Answer to chapter 1-4

Answer to chapter 1-4 MULTIPLE CHOICE 1. ANS: C Substitute each value for y into the equation. 22 = y 6 22 = 28 6? Substitute 28 for y. 22 = 22 So 28 is a solution. A B C D Feedback Check the sign of your answer. Check the rules for integer addition and subtraction. Correct! Check the rules for integer addition and subtraction. PTS: 1 DIF: Average REF: Page 34 OBJ: 1-7.1 Determining Whether a Number is a Solution of an Equation NAT: 8.5.4.a TOP: 1-7 Solving Equations by Adding or Subtracting KEY: equation solving substitute NUMERIC RESPONSE 2. ANS: 6 PTS: 1 DIF: Average REF: Page 15 OBJ: 1-3.1 Evaluating Absolute-Value Expressions NAT: 8.1.1.g TOP: 1-3 Integers and Absolute Value KEY: absolute value integers 3. ANS: $1181 PTS: 1 DIF: Advanced NAT: 8.1.3.c TOP: 1-6 Multiplying and Dividing Integers 4. ANS: 6173 PTS: 1 DIF: Advanced NAT: 8.5.4.a TOP: 1-7 Solving Equations by Adding or Subtracting 5. ANS: KEY: integers division average KEY: solving equation PTS: 1 DIF: Advanced NAT: 8.1.3.a TOP: 2-4 Multiplying Rational Numbers 6. ANS: 4 PTS: 1 DIF: Advanced NAT: 8.1.3.a TOP: 2-7 Solving Equations with Rational Numbers 7. ANS: 5

PTS: 1 DIF: Average NAT: 8.1.3.a TOP: 2-8 Solving Two-Step Equations 8. ANS: 33.60 PTS: 1 DIF: Average NAT: 8.5.3.c TOP: 3-4 Functions KEY: multi-step MATCHING 9. ANS: D PTS: 1 DIF: Basic REF: Page 6 TOP: 1-1 Variables and Expressions 10. ANS: C PTS: 1 DIF: Basic REF: Page 44 TOP: 1-9 Introduction to Inequalities 11. ANS: B PTS: 1 DIF: Basic REF: Page 6 TOP: 1-1 Variables and Expressions 12. ANS: E PTS: 1 DIF: Basic REF: Page 6 TOP: 1-1 Variables and Expressions 13. ANS: H PTS: 1 DIF: Basic REF: Page 6 TOP: 1-1 Variables and Expressions 14. ANS: G PTS: 1 DIF: Basic REF: Page 14 TOP: 1-3 Integers and Absolute Value 15. ANS: F PTS: 1 DIF: Basic REF: Page 6 TOP: 1-1 Variables and Expressions 16. ANS: A PTS: 1 DIF: Basic REF: Page 14 TOP: 1-3 Integers and Absolute Value SHORT ANSWER 17. ANS: a. The variable a represents the number of years Felix has been playing piano. So, 6a represents the number of years Roberto has been playing piano. b. Roberto has been playing piano for 18 years. 6a Substitute 3 for a. 6(3) Multiply. 18 Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 Both solutions are correct, but not all of the work is shown. 2 The solution for part a is correct, but the solution for part b is incorrect. or The solution for part a is incorrect, but the work for part b is correct. 1 Both solutions are incorrect, and the work shows no understanding of the concept. PTS: 1 DIF: Average NAT: 8.5.2.a TOP: 1-2 Algebraic Expressions KEY: algebraic expression word problem writing expressions

18. ANS: The dog buried 8 bones this week. Method one: b + 7 = 15 (Student may simply solve the equation,as shown here, 7 = 7 or may substitute the given values to find the solution, b = 8 as shown below.) Method two: b + 7 = 15 Substitute 22 for b. 22 + 7 = 15? 29 = 15? Not a solution b + 7 = 15 Substitute 8 for b. 8 + 7 = 15? 15 = 15? Yes, 8 is the solution. (It is acceptable if the student stops here.) b + 7 = 15 Substitute 9 for b. 9 + 7 = 15? 16 = 15? Not a solution Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 The solution is correct, but not all of the work is shown. 2 The solution is incorrect, but the work shows understanding of the concept. 1 The solution is incorrect, and the work shows no understanding of the concept. PTS: 1 DIF: Average NAT: 8.5.4.c TOP: 1-7 Solving Equations by Adding or Subtracting KEY: solving equation addition subtraction substitution 19. ANS: She uses 120 apples to make applesauce. fraction of total amount total needed needed = picked so far x = 40 x = 120 Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 The solution is correct, but not all of the work is shown. 2 The solution is incorrect, but the work shows understanding of the concept. 1 The solution is incorrect, and the work shows no understanding of the concept.

PTS: 1 DIF: Average NAT: 8.5.4.c TOP: 1-8 Solving Equations by Multiplying or Dividing KEY: solving equation multiplication division 20. ANS: a. The inequality shown by this graph is x 3.5 b. When the arrow points to the left, it indicates that all of the values less than the number represented by the circle are in the solution set. When the arrow points to the right, it indicates that all of the values greater than the number represented by the circle are in the solution set. An open circle indicates that the number is not in the solution set, while a closed circle indicates that the number is in the solution set. Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 Both solutions are correct, but not all of the work is shown. 2 The solution for part a is correct, but the solution for part b is incorrect or The solution for part a is incorrect, but the work in part b is correct. 1 Both solutions are incorrect, and the work shows no understanding of the concept. PTS: 1 DIF: Average NAT: 8.5.4.a TOP: 1-9 Introduction to Inequalities KEY: solving inequality 21. ANS: 3 students Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 The solution is correct, but not all of the work is shown. 2 The solution is incorrect, but the work shows understanding of the concept. 1 The solution is incorrect, and the work shows no understanding of the concept. PTS: 1 DIF: Average OBJ: 2-4.PA02 Multiplying Rational Numbers NAT: 8.1.3.a TOP: 2-4 Multiplying Rational Numbers KEY: rational number multiplication 22. ANS: a. $15.75 b. 2.3 pounds

Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 Both solutions are correct, but not all of the work is shown. 2 The solution for part a is correct, but the solution for part b is incorrect. or The solution for part a is incorrect, but the work for part b is correct. 1 Both solutions are incorrect, and the work shows no understanding of the concept. PTS: 1 DIF: Average OBJ: 2-4.PA05 Multiplying Rational Numbers NAT: 8.1.3.a TOP: 2-4 Multiplying Rational Numbers KEY: rational number addition subtraction evaluate multiplication 23. ANS: a. 10 books b. 14 books Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 Both solutions are correct, but not all of the work is shown. 2 The solution for part a is correct, but the solution for part b is incorrect. or The solution for part a is incorrect, but the work for part b is correct. 1 Both solutions are incorrect, and the work shows no understanding of the concept.

PTS: 1 DIF: Average OBJ: 2-5.PA03 Dividing Rational Numbers NAT: 8.1.3.a TOP: 2-5 Dividing Rational Numbers KEY: rational number division 24. ANS: Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 The solution is correct, but not all of the work is shown. 2 The solution is incorrect, but the work shows understanding of the concept. 1 The solution is incorrect, and the work shows no understanding of the concept. PTS: 1 DIF: Average OBJ: 2-6.PA04 Adding and Subtracting with Unlike Denominators NAT: 8.1.3.a TOP: 2-6 Adding and Subtracting with Unlike Denominators KEY: fraction addition subtraction unlike denominators rational number 25. ANS: 38.2 feet Scoring Rubric: 4 The solution is correct, and all of the work is shown as above. or A different logical method is used to find the correct solution. 3 The solution is correct, but not all of the work is shown. 2 The solution is incorrect, but the work shows understanding of the concept. 1 The solution is incorrect, and the work shows no understanding of the concept. PTS: 1 DIF: Average REF: Page 186 OBJ: 4-6.2 Problem-Solving Application NAT: 8.1.2.d TOP: 4-6 Estimating Square Roots KEY: square square root 26. ANS:

16 Example: Evaluate 10(n 4) + 5 for n = 7. 10(7 4) + 5 Substitute 7 for n. 10(3) + 5 Subtract within parentheses first. 30 + 5 Multiply. 35 Add. PTS: 1 DIF: Average REF: Page 6 OBJ: 1-1.1 Evaluating Algebraic Expressions with One Variable NAT: 8.5.2.a TOP: 1-1 Variables and Expressions KEY: algebraic expression variable 27. ANS: 12, 12 The square root of a number is another number that, when multiplied by itself, equals the first number. 12 is a square root, since = 144. 12 is also a square root, since = 144. PTS: 1 DIF: Basic REF: Page 182 OBJ: 4-5.1 Finding the Positive and Negative Square Roots of a Number NAT: 8.5.3.b TOP: 4-5 Squares and Square Roots KEY: square square root positive negative 28. ANS: 2.3 10 5 To write a number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. PTS: 1 DIF: Average REF: Page 175 OBJ: 4-4.2 Translating Standard Notation to Scientific Notation NAT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation standard notation 29. ANS: 65,400,000 A positive exponent means move the decimal point to the right. A negative exponent means move the decimal point to the left. PTS: 1 DIF: Average REF: Page 174 OBJ: 4-4.1 Translating Scientific Notation to Standard Notation NAT: 8.1.1.f TOP: 4-4 Scientific Notation KEY: scientific notation standard notation 30. ANS: Example: 8 less than the product of t and 6 Product means multiply : 8 less than 6t And less than means subtract from :

6t 8 PTS: 1 DIF: Basic REF: Page 10 OBJ: 1-2.1 Translating Word Phrases into Math Expressions NAT: 8.5.2.a TOP: 1-2 Algebraic Expressions KEY: algebraic expression math expression word phrase 31. ANS: 18 First, perform the addition or subtraction inside the parentheses. Second, perform the multiplication. PTS: 1 DIF: Basic REF: Page 27 OBJ: 1-6.2 Using the Order of Operations with Integers TOP: 1-6 Multiplying and Dividing Integers KEY: integer order of operations multiplication division 32. ANS: 8, 2, 7 Compare each pair of integers: 8 < 2, 8 < 7, and 2 < 7. So, 8 < 2 < 7. NAT: 8.1.3.a PTS: 1 DIF: Average REF: Page 15 OBJ: 1-3.2 Ordering Integers NAT: 8.1.1.i TOP: 1-3 Integers and Absolute Value 33. ANS: ; 17 sand dollars Example: Isabel has saved 162 sand dollars and wants to give them away equally to y friends. Write an expression to show how many sand dollars each of Isabel s friends will receive. Then evaluate the expression for y = 9. Separate 162 sand dollars into y equal groups. Evaluate for y = 9. 18 Divide. Each of Isabel s friends will receive 18 sand dollars. PTS: 1 DIF: Average REF: Page 11 OBJ: 1-2.3 Writing and Evaluating Expressions in Word Problems NAT: 8.5.2.a TOP: 1-2 Algebraic Expressions KEY: algebraic expression word problem operation 34. ANS: 27 n; 25 points Example: If Carmen scored a total of 11 points in the basketball game and she scored n points in the last half of the game, write an expression to determine the number of points she scored in the first half of the game. Then evaluate the expression for n = 2. 11 n Separate n points from the total of 11 points. 11 2 Evaluate for n = 2. 9 Subtract. Carmen scored 9 points in the first half of the game. PTS: 1 DIF: Average REF: Page 11

OBJ: 1-2.3 Writing and Evaluating Expressions in Word Problems NAT: 8.5.2.a TOP: 1-2 Algebraic Expressions KEY: algebraic expression word problem operation 35. ANS: m 11 30 25 20 15 10 Example: Solve and graph the inequality. z 9 < 17 + 9 + 9 Add 9 to both sides to isolate z. z < 26 5 0 5 10 15 20 25 30 30 25 20 15 A closed circle should be used when the value is included in the graph, such as with or An open circle should be used when the value is not included, such as with > or <. PTS: 1 DIF: Basic REF: Page 45 OBJ: 1-9.2 Solving and Graphing Inequalities NAT: 8.5.4.a TOP: 1-9 Introduction to Inequalities KEY: solving inequality graph 36. ANS:,,, 1.5 10 5 0 5 10 15 20 25 30 Rewrite each fraction as a decimal to compare. The correct order is. So, in order from least to greatest:,,, 1.5 Or locate the numbers on a number line and read them from left to right. -0.25 5/8-1/8 1.5 PTS: 1 DIF: Average REF: Page 69 OBJ: 2-2.3 Application NAT: 8.1.1.i TOP: 2-2 Comparing and Ordering Rational Numbers 37. ANS: ; 17 envelopes in each box Example: At a Saturday morning job, Beatriz stuffs 460 envelopes with 2 pages each and must pack them into n boxes for easy transportation to the post office. If there are 20 boxes, how many envelopes should Beatriz put in each box? Separate 640 envelopes into equal amounts in n boxes.

Evaluate for n = 20. 23 Divide. The information that 2 pages are stuffed into each envelope is not needed to solve this problem. There should be 23 envelopes in each box. PTS: 1 DIF: Basic REF: Page 11 OBJ: 1-2.3 Writing and Evaluating Expressions in Word Problems NAT: 8.5.2.a TOP: 1-2 Algebraic Expressions KEY: algebraic expression word problem writing expressions 38. ANS: or 6 less than the difference of x and 5 6 6 less than less than the difference of x and 5 minus 6 6 Original statement Replace some text with algebraic expressions. Replace less than with minus and reorder the statement. Replace the rest of the text with algebraic expressions. This may be rewritten as. PTS: 1 DIF: Advanced NAT: 8.1.1.i TOP: 1-2 Algebraic Expressions 39. ANS: 9 Additive inverses, or opposites, are numbers that are the same distance from 0, but on opposite sides of 0 on a number line. The additive inverse of 9 is 9. 10 8 6 4 2 0 2 4 6 8 10 PTS: 1 DIF: Average REF: Page 15 OBJ: 1-3.3 Finding Additive Inverses NAT: 8.1.1.g TOP: 1-3 Integers and Absolute Value KEY: integer opposite number line 40. ANS: 33 more buses Example: A city manager wants to reduce morning traffic by increasing the number of buses and reducing the number of automobiles with single occupants on the road. If the goal is to eliminate 494 cars with single occupants each morning and one bus can transport 26 people, how many more buses will the city need each day? Use the given information to write an equation, where n is the number of buses the city will need each day. number of number of total number of

people per bus buses needed = cars to eliminate 26 n = 494 26n = 494 n = 19 Think: n is multiplied by 26, so divide both sides by 26 to isolate n. The city will need 19 more buses each day. PTS: 1 DIF: Basic REF: Page 40 OBJ: 1-8.3 Application NAT: 8.5.4.c TOP: 1-8 Solving Equations by Multiplying or Dividing KEY: solving equation multiplication division 41. ANS: 3 1 + 4 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 The lower vector shows the first integer, and the upper vector shows the second integer. The number at which the upper vector stops is the sum of the two integers. PTS: 1 DIF: Basic REF: Page 18 OBJ: 1-4.1 Using a Number Line to Add Integers NAT: 8.1.3.a TOP: 1-4 Adding Integers KEY: number line addition integer 42. ANS: Cynan, Tamia, Julius, Francis, Jared A diving depth of 46 ft is 46 ft below the surface of the water. This is the deepest any of the students has dived. Thus, Cynan has dived the deepest. Tamia has dived the second deepest, followed by Julius, then Francis, then Jared. The students names in order from the deepest depth to the shallowest depth are: Cynan, Tamia, Julius, Francis, Jared. PTS: 1 DIF: Advanced NAT: 8.1.3.a TOP: 1-3 Integers and Absolute Value 43. ANS: 12 3 + 9 = 3 + 9 3 is 3 units from 0. 9 is 9 units from 0. = 12 Add. PTS: 1 DIF: Average REF: Page 15 OBJ: 1-3.4 Evaluating Absolute-Value Expressions NAT: 8.1.1.g TOP: 1-3 Integers and Absolute Value KEY: absolute value 44. ANS: 11 If the signs are the same, find the sum of the absolute values and use the same sign as the integers. If the signs are different, find the difference of the absolute values and use the sign of the integer with the greater absolute value.

PTS: 1 DIF: Basic REF: Page 19 OBJ: 1-4.2 Using Absolute Value to Add Integers NAT: 8.1.3.a TOP: 1-4 Adding Integers KEY: absolute value addition integer 45. ANS: 27 Substitute for the variable and perform the addition. PTS: 1 DIF: Basic REF: Page 19 OBJ: 1-4.3 Evaluating Expressions with Integers NAT: 8.1.3.a TOP: 1-4 Adding Integers KEY: expression integer evaluate addition 46. ANS: 16 Use positive integers for each of the food items and negative integers for each of the activities. Find the sum. PTS: 1 DIF: Basic REF: Page 19 OBJ: 1-4.4 Application NAT: 8.1.3.g TOP: 1-4 Adding Integers KEY: expression integer evaluate addition 47. ANS: 16 Change the subtraction sign to an addition sign, and change the sign of the second number. PTS: 1 DIF: Basic REF: Page 22 OBJ: 1-5.1 Subtracting Integers NAT: 8.1.3.a TOP: 1-5 Subtracting Integers KEY: integer subtraction 48. ANS: 3 Substitute for the variable. To subtract, add the opposite of the second integer. PTS: 1 DIF: Basic REF: Page 23 OBJ: 1-5.2 Evaluating Expressions with Integers NAT: 8.1.3.a TOP: 1-5 Subtracting Integers KEY: expression integer evaluate subtraction 49. ANS: 45ºF Subtract the low temperature from the high temperature. The difference tells how many degrees the temperature changed. 40 ( 5) = 40 + 5 = 45 PTS: 1 DIF: Average REF: Page 23 OBJ: 1-5.3 Application NAT: 8.1.3.a TOP: 1-5 Subtracting Integers KEY: expression integer evaluate subtraction 50. ANS: Her account balance is approximately $300 greater. Step 1 Estimate values. Step 2 Find approximately how much greater or less the balance is at the end of May than it was on March 1st.

The account balance is approximately $300 greater. PTS: 1 DIF: Advanced NAT: 8.1.3.a TOP: 1-5 Subtracting Integers 51. ANS: 27 Multiply the integers. If the signs are the same, the product will be positive; if the signs are different, the product will be negative. PTS: 1 DIF: Basic REF: Page 26 OBJ: 1-6.1 Multiplying and Dividing Integers NAT: 8.1.3.a TOP: 1-6 Multiplying and Dividing Integers KEY: integer multiplication division 52. ANS: 6 Multiply the integers. If the signs are the same, the product will be positive; if the signs are different, the product will be negative. PTS: 1 DIF: Average REF: Page 26 OBJ: 1-6.1 Multiplying and Dividing Integers NAT: 8.1.3.a TOP: 1-6 Multiplying and Dividing Integers KEY: integer multiplication division 53. ANS: 10 Divide the integers. If the signs are different, the quotient will be positive; if the signs are the same, the quotient will be negative. PTS: 1 DIF: Average REF: Page 26 OBJ: 1-6.1 Multiplying and Dividing Integers NAT: 8.1.3.a TOP: 1-6 Multiplying and Dividing Integers KEY: integer multiplication division 54. ANS: 91 First, perform the addition or subtraction inside the parentheses. Second, perform the multiplication. PTS: 1 DIF: Average REF: Page 27 OBJ: 1-6.2 Using the Order of Operations with Integers TOP: 1-6 Multiplying and Dividing Integers KEY: integer order of operations multiplication division 55. ANS: s = 3 Example: Solve. 14n = 154 NAT: 8.1.3.g Divide both sides by 14 to isolate n. n = 11 Check. 14n = 154 14(11) = 154? Substitute 11 for n. 154 = 154? So 11 is a solution.

PTS: 1 DIF: Basic REF: Page 39 OBJ: 1-8.1 Solving Equations Using Division TOP: 1-8 Solving Equations by Multiplying or Dividing 56. ANS: q = 270 Example: Solve. NAT: 8.5.4.a KEY: solving equation division Multiply both sides by 4 to isolate n. Check. n = 84 Substitute 84 for n. 21 = 21? So 84 is a solution. PTS: 1 DIF: Basic REF: Page 40 OBJ: 1-8.2 Solving Equations Using Multiplication TOP: 1-8 Solving Equations by Multiplying or Dividing 57. ANS: $440.00 Example: NAT: 8.5.4.c KEY: solving equation multiplication Your class earned $150 Saturday afternoon by washing cars to raise money for a class trip. This is money needed for the trip. What is the total amount needed? fraction of total amount total raised needed = raised of the Write the equation. T = 450 The total amount needed is $450. Multiply both sides by 3 to isolate T. PTS: 1 DIF: Average REF: Page 40 OBJ: 1-8.3 Application NAT: 8.5.4.c TOP: 1-8 Solving Equations by Multiplying or Dividing KEY: solving equation multiplication division 58. ANS: n = 4 Example:

Solve 4z + 8 = 20. Step 1: 4z + 8 = 20 Subtract 8 from both sides to isolate 8 = 8 the term with z in it. 4z = 12 Step 2: Divide both sides by 4. z = 3 PTS: 1 DIF: Basic REF: Page 41 OBJ: 1-8.4 Solving a Simple Two-Step Equation TOP: 1-8 Solving Equations by Multiplying or Dividing KEY: solving equation two-step equation 59. ANS: z = 45 Example: Solve. NAT: 8.5.4.a Step 1: Subtract 5 from both sides to isolate 5 = 5 the term with x in it. Step 2: Multiply both sides by 10. x = 150 PTS: 1 DIF: Average REF: Page 41 OBJ: 1-8.4 Solving a Simple Two-Step Equation TOP: 1-8 Solving Equations by Multiplying or Dividing KEY: solving equation two-step equation 60. ANS: NAT: 8.5.4.a n 36 Example: Solve and graph the inequality. 0 5 10 15 20 25 30 35 40 45 50 z < 20 Multiply both sides by 4 to isolate z. 2 0 2 4 6 8 10 12 14 16 18 20 22 A closed circle should be used when the value is included in the graph, such as with or An open circle should be used when the value is not included, such as with > or <. PTS: 1 DIF: Average REF: Page 45 OBJ: 1-9.2 Solving and Graphing Inequalities NAT: 8.5.4.a

Number of Diners Number of Diners TOP: 1-9 Introduction to Inequalities 61. ANS: KEY: solving inequality graph 200 150 100 50 Example: Day 1 2 3 4 5 6 7 Number of Diners 1 2 3 4 5 6 7 8 Day 129 67 44 64 88 175 196 200 150 100 50 1 2 3 4 5 6 7 8 Day PTS: 1 DIF: Basic REF: Page 128 OBJ: 3-3.3 Creating a Graph of a Situation NAT: 8.5.2.a TOP: 3-3 Interpreting Graphs and Tables KEY: graph table situations 62. ANS: 0 100 200 300 400 500 600 700 800 9001000 n The variable n must be greater than or equal to 500 yards for a swimmer to make the team. The graph should include the number 500 (solid circle at 500) and all the numbers to the right of 500 on the number line. PTS: 1 DIF: Advanced NAT: 8.1.1.i TOP: 1-9 Introduction to Inequalities 63. ANS: Since 3 is a common factor, divide the numerator and denominator by 3. = = PTS: 1 DIF: Basic REF: Page 64 OBJ: 2-1.1 Simplifying Fractions NAT: 8.1.1.e TOP: 2-1 Rational Numbers KEY: fraction simplify rational number

64. ANS: 6 Solve the equation. Substitute 7 for x and simplify. PTS: 1 DIF: Advanced NAT: 8.5.4.a TOP: 1-8 Solving Equations by Multiplying or Dividing 65. ANS: 8.875 Write the mixed number as a decimal. Subtract. PTS: 1 DIF: Advanced NAT: 8.1.3.a TOP: 2-3 Adding and Subtracting Rational Numbers 66. ANS: 131 500 The digit farthest to the right is in the thousandths place. So, write 262 as the numerator with 1000 as the denominator. Then, simplify. 0.262 = = PTS: 1 DIF: Average REF: Page 65 OBJ: 2-1.2 Writing Decimals as Fractions NAT: 8.1.1.e TOP: 2-1 Rational Numbers KEY: decimal fraction rational number 67. ANS: 1 Add the numerators. Keep the same denominator. If possible, simplify. = 1 PTS: 1 DIF: Basic REF: Page 73 OBJ: 2-3.3 Adding and Subtracting Fractions with Like Denominators NAT: 8.1.3.a TOP: 2-3 Adding and Subtracting Rational Numbers KEY: fraction like denominators addition subtraction rational number 68. ANS: 35 18 Multiply the numerators, and multiply the denominators. If possible, simplify. = = 131 500 35 18 PTS: 1 DIF: Basic REF: Page 77 OBJ: 2-4.2 Multiplying Fractions NAT: 8.1.3.a TOP: 2-4 Multiplying Rational Numbers KEY: fraction multiplication rational number 69. ANS:

0.6 To write a fraction as a decimal, divide the numerator by the denominator. If the decimal repeats, you can write a bar over the digits that repeat. PTS: 1 DIF: Average REF: Page 65 OBJ: 2-1.3 Writing Fractions as Decimals NAT: 8.1.1.e TOP: 2-1 Rational Numbers KEY: decimal fraction rational number 70. ANS: > Find the LCD. 14: 14, 28, 42, 56, 70, 84, 98, 112,... 21: 21, 42, 63, 84, 105, 126, 147, 168,... List multiples of 14 and 21. The LCM is 42. Write the fractions with a common denominator. > Compare the fractions. PTS: 1 DIF: Basic REF: Page 68 OBJ: 2-2.1 Comparing Fractions by Finding a Common Denominator NAT: 8.1.1.i TOP: 2-2 Comparing and Ordering Rational Numbers 71. ANS: 19 36 = Find a common denominator: 12(9) = 108. Multiply by fractions equal to 1. = Rewrite with a common denominator. 19 36 = Add. If possible, simplify. PTS: 1 DIF: Basic REF: Page 85 OBJ: 2-6.1 Adding and Subtracting Fractions with Unlike Denominators NAT: 8.1.3.a TOP: 2-6 Adding and Subtracting with Unlike Denominators KEY: fraction addition subtraction unlike denominators rational number 72. ANS: 2 1 3 Multiplying a fraction by a whole number is the same as multiplying the whole number by just the numerator of the fraction and keeping the same denominator. If possible, simplify. = = = 2 1 3 PTS: 1 DIF: Basic REF: Page 76 OBJ: 2-4.1 Multiplying a Fraction and an Integer NAT: 8.1.3.a TOP: 2-4 Multiplying Rational Numbers KEY: fraction integer multiplication rational number 73. ANS: >

> and Write the fractions as decimals. Compare the decimals. PTS: 1 DIF: Average REF: Page 69 OBJ: 2-2.2 Comparing by Using Decimals TOP: 2-2 Comparing and Ordering Rational Numbers 74. ANS: 70.2 Substitute 32.5 for x. Then add. = = 70.2 NAT: 8.1.1.i PTS: 1 DIF: Average REF: Page 73 OBJ: 2-3.4 Evaluating Expressions with Rational Numbers NAT: 8.1.3.a TOP: 2-3 Adding and Subtracting Rational Numbers KEY: rational number expression evaluate 75. ANS: 2.268 First, multiply the numbers. Then, place the decimal point in the correct location. = 2.268 PTS: 1 DIF: Average REF: Page 77 OBJ: 2-4.3 Multiplying Decimals NAT: 8.1.3.a TOP: 2-4 Multiplying Rational Numbers KEY: decimal multiplication rational number 76. ANS: 8 3 To divide by a fraction, multiply by the reciprocal. If possible, simplify. = = = 8 3 PTS: 1 DIF: Basic REF: Page 80 OBJ: 2-5.1 Dividing Fractions NAT: 8.1.3.a TOP: 2-5 Dividing Rational Numbers KEY: fraction division rational number 77. ANS: 1.56 When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places is the number of zeros to write after the 1. = = = = 1.56 PTS: 1 DIF: Average REF: Page 81 OBJ: 2-5.2 Dividing Decimals NAT: 8.1.3.a TOP: 2-5 Dividing Rational Numbers KEY: decimal division rational number 78. ANS: 3.5 Substitute 2.5 for n. Then divide. = = 3.5

PTS: 1 DIF: Average REF: Page 81 OBJ: 2-5.3 Evaluating Expressions with Fractions and Decimals NAT: 8.1.3.a TOP: 2-5 Dividing Rational Numbers KEY: fraction decimal rational number expression evaluate 79. ANS: 25 miles per gallon Divide the number of miles gone by the number of gallons of gas used. The car gets 25 miles per gallon. PTS: 1 DIF: Average REF: Page 82 OBJ: 2-5.4 Problem-Solving Application NAT: 8.1.3.a TOP: 2-5 Dividing Rational Numbers KEY: decimal fraction rational number division problem solving 80. ANS: 17 21 Substitute for n. Then add. When adding fractions with unlike denominators, first find a common denominator by multiplying one denominator by the other denominator or finding the least common denominator (LCD). n + 1 2 = 6 + 1 2 17 = 3 7 3 21 PTS: 1 DIF: Average REF: Page 86 OBJ: 2-6.2 Evaluating Expressions with Rational Numbers NAT: 8.1.3.a TOP: 2-6 Adding and Subtracting with Unlike Denominators KEY: fraction addition subtraction unlike denominators rational number expression 81. ANS: 2 7 10 cups 6 7 Add to find the total amount of flour needed. When adding fractions with unlike denominators, first find a common denominator by multiplying one denominator by the other denominator or finding the least common denominator (LCD). 1 1 + 1 1 = 2 7 2 5 10 You will need 2 7 10 cups of flour. PTS: 1 DIF: Average REF: Page 86 OBJ: 2-6.3 Application NAT: 8.1.3.g TOP: 2-6 Adding and Subtracting with Unlike Denominators KEY: fraction addition subtraction unlike denominators rational number 82. ANS: y = 26.1 y = 26.1 Add Solve. to both sides.

PTS: 1 DIF: Basic REF: Page 92 OBJ: 2-7.1 Solving Equations with Decimals TOP: 2-7 Solving Equations with Rational Numbers 83. ANS: p = 2 NAT: 8.1.3.a KEY: solving equation decimal p = 2 Divide both sides by 1.7. Solve. PTS: 1 DIF: Average REF: Page 92 OBJ: 2-7.1 Solving Equations with Decimals TOP: 2-7 Solving Equations with Rational Numbers 84. ANS: t = 224.79 NAT: 8.1.3.a KEY: solving equation decimal Multiply both sides by 17.7. t = 224.79 Solve. PTS: 1 DIF: Average REF: Page 92 OBJ: 2-7.1 Solving Equations with Decimals TOP: 2-7 Solving Equations with Rational Numbers 85. ANS: w = 5 w = 3 6 5 5 w 5 = 3 5 Divide both sides by 5. 6 6 5 6 6 5 w 6 = 3 6 Multiply by the reciprocal. 6 5 5 5 w = 18 25 18 25 Solve. NAT: 8.1.3.a KEY: solving equation decimal PTS: 1 DIF: Average REF: Page 92 OBJ: 2-7.2 Solving Equations with Fractions NAT: 8.1.3.a TOP: 2-7 Solving Equations with Rational Numbers KEY: solving equation fraction 86. ANS: 6 hours Step 1 Write an equation. Let h represent the number of hours Genna can have the magician stay. Total cost = Initial fee + Cost for h hours 189 = 45 + Step 2 Solve. 189 = 45 + Subtract 45 from both sides. = Divide both sides by 24.

6 = h Solve. Genna have the magician stay for 6 hours. PTS: 1 DIF: Average REF: Page 98 OBJ: 2-8.1 Problem-Solving Application NAT: 8.5.4.c TOP: 2-8 Solving Two-Step Equations KEY: problem solving 87. ANS: x y (x, y) 1 20 (1, 20) Substitute 1 for x and simplify. 2 36 (2, 36) Substitute 2 for x and simplify. 3 52 (3, 52) Substitute 3 for x and simplify. 4 68 (4, 68) Substitute 4 for x and simplify. PTS: 1 DIF: Average REF: Page 119 OBJ: 3-1.2 Creating a Table of Ordered Pair Solutions NAT: 8.5.2.b TOP: 3-1 Ordered Pairs KEY: table ordered pair 88. ANS: Yes (10, 44): y = 4x + 4 44 = 4(10) + 4? Substitute 10 for x and 44 for y. 44 = 40 + 4? Simplify. 44 = 44 Yes. (10, 44) is a solution PTS: 1 DIF: Basic REF: Page 118 OBJ: 3-1.1 Deciding Whether an Ordered Pair Is a Solution of an Equation NAT: 8.5.2.b TOP: 3-1 Ordered Pairs KEY: ordered pair solving equation 89. ANS: $910 c = 0.13(7000) = 910 The commission is $910. PTS: 1 DIF: Average REF: Page 119 OBJ: 3-1.3 Application NAT: 8.5.2.d TOP: 3-1 Ordered Pairs KEY: commission 90. ANS: Point A is at (0, 5). Point B is at ( 1, 2). Point C is at (4, 2).

Point D is at ( 5, 3). Point A is at (0, 5). Point B is at ( 1, 2). Point C is at (4, 2). Point D is at ( 5, 3). PTS: 1 DIF: Basic REF: Page 122 OBJ: 3-2.1 Finding the Coordinates and Quadrants of Points on a Plane NAT: 8.5.2.c TOP: 3-2 Graphing on a Coordinate Plane KEY: coordinate plane graph point 91. ANS: y 8 4 (0, 4) (2, 0) 8 4 4 8 x 4 ( 2, 8) 8 Make a function table. Then, plot each ordered pair on the coordinate plane and connect the points with a line. x y = 2x 4 y (x, y) 2 y = 2x 4 8 ( 2, 8) 0 y = 2x 4 4 (0, 4) 2 y = 2x 4 0 (2, 0) PTS: 1 DIF: Basic REF: Page 123 OBJ: 3-2.3 Graphing an Equation of a Line TOP: 3-2 Graphing on a Coordinate Plane KEY: integer equation plot points coordinate plane 92. ANS: ; Area = 72 square units Step 1 Plot the points. NAT: 8.5.2.a

y 5 4 3 2 1 B C 1 1 2 3 4 5 6 7 8 9 10 x 2 3 4 5 A Step 2 Find the fourth vertex. The fourth vertex will have the same x-coordinate as and the same y-coordinate as. x-coordinate: 10 y-coordinate: The fourth vertex is. 5 y 4 3 2 1 B C 1 2 3 4 5 A 1 2 3 4 5 6 7 8 9 10 x D Step 3 Find the area of the rectangle. square units PTS: 1 DIF: Advanced NAT: 8.3.4.a TOP: 3-2 Graphing on a Coordinate Plane KEY: multi-step 93. ANS: Horse 3 Horse 3 is Sumio s. The horse s speed is 0 to start. The speed is a small positive number when the horse is moving slowly. The speed is a greater number when it bolts. Then the number gets smaller again and returns to 0 when the horse stops to rest. PTS: 1 DIF: Average REF: Page 127 OBJ: 3-3.1 Matching Situations to Tables

NAT: 8.5.2.b TOP: 3-3 Interpreting Graphs and Tables KEY: table situations 94. ANS: Graph 1 Graph 1 does. The horse s speed is not 0 when the graph starts, but the speed drops to 0 twice. PTS: 1 DIF: Basic REF: Page 128 OBJ: 3-3.2 Matching Situations to Graphs TOP: 3-3 Interpreting Graphs and Tables 95. ANS: NAT: 8.5.2.b KEY: graph situations y = x + 5 Choose points from the graph to make the table. 9 8 7 6 5 4 3 2 1 y 4 3 2 1 1 1 2 3 4 x 2 3 To write the equation, look for a pattern in the values. 3 = 2 + 5 4 = 1 + 5 5 = 0 + 5 6 = 1 + 5 7 = 2 + 5 y = x + 5 PTS: 1 DIF: Average REF: Page 139 OBJ: 3-5.3 Using Graphs to Generate Different Representations of Data NAT: 8.4.1.b TOP: 3-5 Equations Tables and Graphs KEY: table graph function equation 96. ANS: Filo earns $2 per hour but then buys lunch for $5. How much money does he have left? Situation 1 At the mall, Pena buys 2 CDs and spends $5 on lunch. How much money does she have left? Both the purchase of CDs and lunch are expenses, so they are negative values. If x represents the cost per CD, then the money y Pena has left is. This does not match the given relationship. Situation 2 Filo s allowance is twice Rachel s allowance less than $5. What is Filo s allowance? Let x represent Rachel s allowance and y represent Filo s allowance. The difference between $5 and twice Rachel s allowance is Filo s allowance 5 2x = y

This does not match the given relationship. Situation 3 Marcus works out at the gym for half as many minutes as he spends eating lunch minus 5 minutes. How long does Marcus work out at the gym? Let y represent the amount of time Marcus works out at the gym and x represent the amount of time he spends eating lunch. Marcus works out at the gym half as many minutes as he spends eating lunch minus 5 minutes y = y 5 This does not match the relationship. Situation 4 Filo earns $2 per hour but then buys lunch for $5. How much money does he have left? Let x represent the amount of hours Filo works and y represent the amount of money he has left. Filo earns $2 per hour but then buys lunch for $5 2x 5 represents how much money he has left so This matches the relationship and is the correct answer. PTS: 1 DIF: Advanced NAT: 8.5.2.a TOP: 3-5 Equations Tables and Graphs 97. ANS: y = 19.50n + 60.00; $196.50 Use a function table to help you identify the pattern in a sequence and to find the missing terms. n 60.00+ 19.50n y 1 60.00+ 19.50(1) 79.50 2 60.00+ 19.50(2) 99.00 3 60.00+ 19.50(3) 118.50 4 60.00+ 19.50(4) 138.00 n 60.00+ 19.50(n) 19.50n + 60.00 Then substitute 7 for n. 19.50n + 60.00 19.50(7) + 60.00 136.50 + 60.00 196.50 A 7-hour job will cost $196.50. PTS: 1 DIF: Average REF: Page 143 OBJ: 3-6.4 Application NAT: 8.5.1.a TOP: 3-6 Arithmetic Sequences KEY: function sequence 98. ANS: Identify how many times = is a factor. PTS: 1 DIF: Basic REF: Page 162 OBJ: 4-1.1 Writing Exponents NAT: 8.5.3.c TOP: 4-1 Exponents KEY: exponent write

ESSAY 99. ANS: Gloria divided the total ounces in the box by the number of ounces she eats each day to find the number of days the cereal will last, 18 3 = 6. Carlos started with the total number of ounces in the box and kept subtracting the number of ounces he eats each day until he reached 0. Then he counted the number of times he had to subtract to find the number of days the cereal will last, 18 3 3 3 3 3 3 = 0. He subtracted 3 from 18 a total of 6 times. They got the same answer because they basically did the same thing. When Gloria divided 18 by 3, she found how many groups of 3 there are in 18. When Carlos repeatedly subtracted 3 from 18, he also found how many groups of 3 there are in 18. Scoring Rubric: 4 The solution is correct, and the explanation is complete as above. or The solution is correct, and a different logical explanation is given. 3 The solution is correct, but the explanation is incomplete. 2 The solution is incorrect, but the explanation shows some understanding of the concept. 1 The solution is incorrect, and the explanation is missing or shows no understanding of the concept. PTS: 1 DIF: Average NAT: 8.5.2.a TOP: 1-2 Algebraic Expressions KEY: algebraic expression word problem writing expressions 100. ANS: $48 times the number of hours worked, h, is equal to the total amount, $347, minus the fixed fee, $35. It took the electrician 6.5 hours to rewire Carlos basement. Scoring Rubric: 4 The solution is correct, and the explanation is complete as above. or The solution is correct, and a different logical explanation is given. 3 The solution is correct, but the explanation is incomplete. 2 The solution is incorrect, but the explanation shows some understanding of the concept. 1 The solution is incorrect, and the explanation is missing or shows no understanding of the concept. PTS: 1 DIF: Average NAT: 8.5.4.c TOP: 1-8 Solving Equations by Multiplying or Dividing KEY: solving equation multiplication division

Answer to chapter 5 and 6 NUMERIC RESPONSE 1. ANS: 32 PTS: 1 DIF: Average NAT: 8.2.1.k TOP: 5-5 Similar Figures KEY: proportion similar figures 2. ANS: $31.05 PTS: 1 DIF: Advanced NAT: 8.1.4.d TOP: 6-5 Percent Increase and Decrease KEY: multi-step percent increase percent decrease percent SHORT ANSWER 3. ANS: no If the fractions are equal when simplified, then the ratios are proportional. PTS: 1 DIF: Basic REF: Page 217 OBJ: 5-1.2 Determining Whether Two Ratios are in Proportion NAT: 8.1.4.c TOP: 5-1 Ratios and Proportions KEY: proportion ratio 4. ANS: yes Set up the proportion the salaries are proportional., and simplify. If the fractions are equal, then PTS: 1 DIF: Average REF: Page 217 OBJ: 5-1.3 Application NAT: 8.1.4.c TOP: 5-1 Ratios and Proportions KEY: proportion ratio 5. ANS: 10 Write the rate. Divide to find games per minute. games per minute PTS: 1 DIF: Basic REF: Page 220 OBJ: 5-2.1 Finding Unit Rates NAT: 8.1.4.a TOP: 5-2 Ratios Rates and Unit Rates KEY: compare order ratio 6. ANS: 10-oz. box Find the unit rate for each box by dividing the price by the number of ounces. The lower price per ounce is the better buy. Unit rate for 10-ounce box = Unit rate for 14-ounce box =

The 10-oz. box box is the better buy. PTS: 1 DIF: Average REF: Page 221 OBJ: 5-2.4 Finding Unit Prices to Compare Costs TOP: 5-2 Ratios Rates and Unit Rates KEY: unit price 7. ANS: 520 cities There are about 52 weeks in one year. (52 weeks = 364 days) NAT: 8.1.4.c PTS: 1 DIF: Average REF: Page 224 OBJ: 5-3.2 Using Conversion Factors to Solve Problems NAT: 8.2.2.b TOP: 5-3 Dimensional Analysis KEY: conversion factor solving 8. ANS: 75 pages PTS: 1 DIF: Average REF: Page 226 OBJ: 5-3.4 Application NAT: 8.2.2.b TOP: 5-3 Dimensional Analysis KEY: conversion factor solving 9. ANS: 36.25 cm Find the scale factor by dividing the length of the enlarged picture by the length of the original. Next, multiply the width of the original by the scale factor to obtain the width of the enlarged picture. PTS: 1 DIF: Average REF: Page 239 OBJ: 5-5.2 Using Scale Factors to Find Missing Dimensions NAT: 8.3.2.e TOP: 5-5 Similar Figures KEY: scale factor 10. ANS: 56 in. Because 3 inches on the sketch represents 12 inches in the mural, the mural is a dilation of the sketch by a factor of 4. Find the dimensions of the door in the mural. in. Multiply each dimension by 4. in. Find the perimeter of the door. in. PTS: 1 DIF: Advanced NAT: 8.1.4.c TOP: 5-6 Dilations 11. ANS: k = 6.6 To solve using equivalent fractions, multiply the numerator and denominator of by 5. The numerators are equal because the denominators are equal. 5k = 33

k = 6.6 PTS: 1 DIF: Basic REF: Page 230 OBJ: 5-4.3 Solving Proportions Using Equivalent Fractions TOP: 5-4 Solving Proportions KEY: proportion 12. ANS: 171 m NAT: 8.1.4.c Set up the proportion. Find cross products, and solve for x. PTS: 1 DIF: Average REF: Page 252 OBJ: 5-8.1 Using Proportions to Find Unknown Scales TOP: 5-8 Scale Drawings and Scale Models 13. ANS: 425.25 g; 1.75 lb Step 1 Convert 15 oz into grams. NAT: 8.2.2.f KEY: proportion Step 2 Convert 793.8 g into pounds. PTS: 1 DIF: Advanced NAT: 8.2.2.b TOP: 5-3 Dimensional Analysis 14. ANS: 1 and 2 Compare the ratios of corresponding sides to see which rectangles are similar. The two rectangles with equal ratios are similar. PTS: 1 DIF: Basic REF: Page 238 OBJ: 5-5.1 Identifying Similar Figures NAT: 8.3.2.e TOP: 5-5 Similar Figures KEY: similar 15. ANS: 13 20 b =25%; c = ; d = 71.43% To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. To convert a percent to a fraction, place the percent over 100 and simplify the fraction. PTS: 1 DIF: Average REF: Page 274 OBJ: 6-1.1 Finding Equivalent Ratios and Percents NAT: 8.1.1.i TOP: 6-1 Relating Decimals Fractions and Percents KEY: fraction number line percent ratio 16. ANS: > Write the decimal as a percent, and then compare. To convert a decimal to a percent, multiply by 100 and insert the percent symbol. PTS: 1 DIF: Basic REF: Page 275

OBJ: 6-1.2 Comparing Fractions Decimals and Percents NAT: 8.1.1.i TOP: 6-1 Relating Decimals Fractions and Percents 17. ANS: > Write the fraction as a percent, and then compare. To convert a fraction to a percent, first divide the numerator by the denominator to get a decimal. Then, multiply the decimal by 100 and insert the percent symbol. PTS: 1 DIF: Basic REF: Page 275 OBJ: 6-1.2 Comparing Fractions Decimals and Percents TOP: 6-1 Relating Decimals Fractions and Percents 18. ANS: 81 100 0.1%, 0.68,, and 148% Write the numbers as percents, and then compare. NAT: 8.1.1.i To convert a decimal to a percent, multiply by 100 and insert the percent symbol. To convert a fraction to a percent, first divide the numerator by the denominator to get a decimal. Then, multiply the decimal by 100 and insert the percent symbol. PTS: 1 DIF: Average REF: Page 275 OBJ: 6-1.3 Ordering Fractions Decimals and Percents NAT: 8.1.1.e TOP: 6-1 Relating Decimals Fractions and Percents 19. ANS: 96% Divide the current amount of gas by the total amount of gas allowed, and multiply the result by 100. PTS: 1 DIF: Average REF: Page 275 OBJ: 6-1.4 Application NAT: 8.1.1.e TOP: 6-1 Relating Decimals Fractions and Percents KEY: convert decimal fraction percent 20. ANS: 40 Use the table of benchmarks to help you estimate percents. Percent Decimal Fraction 5% 0.05 10% 0.1 25% 0.25 50% 0.5 75% 0.75 100% 1 1

PTS: 1 DIF: Average REF: Page 278 OBJ: 6-2.1 Estimating with Percents NAT: 8.1.4.d TOP: 6-2 Estimate with Percents KEY: estimate percent 21. ANS: 2,869.23% Set up an equation to find the percent. Divide both sides by 373 to isolate the variable, and simplify. If necessary, round your answer to the nearest hundredth of a percent. PTS: 1 DIF: Average REF: Page 284 OBJ: 6-3.1 Finding the Percent One Number Is of Another TOP: 6-3 Finding Percents KEY: percent 22. ANS: 20% NAT: 8.1.4.d PTS: 1 DIF: Advanced NAT: 8.1.4.d TOP: 6-2 Estimate with Percents 23. ANS: $3.75 The percent is already a compatible number. Round the price to the nearest $5, multiply the rounded price by the percent, and divide the resulting product by 100. PTS: 1 DIF: Average REF: Page 279 OBJ: 6-2.2 Problem-Solving Application NAT: 8.1.4.d TOP: 6-2 Estimate with Percents KEY: estimate percent 24. ANS: 9.17% Set up a proportion. Find the cross products. Since x is multiplied by 120, divide both sides by 120 to undo the multiplication. 9.17% of the compound is made up of zinc. PTS: 1 DIF: Advanced NAT: 8.1.4.d TOP: 6-3 Finding Percents KEY: convert decimal fraction percent 25. ANS: 129.63 Set up an equation to find the number. Divide to undo the multiplication, and simplify.

PTS: 1 DIF: Basic REF: Page 288 OBJ: 6-4.1 Finding a Number When the Percent Is Known NAT: 8.1.4.d TOP: 6-4 Finding a Number When the Percent Is Known KEY: percent 26. ANS: 15.5 lb Set up an equation to find the weight of all of the rocks. Divide to undo the multiplication, and simplify. PTS: 1 DIF: Average REF: Page 288 OBJ: 6-4.2 Application NAT: 8.1.4.d TOP: 6-4 Finding a Number When the Percent Is Known KEY: percent 27. ANS: 14 ft Set up a proportion. Find the cross products. Since x is multiplied by??, divide both sides by?? to undo the multiplication. PTS: 1 DIF: Average REF: Page 289 OBJ: 6-4.3 Application NAT: 8.1.4.d TOP: 6-4 Finding a Number When the Percent Is Known KEY: percent 28. ANS: 70% decrease Percent increase describes how much the original amount increases. Percent decrease describes how much the original amount decreases. The percent change is the ratio of the amount of change to the original amount, or percent change =. PTS: 1 DIF: Basic REF: Page 294 OBJ: 6-5.1 Finding Percent Increase or Decrease NAT: 8.1.4.d TOP: 6-5 Percent Increase and Decrease KEY: percent decrease percent increase

29. ANS: $573.00 First, find the discount amount. Then, subtract the discount amount from the original price. PTS: 1 DIF: Basic REF: Page 295 OBJ: 6-5.3 Using Percent Increase or Decrease to Find Prices NAT: 8.1.4.d TOP: 6-5 Percent Increase and Decrease KEY: percent decrease percent increase 30. ANS: $693.00 Find the amount of increase and add the increase to the original price. PTS: 1 DIF: Average REF: Page 295 OBJ: 6-5.3 Using Percent Increase or Decrease to Find Prices NAT: 8.1.4.d TOP: 6-5 Percent Increase and Decrease KEY: percent decrease percent increase 31. ANS: $443.24 Set up an equation and solve. sale percent = commission PTS: 1 DIF: Average REF: Page 299 OBJ: 6-6.4 Dividing by Percents to Find Total Sales NAT: 8.1.4.d TOP: 6-6 Applications of Percents KEY: division percent 32. ANS: and Multiply or divide the numerator and denominator by the same nonzero number. PTS: 1 DIF: Average REF: Page 216 OBJ: 5-1.1 Finding Equivalent Ratios NAT: 8.1.4.b TOP: 5-1 Ratios and Proportions KEY: equivalent fraction ratio Answer to chapter 7 and 8 SHORT ANSWER 1. ANS: Point M, point N, point O, point P A point names a location. There are four labeled points in this diagram: point M, point N, point O, and point P. PTS: 1 DIF: Basic REF: Page 324 OBJ: 7-1.1 Naming Points Lines Planes Segments and Rays TOP: 7-1 Points Lines Planes and Angles 2. ANS: NAT: 8.3.1.b KEY: line plane point ray segment A line is straight and extends forever in both directions.

A line is named by two points on the line. When naming a line, be sure to include the naming the points. over the letters There are three ways to name the line shown in this diagram:. PTS: 1 DIF: Basic REF: Page 324 OBJ: 7-1.1 Naming Points Lines Planes Segments and Rays NAT: 8.3.1.b TOP: 7-1 Points Lines Planes and Angles KEY: line plane point ray segment 3. ANS: QRV A right angle measures 90, so SRV and QRV are the right angles in the diagram. PTS: 1 DIF: Basic REF: Page 325 OBJ: 7-1.2 Classifying Angles NAT: 8.3.1.b TOP: 7-1 Points Lines Planes and Angles KEY: acute angle angle obtuse angle right angle 4. ANS: 30 Vertical angles are always congruent. Since m 2 = 30, m 4 = 30. PTS: 1 DIF: Basic REF: Page 326 OBJ: 7-1.3 Finding the Measures of Vertical Angles NAT: 8.3.3.g TOP: 7-1 Points Lines Planes and Angles KEY: angle vertical angles 5. ANS: 62 The three angle measures in a triangle add up to 180. Add the two given angle measures, and subtract the sum from 180. PTS: 1 DIF: Basic REF: Page 336 OBJ: 7-3.1 Finding Angles in Acute Right and Obtuse Triangles NAT: 8.3.3.f TOP: 7-3 Angles in Triangles KEY: acute triangle angle measure obtuse triangle right triangle triangle 6. ANS: 20 The three angle measures in a triangle add up to 180. Add the two given angle measures, and subtract the sum from 180. PTS: 1 DIF: Basic REF: Page 336 OBJ: 7-3.1 Finding Angles in Acute Right and Obtuse Triangles NAT: 8.3.3.f TOP: 7-3 Angles in Triangles KEY: acute triangle angle measure obtuse triangle right triangle triangle 7. ANS: 34 The three angle measures in a triangle add up to 180. Add the two given angle measures, and subtract the sum from 180. PTS: 1 DIF: Basic REF: Page 336 OBJ: 7-3.1 Finding Angles in Acute Right and Obtuse Triangles NAT: 8.3.3.f TOP: 7-3 Angles in Triangles

KEY: acute triangle angle measure obtuse triangle right triangle triangle 8. ANS: Rotation In a rotation, a figure is turned about a point. This is a rotation. PTS: 1 DIF: Basic REF: Page 358 OBJ: 7-7.1 Identifying Transformations NAT: 8.3.2.c TOP: 7-7 Transformations KEY: reflection rotation transformation translation 9. ANS: Rotation In a rotation, a figure is turned about a point. This is a rotation. PTS: 1 DIF: Basic REF: Page 358 OBJ: 7-7.1 Identifying Transformations NAT: 8.3.2.c TOP: 7-7 Transformations KEY: reflection rotation transformation translation 10. ANS: Reflection In a reflection, a mirror image is created when a figure is flipped the figure across a line. This is a reflection. PTS: 1 DIF: Basic REF: Page 358 OBJ: 7-7.1 Identifying Transformations NAT: 8.3.2.c TOP: 7-7 Transformations KEY: reflection rotation transformation translation 11. ANS: 5 4 3 2 1 y 5 4 3 2 1 1 2 3 4 5 x 1 2 3 4 5 Graph the given points and perform the indicated transformation. In a rotation the figure will be rotated about the origin, (0, 0). PTS: 1 DIF: Average REF: Page 359 OBJ: 7-7.2 Graphing Transformations NAT: 8.3.2.c TOP: 7-7 Transformations KEY: coordinate plane graph reflection rotation transformation translation 12. ANS: 129 m To find the perimeter of a figure, add the lengths of all the sides. PTS: 1 DIF: Basic REF: Page 388 OBJ: 8-1.1 Finding the Perimeter of Rectangles and Parallelograms NAT: 8.2.1.h TOP: 8-1 Perimeter and Area of Rectangles and Parallelograms

KEY: perimeter rectangle parallelogram 13. ANS: 47.5 cm Area of a trapezoid Substitute 5 for h, 7 for, and 12 for. Simplify. PTS: 1 DIF: Advanced NAT: 8.2.1.h TOP: 8-2 Perimeter and Area of Triangles and Trapezoids 14. ANS: C = 20.4 ft 64.1 ft The circumference of a circle is times the radius. PTS: 1 DIF: Average REF: Page 400 OBJ: 8-3.1 Finding the Circumference of a Circle TOP: 8-3 Circles KEY: circumference circle 15. ANS: cubic units Volume of a prism Substitute for l, x for w, and 3x for h. Simplify. NAT: 8.2.1.h PTS: 1 DIF: Advanced NAT: 8.2.1.j TOP: 8-5 Volume of Prisms and Cylinders 16. ANS: 338.08 cm 2 The surface area of a prism can be found using the formula, where B is the area of the base of the figure, P is the perimeter of the base of the figure, and h is the height of the figure. PTS: 1 DIF: Basic REF: Page 427 OBJ: 8-7.1 Finding Surface Area NAT: 8.2.1.j TOP: 8-7 Surface Area of Prisms and Cylinders KEY: surface area prism cylinder Answer to chapter 9 and 10 NUMERIC RESPONSE 1. ANS: 215 PTS: 1 DIF: Advanced NAT: 8.4.2.a TOP: 9-3 Measures of Central Tendency 2. ANS: 31 52