 0, there is exactly one number such that 1.. Reflexive Property. For any number a, a a.. Symmetric Property. For any numbers a and b, if a b, then b a.. b. a. Transitive Property. For any numbers a, b, and c, if a b and b c, then a c.. Substitution Property. If a b, then a may be replaced by b in any expression.. a. 8n 8 Multiplicative Identity Property n 1, since 8 1 8. a 5454 Reflexive Property b. If n 12, then 4n 4 12. Substitution Property. 1 3. 1 3. n , since 3 1 Exercises Name the property used in each equation. Then find the value of n. 1. 6n 6. 2. n 1 8. 3. 6 n 6 9. 4. 9 n 9. 3 5. n 0 8. 6. n 1. Mult. Identity; 1. Mult. Identity; 8. Add. Identity; 0. Answers. Glencoe Algebra 1. Substitution Property; 9. 3 Add. Identity; 8. 3 4. 4 Mult. Inverse; 3. Name the property used in each equation. 7. If 4 5 9, then 9 4 5.. Symmetric Property. 9. 0(15) 0 Mult. Prop. of Zero. 8. 0 21 21. Add. Identity. 10. (1)94 94 Mult. Identity. 11. If 3 3 6 and 6 3 2, then 3 3 3 2. Transitive Property 13. (14 6) 3 8 3. Reflexive Property 28. a. Example 2 Name the property used to justify each statement.. 12. 4 3 4 3. Chapter 1. b. Example 1 Name the property used in each equation. Then find the value of n.. b. n 3 1 Multiplicative Inverse Property. IV. If 12 8 4, then 8 4 12. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. f. Symmetric Property. III. 3 1 3. For any number a, a 0 0.. Multiplicative Inverse Property. (Lesson 1-4). A13. c. Multiplicative Property of Zero. e. Reflexive Property. 7 5. I. 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. a. additive identity. For any number a, a 1 a.. Multiplicative Property of 0. Answers. Read the Lesson. For any number a, a 0 a.. Multiplicative Identity. Chapter 1. Substitution Property 29. Glencoe Algebra 1. Lesson 1-4. 2 r 2; Sample answer: The rank did not change for either team from week 6 to week 7.. Additive Identity. Page A13. Write an open sentence to represent the change in rank r of Auburn from week 6 to week 7. Explain why the solution is the same as the solution in the introduction..
(17) Study Guide and Intervention. NAME ______________________________________________ DATE______________ PERIOD _____. 1-4 1-4. (continued). Identity and Equality Properties. 1. n 0 19. Substitution; 9 3 3 Substitution; 3 3 0. Substitution; 24 8 16 Additive Identity; 16 0 16. Multiplicative Identity; 1. 4. 18 1 3 2 2(6 3 2). 1 2(151 14) 4 Subst.. 18 1 3 2 2(2 2) Subst.. 1 2(15 14) 4 Mult. Identity. 18 1 3 2 2(0) Substitution. 4. 1 2(1) 4 1 24. 4. 4. 4. Substitution Mult. Identity. Mult. Prop. Zero Substitution Add. Identity. 6. 3(5 5 12) 21 7. 13 Subst. Substitution Substitution Substitution Additive Identity. 3(5 5 1) 21 7 Subst. 3(5 5) 21 7 Mult. Identity 3(0) 21 7 Substitution 0 21 7 Mult. Prop. Zero 03 Substitution 3 Additive Identity. 30. Glencoe Algebra 1. Multiplicative Prop. of Zero; 0 14. 11 (18 2) 11 n. 1 Multiplicative Inverse; . Substitution Prop.; 9. 3. Evaluate each expression. Name the property used in each step. 16. 2[5 (15 3)]. 15. 7(16 42). 7(16 16) Substitution 7(1) Substitution 7 Multiplicative Identity 17. 4 3[7 (2 3)]. . 4(8 8) 1 Substitution 4(0) 1 Substitution 01 Mult. Prop. of Zero 1 Additive Identity 1 2. 19. 6 9[10 2(2 3)]. 20. 2(6 3 1) . 6 9[10 2(5)] Substitution 6 9(10 10) Substitution 6 9(0) Substitution 60 Mult. Prop. of Zero. Chapter 1. 2(5 5) Substitution 2(0) Substitution 0 Mult. Prop. of Zero. 18. 4[8 (4 2)] 1. 4 3(7 6) Substitution 4 3(1) Substitution 4 3 Multiplicative Identity 1 Substitution. 6. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. 10 5 4 2 2 4 2 13 2 2 13 0 13 13. Mult. Identity Substitution. 18 6 0 12 0 12. Mult. Inverse Substitution. 5. 10 5 22 2 13. 18 3 2 2(0) 18 6 2(0). Reflexive Prop.; 5. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 1 4. 3. 2(3 5 1 14) 4 . 12. n 14 0. 13. 3n 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Substitution Mult. Inverse. Substitution Prop.; 21. 11. 5 4 n 4. (Lesson 1-4). A14. 1. 10. (7 3) 4 n 4. Substitution Prop.; 6. 15 1 9 2(5 5) Substitution 15 1 9 2(0) Substitution 15 1 9 0 Mult. Prop. Zero 15 9 0 Mult. Identity 60 Substitution 6 Substitution. Substitution. Reflexive Prop.; 3. 9. 2(9 3) 2(n). 2. 15 1 9 2(15 3 5). . 8. 2 n 2 3. Additive Identity; 0. Additive Identity 31. 1 2(2 1) Substitution 1 2(1) 1 2 2. 1. 2. 2. Substitution Multiplicative Identity Multiplicative Inverse Glencoe Algebra 1. Page A14. Multiplicative Inverse; 4. Answers. 冢 冣冥. 1 1 2 4 4 1 2 2. Chapter 1. 6. n 9 9. 7. 5 n 5. 1 1 2 1. 2 4 2. 21 1. Additive Identity; 22. 1 4. 5. n 1. Exercises. . 4. 0 n 22. Multiplicative Prop. of Zero; 0. Multiplicative Identity; 24 1 24 Multiplicative Property of Zero; 5(0) 0. Evaluate each expression. Name the property used in each step.. 冤. Multiplicative Identity; 8. 3. 28 n 0. 10:27 AM. 1 8 5(3 3) 1 8 5(0) 8 5(0) 80 0. 2. 1 n 8. Additive Identity; 19. Evaluate 24 1 8 5(9 3 3). Name the property used in each step.. 24 1 8 5(9 3 3) 24 24 24 24 16 16. 5/10/06. Identity and Equality Properties Name the property used in each equation. Then find the value of n.. Use Identity and Equality Properties The properties of identity and equality can be used to justify each step when evaluating an expression. Example. Skills Practice. Lesson 1-4. 1-4. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(18) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 1-4. NAME ______________________________________________ DATE______________ PERIOD _____. 1-4 1-4. Practice. Word Problem Practice. Identity and Equality Properties. 1. EXERCISE Annika goes on a walk every day in order to get the exercise her doctor recommends. If she walks at a 1 rate of 3 miles per hour for of an hour,. 2. (8 7)(4) n(4). Additive Identity; 0. Substitution Prop.; 15 4. n 0.5 0.1 0.5. 5. 49n 0. 6. 12 12 n. 1 Multiplicative Inverse; 5. 3. 1. then she will have walked 3 miles. 3 Evaluate the expression and name the property used.. Reflexive Prop.; 0.1. Multiplicative Prop. of Zero; 0. 4. PARTY PLANNING Chase is planning a dinner party for 18 guests. He needs to have the same number of place settings as guests, and the same number of water glasses as place settings. What property must be used to determine the number of water glasses he needs for the party? Explain. The Transitive Property;. 1 mi; Multiplicative Inverse. Multiplicative Identity; 1. Page A15. 3. 5n 1. 10:27 AM. Identity and Equality Properties. Name the property used in each equation. Then find the value of n. 1. n 9 9. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____. if guests settings and settings glasses, then guests glasses.. Evaluate each expression. Name the property used in each step.. 2 Substitution Substitution Mult. Prop. of Zero Additive Identity Substitution. 51 6. USPS First Class Mail: Standard Letter Rates. Multiplicative Inverse Substitution. Weight (ounces). Cost. 0.25. $0.39. 2(15 5) 3(9 8) 2(10) 3(1) 20 3(1) 20 3 23. Substitution Substitution Multiplicative Identity Substitution. GARDENING For Exercises 11 and 12, use the following information. Mr. Katz harvested 15 tomatoes from each of four plants. Two other plants produced four tomatoes each, but Mr. Katz only harvested one fourth of the tomatoes from each of these.. 1 11. Write an expression for the total number of tomatoes harvested. 4(15) 2 4 4. . . Glencoe Algebra 1. 12. Evaluate the expression. Name the property used in each step.. 1 1 4(15) 2 4 60 2 4 4 4. . . . 60 2(1) 60 2 62. Chapter 1. . Substitution Multiplicative Inverse Multiplicative identity Substitution 32. Answers. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 10. Evaluate the expression. Name the property used in each step.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 9. Write an expression that represents the profit Althea made. 2(15 5) 3(9 8). the following information. Some toll highways assess tolls based on where a car entered and exited. The table below shows the highway tolls for a car entering and exiting at a variety of exits. Assume that the toll for the reverse direction is the same.. 0.5. $0.39. Entered. Exited. Toll. 0.75. $0.39. Exit 5. Exit 8. $0.50. 1. $0.39. Exit 8. Exit 10. $0.25. 1.25. $0.60. Exit 10. Exit 15. $1.00. 1.5. $0.60. Exit 15. Exit 18. $0.50. 1.75. $0.60. Exit 18. Exit 22. $0.75. SALES For Exercises 9 and 10, use the following information. Althea paid $5.00 each for two bracelets and later sold each for $15.00. She paid $8.00 each for three bracelets and sold each of them for $9.00.. TOLL ROADS For Exercises 5 and 6, use. Source: www.usps.gov. 5. Running an errand, Julio travels from Exit 8 to Exit 5. What property would you use to determine the toll?. Write an equation that represents the difference between the cost of mailing a 0.5 ounce and a 1.0 ounce letter. Name the property illustrated.. Symmetric Property of Equality. $0.39 $0.39 0; Additive Inverse. 6. Gordon travels from home to work and back each day. He lives at Exit 15 on the toll road and works at Exit 22. Write and evaluate an expression to find his daily toll cost. What property or properties did you use? t 2 ($0.50 $0.75);. 3. CAPACITY Use the substitution and transitive properties to find how many 1-cup servings there are in 1 gallon of sports drink. 16 c. Chapter 1. t $2.50; Substitution. 33. Glencoe Algebra 1. Lesson 1-4. 1 5(14 13) 4 Substitution 4 1 5(1) 4 Substitution 4 1 5 4 Multiplicative Identity 4. (Lesson 1-4). A15. 2 6(9 9) 2 6(0) 2 202 22 0. 2. MAIL The chart below shows the cost of mailing letters of various weight through the United States Postal Service.. 8. 5(14 39 3) 4 . Answers. 1 4. 7. 2 6(9 32) 2.
(19) 1-4. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____. NAME ______________________________________________ DATE______________ PERIOD _____. 1-5 1-5. Enrichment. Lesson Reading Guide. Closure. Get Ready for the Lesson. A binary operation matches two numbers in a set to just one number. Addition is a binary operation on the set of whole numbers. It matches two numbers such as 4 and 5 to a single number, their sum.. Read the introduction to Lesson 1-5 in your textbook.. If the result of a binary operation is always a member of the original set, the set is said to be closed under the operation. For example, the set of whole numbers is closed under addition because 4 5 is a whole number. The set of whole numbers is not closed under subtraction because 4 5 is not a whole number.. Add $14.95 and $34.95.. 5/10/06. The Distributive Property. 10:27 AM. How would you find the amount spent by each of the first eight customers at Instant Replay Video Games on Saturday?. 1. Explain how the Distributive Property could be used to rewrite 3(1 5).. Find the sum of 3 times 1 and 3 times 5.. Tell whether each operation is binary. Write yes or no.. ↵, where a ↵ b means to choose the lesser number from a and b yes 2. Explain how the Distributive Property can be used to rewrite 5(6 4).. 2. the operation ©, where a © b means to cube the sum of a and b yes. Write the difference of 5 times 6 and 5 times 4, that is 5 6 5 4.. Term. 5. the operation ⇑, where a ⇑ b means to match a and b to any number greater than either number no. Tell whether each set is closed under addition. Write yes or no. If your answer is no, give an example. 8. odd numbers no; 3 7 10. 9. multiples of 3 yes. 10. multiples of 5 yes. 11. prime numbers no; 3 5 8. 12. nonprime numbers no; 22 9 31. 13. multiplication: a b yes. 14. division: a b no; 4 3 is not a. 15. exponentation: ab yes. 16. squaring the sum: (a b)2 yes. Chapter 1. whole number. 34. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. Tell whether the set of whole numbers is closed under each operation. Write yes or no. If your answer is no, give an example.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 6. the operation ⇒, where a ⇒ b means to round the product of a and b up to the nearest 10 yes. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. A16. 3. Write three examples of each type of term. Sample answers are given.. 4. the operation exp, where exp(a, b) means to find the value of ab yes. 7. even numbers yes. (Lessons 1-4 and 1-5). 3. the operation sq, where sq(a) means to square the number a no. Example. number. 3, 17, 0.25. variable. w, t 2, x. product of a number and a variable. 4y, 0.78z, r. quotient of a number and variable. x 2s 6 , , 3 7 5t. 1 8. 4. Tell how you can use the Distributive Property to write 12m 8m in simplest form. Use the word coefficient in your explanation.. Sample answer: Add the coefficients of the two terms and multiply by m.. Remember What You Learned 5. How can the everyday meaning of the word identity help you to understand and remember what the additive identity is and what the multiplicative identity is?. Sample answer: When you add 0 (the additive identity) to a number, the result is the very same number you started with. The same is true if you multiply the number by 1 (the multiplicative identity).. Chapter 1. 35. Glencoe Algebra 1. Lesson 1-5. 1. the operation. Page A16. Answers. Read the Lesson.
(20) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 1-5. NAME ______________________________________________ DATE______________ PERIOD _____. 1-5 1-5. Study Guide and Intervention. Study Guide and Intervention. The Distributive Property. The Distributive Property Simplify Expressions. The Distributive Property can be used to help evaluate. A term is a number, a variable, or a product or quotient of numbers and variables. Like terms are terms that contain the same variables, with corresponding variables having the same powers. The Distributive Property and properties of equalities can be used to simplify expressions. An expression is in simplest form if it is replaced by an equivalent expression with no like terms or parentheses.. expressions. Distributive Property. For any numbers a, b, and c, a(b c) ab ac and (b c)a ba ca and a(b c) ab ac and (b c)a ba ca.. Example. Rewrite 6(8 10) using the Distributive Property. Then evaluate.. 6(8 10) 6 8 6 10 48 60 108. Multiply. Add.. Rewrite 2(3x2 5x 1) using the Distributive Property. Then simplify.. 2(3x2 5x 1) 2(3x2) (2)(5x) (2)(1) 6x2 (10x) (2) 6x2 10x 2. 4(a2 3ab) 1ab 4a2 12ab 1ab 4a2 (12 1)ab 4a2 11ab. Multiplicative Identity Distributive Property Distributive Property Substitution. Exercises. Distributive Property. Simplify each expression. If not possible, write simplified.. Multiply.. 1. 12a a. Simplify.. 11a. 2. 3x 6x. 3. 3x 1. 9x. simplified. (Lesson 1-5). Exercises. 2. 6(12 t) 72 6t. 3. 3(x 1) 3x 3. 4. 6(12 5) 102. 5. (x 4)3 3x 12. 6. 2(x 3) 2x 6. 7. 5(4x 9) 20x 45. 8. 3(8 2x) 24 6x. 9. 12 6 x 72 6x. 冢. 1 2. 冣. 10. 12 2 x 24 6x. Glencoe Algebra 1. 13. 2(3x 2y z). 6x 4y 2z 1 4. 16. (16x 12y 4z). 4x 3y z Chapter 1. 1 4. 11. (12 4t) 3 t. 14. (x 2)y. 冢. 1 2. 冣. 12. 3(2x y) 6x 3y. 15. 2(3a 2b c). xy 2y. 2g 1 7. 20a 12a 8. 32a 8 1 2. 10. 2p q. simplified 13. 3x 2x 2y 2y. x. 5. 2x 12. 6. 4x2 3x 7. simplified 8. 3x2 2x2. simplified 9. 6x 3x2 10x2. 5x 2. 6x 13x2. 11. 10xy 4(xy xy). 12. 21c 18c 31b 3b. 2xy. 39c 28b. 14. xy 2xy. 15. 12a 12b 12c. simplified. xy. 6a 4b 2c. 17. (2 3x x2)3. 6 9x 3x2 36. Answers. 18. 2(2x2 3x 1). 4x2 6x 2 Glencoe Algebra 1. 1 4. 16. 4x (16x 20y). 8x 5y Chapter 1. 17. 2 1 6x x2. 18. 4x2 3x2 2x. 1 6x x2. 7x2 2x. 37. Glencoe Algebra 1. Lesson 1-5. 1. 2(10 5) 10. 4. 12g 10g 1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Rewrite each expression using the Distributive Property. Then simplify.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. A17. Answers. Example 2. Simplify 4(a2 3ab) ab.. 4(a2 3ab) ab . Distributive Property. Page A17. Example 1. (continued). 10:27 AM. Evaluate Expressions. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(21) 1-5. NAME ______________________________________________ DATE______________ PERIOD _____. 1-5 1-5. Skills Practice. Practice. The Distributive Property. Rewrite each expression using the Distributive Property. Then simplify.. 1. 4(3 5) 4 3 4 5; 32. 2. 2(6 10) 2 6 2 10; 32. 1. 9(7 8). 2. 7(6 4). 3. 6(b 4). 3. 5(7 4) 5 7 5 4; 15. 4. (6 2)8 6 8 2 8; 32. 4. (9 p)3. 5. (5y 3)7. 6. 15 f . 5. (a 7)2 a 2 7 2; 2a 14. 6. 7(h 10) 7 h 7 10; 7h 70. 9 7 9 8; 135. m n m 4; mn 4m. 冣 1. 5y 7 3 7; 35y 21 8. m(n 4). 1 3. 15 f 15 ; 3 15f 5 9. (c 4)d. c d 4 d; cd 4d. Use the Distributive Property to find each product.. 10. 3(a b 1). 2(x) 2(y) 2(1); 2x 2y 2. 冢. Answers. 8. (x y)6 x 6 y 6; 6x 6y. 6 b 6 4; 6b 24. 3(a) 3(b) 3(1); 3a 3b 3. 10. 9 499 4491. 11. 7 110 770. 13. 12 2.5 30. 14. 27 2 63. 冢 冣 1 3. 12. 21 1004 21,084. 冢 14 冣. 15. 16 4 68. Use the Distributive Property to find each product. Simplify each expression. If not possible, write simplified.. 冢 18 冣. 15. 12 1 15. 16. 8 3 25. Simplify each expression. If not possible, write simplified. 18. 17g g 18g. 19. 16m 10m 6m. 20. 12p 8p 4p. 21. 2x2 6x2 8x2. 22. 7a2 2a2 5a2. 23. 3y2 2y simplified. 24. 2(n 2n) 6n. 25. 4(2b b) 4b Chapter 1. 26. 3q2 q q2 2q2 q. 38. 17. 3(5 6h) 15 18h. 18. 14(2r 3) 28r 42. 19. 12b2 9b2 21b 2. 20. 25t3 17t3 8t 3. 21. c2 4d 2 d 2 c 2 3d 2. 6a . 23. 4(6p 2q 2p). 24. x x . 22.. 3a2. simplified. 2b2. 16p 8q. 2x. 2 3. x 3. DINING OUT For Exercises 25 and 26, use the following information. The Ross family recently dined at an Italian restaurant. Each of the four family members ordered a pasta dish that cost $11.50, a drink that cost $1.50, and dessert that cost $2.75. 25. Write an expression that could be used to calculate the cost of the Ross’ dinner before adding tax and a tip. 4(11. 5 1.5 2.75) 26. What was the cost of dining out for the Ross family? $63.00. ORIENTATION For Exercises 27 and 28, use the following information. Madison College conducted a three-day orientation for incoming freshmen. Each day, an average of 110 students attended the morning session and an average of 160 students attended the afternoon session. 27. Write an expression that could be used to determine the total number of incoming freshmen who attended the orientation. 3(110 160) 28. What was the attendance for all three days of orientation? 810. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. 17. 2x 8x 10x. 16. w 14w 6w 9w. Chapter 1. 39. Glencoe Algebra 1. Lesson 1-5. 冢 14 冣. 冢 13 冣. 14. 15 2 35. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 13. 15 104 1560. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 12. 9 99 891. (Lesson 1-5). A18. 11. 5 89 445. Page A18. 16 3b 16 0.25; 48b 4. 7 6 7 4; 14. 10:27 AM. 9 3 p 3; 27 3p 7. 16(3b 0.25). 9. 2(x y 1). 5/10/06. The Distributive Property. Rewrite each expression using the Distributive Property. Then simplify.. 7. 3(m n) 3 m 3 n; 3m 3n. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(22) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 1-5. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____. NAME ______________________________________________ DATE______________ PERIOD _____. 1-5. Word Problem Practice. Enrichment. The Maya. 4(200 3) 800 12 788. use the following information. Letisha and Noel each opened a checking account, a savings account, and a college fund. The chart below shows the amounts that they deposited into each account. Savings. College. Letisha. $125. $75. $50. Noel. $250. $50. $50. 6. If Noel used only $50 bills when he deposited the money to open his accounts, how many $50 bills did he deposit? 7 $50 bills. 4. FENCES Demonstrate the Distributive Property by writing two equivalent expressions to represent the perimeter of the fenced dog pen below.. 7. If all accounts earn 1.5% interest per year and no further deposits are made, how much interest will Letisha have earned one year after her accounts were opened? $3.75. 2n 2m and 2(n m) m. Glencoe Algebra 1. Dog Pen. ••. •• _____ 12 _____. 3. •••. ••• _____ 13 _____. 4. ••••. •••• _____ 14 _____. The Maya developed a system of numeration that was based on the number twenty. The basic symbols of this system are shown in the table at the right. The places in a Mayan numeral are written vertically—the bottom place represents ones, the place above represents twenties, the place above that represents 20 20, or four hundreds, and so on. For instance, this is how to write the number 997 in Mayan numerals.. 5 _____. _____ 15 _____ _____ • _____ 16 _____ _____. ←. 2 400 800. _____ ••••. ←. 9 . _____ •• _____ _____. ← 17 . n. 20. 180. 1. . • 6 _____ •• 7 _____ ••• 8 _____. _____ •• 17 _____ _____ _____ ••• 18 _____ _____. •••• 9 _____. _____ •••• 19 _____ _____. 17 997. z w. 1. . vwz •••• 2. _____. •••. 4. vxy. 3. xv. x. 5. wx z. ● ●. •••. 6. vz xy. ● ●. •••• _____ _____ 7. w(v x z) _____. 8. vwz. _____ • _____ _____. • ••••. ••• •••• _____ • _____ _____. ••• _____ •• _____ ••. 9. z(wx x). ● ● _____ • _____ _____. Tell whether each statement is true or false. • • • _____ • • ••• _____ _____ 10. _____ _____ _____. true. _____ ••• _____. _____ •. 11. _____ _____ ••• _____ •. false. _____ •••. _____ ••• _____. 12. _____ _____ _____. false. _____ • • • ( _____ _____ _____ ) true 13. ( • • • _____ ) _____. 14. How are Exercises 10 and 11 alike? How are they different?. Both involve changing the order of the symbols. Exercise 10 involves changing the order of the addends in an addition problem. Exercise 11 involves changing the order of the digits in a numeral. Chapter 1. 40. Answers. Glencoe Algebra 1. Chapter 1. 41. Glencoe Algebra 1. Lesson 1-5. 3. 53 53 5(3) 5 5 5 5 15 3 18. Checking. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 3. • _____ 11 _____. 2. ••• ,x ••••,y ● _____ • , w _____ ● , and _____ Evaluate each expression when v _____ • • . Then write the answer in Mayan numerals. Exercise 5 is done for you. _____ z _____. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. of fabric. Use the Distributive Property to find the number of yards of fabric needed for 5 costumes. (Hint: a mixed number can be written as the sum of an integer and a fraction.). 3. _____ 10 _____. •. (Lesson 1-5). A19. 5. ● ●. 1. ••. INVESTMENTS For Exercises 6 and 7, 3. COSTUMES Isabella’s ballet class is performing a spring recital for which they need butterfly costumes. Each 3 butterfly costume is made from 3 yards. 0. Answers. 2. LIBRARY In Cook County Library’s children’s section there are 7 shelves and 4 tables. Each shelf and table displays 12 books. Write and evaluate an expression to find how many books are in the children’s section. 12(7 4) 132. The Maya were a Native American people who lived from about 1500 B.C. to about 1500 A.D. in the region that today encompasses much of Central America and southern Mexico. Their many accomplishments include exceptional architecture, pottery, painting, and sculpture, as well as significant advances in the fields of astronomy and mathematics.. Page A19. 5. MENTAL MATH During a math facts speed contest, Jamal calculated the following expression faster than anyone else in his class. 197 4 When classmates asked him how he was able to answer so quickly, he told them he used the Distributive Property to think of the problem differently. Write and evaluate an expression using the Distributive Property that would help Jamal perform the calculation quickly.. $39(23 2) $975. 10:27 AM. The Distributive Property 1. OPERA Mr. Delong’s drama class is planning a field trip to see Mozart’s famous opera Don Giovanni. Tickets cost $39 each, and there are 23 students and 2 teachers going on the field trip. Write and evaluate an expression to find the group’s total ticket cost..
(23) NAME ______________________________________________ DATE______________ PERIOD _____. 3-6 1-6. Lesson Reading Guide. Get Ready for the Lesson How are the expressions 0.4 1.5 and 1.5 0.4 alike? different?. The numbers and the operation are the same; the order of the numbers is different.. Example 1. 1. Write the Roman numeral of the term that best matches each equation. I. Associative Property of Addition. I. c. 2 (3 4) (2 3) 4. IV. Commutative Property. Evaluate 8.2 2.5 2.5 1.8.. 8.2 2.5 2.5 1.8 8.2 1.8 2.5 2.5 (8.2 1.8) (2.5 2.5) 10 5 15. Associative Property Multiply. Multiply.. The product is 180. III. Commutative Property of Addition. Commutative Prop. Associative Prop. Add. Add.. The sum is 15. IV. Commutative Property of Multiplication Exercises. 2. What property can you use to change the order of the terms in an expression?. Commutative Property of Addition Associative Property of Multiplication 4. What property can you use to combine two like terms to get a single term?. Distributive Property 5. To use the Associative Property of Addition to rewrite the sum of a group of terms, what is the least number of terms you need? three. Remember What You Learned. Sample answer: To travel back and forth, as between a suburb and a city; in the Commutative Property of Addition, a b b a, the quantities a and b are switched back and forth. 42. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. 6. Look up the word commute in a dictionary. Find an everyday meaning that is close to the mathematical meaning and explain how it can help you remember the mathematical meaning.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 3. What property can you use to change the way three factors are grouped?. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Evaluate each expression. 1. 12 10 8 5 35. 2. 16 8 22 12 58. 3. 10 7 2.5 175. 4. 4 8 5 3 480. 5. 12 20 10 5 47. 6. 26 8 4 22 60. 1 2. 1 2. 7. 3 4 2 3 13. 1 2. 1 2. 10. 4 5 3 13. 4 5. 2 9. 3 4. 8. 12 4 2 72. 11. 0.5 2.8 4 5.6. 1 5. 1 2. 13. 18 25 80. 14. 32 10 32. 16. 3.5 8 2.5 2 16. 17. 18 8 8. Chapter 1. 1 2. 1 9. 43. 9. 3.5 2.4 3.6 4.2 13.7. 12. 2.5 2.4 2.5 3.6 11. 1 4. 1 7. 15. 7 16 4. 3 4. 1 2. 18. 10 16 60. Glencoe Algebra 1. (Lesson 1-6). A20. d. 2 (3 4) 2 (4 3). II. II. Associative Property of Multiplication. Example 2. Evaluate 6 2 3 5.. 62356325 (6 3)(2 5) 18 10 180. Answers. III. b. 2 (3 4) (2 3) 4. Chapter 1. For any numbers a and b, a b b a and a b b a. For any numbers a, b, and c, (a b) c a (b c ) and (ab)c a(bc).. Page A20. Read the Lesson. Commutative Properties Associative Properties. 10:27 AM. Commutative and Associative Properties The Commutative and Associative Properties can be used to simplify expressions. The Commutative Properties state that the order in which you add or multiply numbers does not change their sum or product. The Associative Properties state that the way you group three or more numbers when adding or multiplying does not change their sum or product.. Read the introduction to Lesson 1-6 in your textbook.. 5/10/06. Commutative and Associative Properties. Commutative and Associative Properties. a. 3 6 6 3. Study Guide and Intervention Lesson 1-6. 1-6. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(24) A1-A34_CRM01-873944. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Study Guide and Intervention. NAME ______________________________________________ DATE______________ PERIOD _____. 3-6 1-6. (continued). Commutative and Associative Properties The Commutative and Associative Properties can be used along with other properties when evaluating and simplifying expressions. Example. 8y 16x 7y 8y 7y 16x (8 7)y 16x 15y 16x. Commutative () Distributive Property Substitution. 1. 4x 3y x. 2. 3a 4b a. 5x 3y. 4a 4b. 16x 21y 4 3. 1.7x 0.5y 1 3. 11. z2 9x2 z2 x2. 7 28 z 2 x 2 3 3. 9. 5(0.3x 0.1y) 0.2x. 12. 6(2x 4y) 2(x 9). 14x 24y 18. Write an algebraic expression for each verbal expression. Then simplify. 13. twice the sum of y and z is increased by y. 3y 2z. 14. four times the product of x and y decreased by 2xy. 2xy. Glencoe Algebra 1. 15. the product of five and the square of a, increased by the sum of eight, a2, and 4. 6a 2 12. 16. three times the sum of x and y increased by twice the sum of x and y. 5x 5y. Chapter 1. 8. 1.6 0.9 2.4 4.9. 9. 4 6 5 16. 1 2. 1 2. 44. Answers. 10. 2x 5y 9x 11x 5y. 11. a 9b 6a 7a 9b. 12. 2p 3q 5p 2q 7p 5q. 13. r 3s 5r s 6r 4s. 14. 5m2 3m m2 6m2 3m. 15. 6k2 6k k2 9k 7k2 15k. 16. 2a 3(4 a) 5a 12. 17. 5(7 2g) 3g 35 13g. Write an algebraic expression for each verbal expression. Then simplify, indicating the properties used.. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 1 2. 7 x. 7. 1.7 0.8 1.3 3.8. 6. 6n 2(4n 5). 14n 10. 8. 5(2x 3y) 6( y x). 4 3. 2rs 2. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. 1 2. 15rs . 10x 8y. 10. (x 10) . 6. 5 7 10 4 1400. 18. three times the sum of a and b increased by a. 3(a b) a 3(a) 3(b) a 3a 3b a 3a a 3b (3a a) 3b (3 1)a 3b 4a 3b. Distributive Property Multiply Commutative () Associative () Distributive Property Substitution. 19. twice the sum of p and q increased by twice the sum of 2p and 3q. 2(p q) 2(2p 3q) 2(p) 2(q) 2(2p) 2(3q) 2p 2q 4p 6q 2p 4p 2q 6q (2p 4p) (2q 6q) (2 4)p (2 6)q 6p 8q Chapter 1. Distributive Property Multiply Commutative () Associative () Distributive Property Substitution 45. Glencoe Algebra 1. (Lesson 1-6). A21. 2 3. 3. 8rs 2rs2 7rs. 5. 6(x y) 2(2x y). 7a 9b. 5. 2 4 5 3 120. Answers. Exercises. 7. 6(a b) a 3b. 4. 5 3 4 3 180. Simplify each expression.. Simplify each expression.. 13a 2 4b. 3. 32 14 18 11 75. Distributive Property. The simplified expression is 15y 16x.. 4. 3a2 4b 10a2. 2. 36 23 14 7 80. Page A21. Simplify 8(y 2x) 7y.. 1. 16 8 14 12 50. 10:27 AM. Commutative and Associative Properties Evaluate each expression.. Simplify Expressions. 8(y 2x) 7y . Skills Practice Lesson 1-6. 1-6. 5/10/06. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
(25) NAME ______________________________________________ DATE______________ PERIOD _____. 1-6. Practice. Word Problem Practice. Commutative and Associative Properties 2. 6 5 10 3 900. 3. 7.6 3.2 9.4 1.3 21.5. 4. 3.6 0.7 5 12.6. 1 2 5. 7 2 1 9 9. 1 10 3. 3 4. 1 3. 6. 3 3 16 200. 7. 9s2 3t s2 t 10s 2 4t. 10. 2(3x y) 5(x 2y) 11x 12y. 11. 3(2c d) 4(c 4d) 10c 19d. 12. 6s 2(t 3s) 5(s 4t) 17s 22t. 13. 5(0.6b 0.4c) b 4b 2c. 1 1 1 14. q 2 q r 2 4 2. 冢. Bus Route. 冣 qr. 15. Write an algebraic expression for four times the sum of 2a and b increased by twice the sum of 6a and 2b. Then simplify, indicating the properties used.. 12 people got on. Second stop. 4 people off; 15 on. Third stop. 16 people off; 7 on. Fourth stop. 11 people off; 14 on. following information. Kim, Doug, and Conner all run on the cross country team. In the last race Doug finished first, Kim finished 3 minutes after Doug, and Conner finished with a time that was twice Doug’s time. 5. What is the sum of their times?. SCHOOL SUPPLIES For Exercises 16 and 17, use the following information. Kristen purchased two binders that cost $1.25 each, two binders that cost $4.75 each, two packages of paper that cost $1.50 per package, four blue pens that cost $1.15 each, and four pencils that cost $.35 each. 16. Write an expression to represent the total cost of supplies before tax.. 2(1.25 4.75 1.50) 4(1.15 0.35) 17. What was the total cost of supplies before tax? $21.00. GEOMETRY For Exercises 18 and 19, use the following information. 18. Using the commutative and associative properties to group the terms in a way that makes evaluation convenient, write an expression to represent the perimeter of the pentagon. Sample answer: (1.25 0.25) (0.9 1.1) 2.5. x (x 3) (2x) x x 2x 3 4x 3 min. 3. MENTAL MATH The triangular banner has a base of 9 centimeters and a height of 6 centimeters. Using the formula for area of a triangle, the banner’s area can 1 be expressed as 9 6 . Gabrielle 2. 6. What property or properties did you use?. finds it easier to write and evaluate. 冢. Associative and Commutative Properties of Addition, and Distributive Property. 冣. 1 6 9 to find the area. Is 2. Gabrielle’s expression equivalent to the area formula? Explain.. 7. Evaluate the expression if Doug ran the race in 27 minutes. 111 min. h b. Yes; the Commutative and Associative Properties of Multiplication allow it to be rewritten.. 19. What is the perimeter of the pentagon? 6 in. Chapter 1. 46. Glencoe Algebra 1. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Glencoe Algebra 1. The lengths of the sides of a pentagon in inches are 1.25, 0.9, 2.5, 1.1, and 0.25.. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. Distributive Property Multiply Commutative () Associative () Distributive Property Substitution. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.. How many people are on the bus after the fourth stop? 17. Chapter 1. 47. Glencoe Algebra 1. (Lesson 1-6). A22. 4(2a b) 2(6a 2b) 4(2a) 4(b) 2(6a) 2(2b) 8a 4b 12a 4b 8a 12a 4b 4b (8a 12a) (4b 4b) (8 12)a (4 4)b 20a 8b. First stop. SPORTS For Exercises 5–7, use the. Answers. 9. 6y 2(4y 6) 14y 12. 8. (p 2n) 7p 8p 2n. Sample answer: (60 84) 62 84 (60 62) 206. Page A22. 2. BUS STOPS Mr. McGowan drives a city bus. Occasionally he keeps track of the number of riders for market research. The chart below shows a morning route.. Simplify each expression.. 4. ANATOMY The human body has 60 bones in the arms and hands, 84 bones in the upper body and head, and 62 bones in the legs and feet. Use the Associative Property to write and evaluate an expression that represents the total number of bones in the human body.. 10:27 AM. 1. 13 23 12 7 55. 1. SCHOOL SUPPLIES At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Use mental math and the Associative Property of Addition to find the total cost if one of each item is purchased. $4.80. 5/10/06. Commutative and Associative Properties. Evaluate each expression.. Lesson 1-6. 1-6. A1-A34_CRM01-873944. Chapter 1. NAME ______________________________________________ DATE______________ PERIOD _____.
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