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Answer Key Page 1 1. 9 3. 1 2. 7 4. 6 Page 2 5. 7 8 15 8 7 15 15 7 8 15 8 7 6. 9 2 11 2 9 11 11 9 2 11 2 9 7. 6 8 14 8 6 14 14 6 8 14 8 6 8. 40 50 90 50 40 90 90 40 50 90 50 40 9. 60 50 110 50 60 110 110 60 50 110 50 60 10. 79 21 100 21 79 100 100 79 21 100 21 79 11. 9 12. 13. 5 14. 15. 9 16. 17. 25 18. 19. 37 15. k 70 35; 16. m 85 60; Page 5 1. 8 3. 11 5. 40 7. 180 Page 6 8. 28 10. 40 12. 11 14. 14 16. 8 18. 22 20. 148 22. 60 24. a b 26. b a 6 17 22 18 Page 3 1. a 25 3; 2. b 49 39; 3. c 70 57; 4. x 75 25; 5. n 100 11; a 22 b 10 c 13 x 50 n 89 Page 4 6. a 30 7; 7. b 87 67; 8. c 90 50; 9. d 100 75; 10. e 100 47; 11. f 125 25; 12. g 35 15; 13. h 100 45; 14. j 80 62; a 23 b 20 c 40 d 25 e 53 f 100 g 20 h 55 j 18 © CSL Associates, Inc. (877) 790-7915 k 35 m 25 2. 9 4. 18 6. 40 9. 11. 13. 15. 17. 19. 21. 23. 25. 35 280 19 27 23 65 125 155 ab Page 7 1. The sum of 3 plus 8 is the same as the sum of 5 plus 6. 2. The product of 2 times 9 is the same as the product of 3 times 6. 3. The difference of 15 minus 5 is the same as the difference of 20 minus 10. 4. The quotient of 20 divided by 5 is the same as the quotient of 12 divided by 3. Page 8 5. The product of 3 times 8 is the same as the product of 4 times 6. 6. The sum of 2 plus 9 is the same as the sum of 5 plus 6. 7. The quotient of 15 divided by 5 is the same as the quotient of 21 divided by 7. 8. The difference of 20 minus 5 is the same as the difference of 32 minus 17. 9. a, c 10. b, d 11. a, b 12. a, d 13. a, b, d 14. a, d Page 9 1. true; 2. false; 3. true; 4. false; 28 24 24 61 ≠ ≠ 28 23 24 60 Page 10 5. false; 18 ≠ 16 6. true; 60 60 7. false; 24 ≠ 28 8. true; 130 130 9. false; 71 ≠ 69 10. true; 40 40 11. true; 192 192 12. true; 17 17 13. 58 103 14. 87 61 15. 2 37 16. 3 3 3 17. 120 34 18. 5 13 Page 11 1. 3. Page 12 5. ; 6. ; 7. ; 8. ; 9. ; 10. ; 11. ; 12. ; 13. ; 14. ; 15. ; 16. ; 17. true 19. false 21. true 2. 4. 60 64 30 = 30 32 = 32 13 17 35 42 25 24 72 80 16 14 216 288 69 73 48 48 82 81 18. false 20. false 22. false Page 13 1. 22 15 7 22 7 15 2. 15 20 35 20 15 35 3. 72 ÷ 12 6 72 ÷ 6 12 4. 7 20 140 20 7 140 Page 14 5. 42 24 18 42 18 24 6. 153 ÷ 17 9 153 ÷ 9 17 ARITHMETIC TO ALGEBRA IL Workbook R 59 Answer Key 7. 26 32 58 32 26 58 8. 65 38 27 65 27 38 9. 4 39 156 39 4 156 10. 19 54 73 54 19 73 11. 184 ÷ 23 8 184 ÷ 8 23 12. 5 35 175 35 5 175 13. Checks 14. Wrong 706 349 357 15. Checks 16. Wrong 582 769 1,351 17. Checks 18. Wrong 245 164 81 19. c a b or c b a 20. t ÷ r s or t ÷ s r Page 15 1. 1, 12, 2, 6 2. 1, 28 2, 14, 3. 2 2 2 = 8 4. 5 5 = 25 3, 4 4, 7 Page 16 5. Check students’ arrays: 1 dot by 16 dots; 2 dots by 8 dots; 4 dots by 4 dots 6. Check students’ arrays: 1 dot by 18 dots; 2 dots by 9 dots; 3 dots by 6 dots 7. Check students’ arrays: 1 dot by 23 dots 8. Check students’ arrays: 1 dot by 36 dots; 2 dots by 18 dots; 3 dots by 12 dots; 4 dots by 9 dots; 6 dots by 6 dots 9. 1, 2, 5, 10 10. 1, 3, 5, 15 11. 1, 17 12. 1, 2, 4, 5, 10, 20 13. 1, 5, 25 14. 1, 2, 4, 8, 16, 32 15. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 16. 1, 2, 4, 8, 16, 32, 64 17. 2 2 2 2 16 60 IL Workbook R 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 5 5 5 125 3 3 3 27 4 4 16 6 6 6 216 3 3 3 3 81 10 10 100 10 10 10 10 10,000 34 62 93 105 Page 17 1. 1, 7; prime 2. 1, 2, 5, 10; composite 3. 1, 17; prime 4. 1, 3, 7, 21; composite 5. 1, 23; prime 6. 1, 3, 9, 27; composite 7. 2 2 2 or 23 8. 2 2 5 or 22 5 Page 18 9. 1, 5; prime 10. 1, 2, 3, 6; composite 11. 1, 3, 9; composite 12. 1, 11; prime 13. 1, 2, 7, 14; composite 14. 1, 19; prime 15. 1, 5, 25; composite 16. 1, 31; prime 17. 1, 3, 11, 33; composite 18. 2 2 3 or 22 3 19. 2 3 3 or 2 32 20. 2 2 7 or 22 7 21. 2 2 2 5 or 23 5 22. 1 41 23. 2 2 2 7 or 23 7 24. 3 3 3 3 or 34 25. 2 2 5 5 or 22 52 Page 19 1. 3 7 2. 3 5 ARITHMETIC TO ALGEBRA Page 20 3. 3 8 4. 9 10 5. 223 2225 3 25 3 10 6. 235 2233 5 23 5 6 7. 227 7 2235 35 8. 335 357 3 7 9. 333 2233 3 22 10. 235 2355 1 5 11. 237 77 23 7 12. 2233 337 13. 6 7 22 7 2223 2235 2 5 14. 255 557 2 7 15. 77 257 7 25 7 10 16. 333 355 33 55 9 25 17. 22223 35 2222 5 18. 337 235 7 15 3 4 4 7 16 5 37 25 Page 21 1. factors of 4: 1, 2, 4 factors of 10: 1, 2, 5, GCF 2 2. factors of 9: 1, 3, 9 factors of 12: 1, 2, 3, GCF 3 3. factors of 15: 1, 3, 5, factors of 21: 1, 3, 7, CGF 3 21 10 10 4, 6, 12 15 21 Page 22 4. factors of 9: 1, 3, 9 factors of 15: 1, 3, 5, 15 GCF 3 5. factors of 6: 1, 2, 3, 6 factors of 18: 1, 2, 3, 6, 9, 18 GCF 6 © CSL Associates, Inc. (877) 790-7915 Answer Key 6. factors of 5: 1, 5 factors of 18: 1, 2, 3, 6, 9, 18 GCF 1 7. factors of 16: 1, 2, 4, 8, 16 factors of 20: 1, 2, 4, 5, 10, 20 GCF 4 8. 36 2 2 3 3 48 2 2 2 2 3 GCF 12 9. 40 2 2 2 5 80 2 2 2 2 5 GCF 40 10. factors of 18: 1, 2, 3, 6, 9, 18 factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 factors of 72: 1, 2, 3, 4, 6, 9, 12, 18, 24, 36, 72 GCF 18 11. factors of 20: 1, 2, 4, 5, 10, 20 factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 factors of 50: 1, 2, 5, 10, 25, 50 GCF 10 Page 23 1. yes 3. no 2. yes Page 24 4. yes 6. yes 8. yes 10. 36 12. 18 14. 144 16. 36 18. 30 5. 7. 9. 11. 13. 15. 17. 19. Page 25 1. n 3 Page 26 3. n 5. n 7. n 9. n 11. n 13. n 15. n 5 4 5 9 6 9 8 yes yes no 90 80 80 75 24 2. n 4 4. 6. 8. 10. 12. 14. n n n n n n 3 4 8 3 4 10 © CSL Associates, Inc. (877) 790-7915 Page 27 1. 9n = 54; 2. 12n = 36; 3. n = 2 x 12; 4. n = 27 x 3; 5. 25n = 75; 6. n = 2 x 8; n n n n n n 6 3 24 81 3 16 Page 28 7. 54 = 2n; 8. n = 4 x 20; 9. 112 = 8n; 10. n = 3 x 12; 11. 125 = 25n; 12. n = 2 x 18; 13. n = 6 x 15; 14. 5n = 45; 15. 25n = 150; 16. n = 73 - 45; 17. n = 84/14; 18. n = 16 + 82; 19. n = 23 - 18; 20. n = 7 x 32; 21. n = 91/13; n n n n n n n n n n n n n n n 27 80 14 36 5 36 90 9 6 28 6 98 5 224 7 Page 30 1. Commutative Property of Addition 2. Identity Property of Addition 3. Associative Property of Addition 4. Additive Inverse Property 5. Commutative Property of Addition 6. Commutative Property of Addition 7. –3 8. 5 9. 10 10. 0 11. –45 12. 52 13. –18 14. 0 15. 39 16. –30 17. 80 Page 32 1. Commutative Property of Multiplication 2. Associative Property of Multiplication 3. Zero Property of Multiplication 4. Commutative Property of Multiplication 5. Commutative Property of Multiplication 6. Identity Property of Multiplication 7. –3 8. 5 9. 0 10. 1 11. –45 12. 52 13. 1 14. –64 15. 540 16. 0 17. 700 Page 33 1. Identity Property of Division 2. Division Property of 0 3. Identity Property of Division 4. Identity Property of Division 5. Identity Property of Division 6. Identity Property of Division Page 34 7. 1 8. 1 9. 0 10. 1 11. 1 12. 0 13. 0 14. 76 15. 1 16. 67 17. Identity Property of Addition 18. Associative Property of Multiplication 19. Identity Property of Division 20. Commutative Property of Addition 21. Identity Property of Multiplication 22. Division Property of 0 23. Associative Property of Addition 24. Multiplication Property of 0 Page 35 1. 10 3. 12 5. 2 Page 36 7. 9 9. 15 11. 17 13. –10 15. –23 17. 77 19. 16 21. 60 23. 5 25. 6 ARITHMETIC TO ALGEBRA 2. 2 4. 7 6. 8 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. 2 7 30 12 61 50 24 3 72 180 IL Workbook R 61 Answer Key 27. 29. 31. 33. 35. 37. 39. 41. 43. 45. 47. 49. 51. 53. 29 94 6 17 2 26 0 5 14 64 13 4 40 21 28. 30. 32. 34. 36. 38. 40. 42. 44. 46. 48. 50. 52. 54. 26 120 14 120 200 20 18 6 4 128 32 2 80 1 Page 37 1. 3. 5. 7. 9. 2. 4. 6. 8. Page 38 10. 12. 14. 16. 18. 20. 22. 24. 26. 28. 30. 32. 34. 36. 11. 13. 15. 17. 19. 21. 23. 25. 27. 29. 31. 33. 35. Page 39 1. 7 9 3. 17 3 Page 40 5. 15 7 7. 5 9 9. 17 9 11. 15 13. 16 15. 42 17. 5 19. 1 21. 1 62 IL Workbook R 2. 52 4. 9 7 6. 8. 10. 12. 14. 16. 18. 20. 22. 65 23 96 13 39 7 3 2 2 23. 24. 25. 26. 16 (7 5) 4 (16 7) 5 14 (54 ÷ 3) 6 108 54 ÷ (-3 6) 3 Page 41 1. 12 d 2. 12 ÷ 10 3. 12 10 Page 44 5. 4 7. 12 9. 8 11. 7 13. yes 15. no 17. n 19. n 21. n 23. n 2 23 17 8 Page 45 1. divide 3. multiply Page 46 5. 6 7. 12 9. 2 11. 7 Page 48 7. yes 9. yes 11. n 13. n 15. n 17. n 19. n 2. add 4. subtract 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 8 7 6 12 no yes n n n n 20 12 2 61 2. multiply 4. divide 6. 8. 10. 12. 8 5 6 12 ARITHMETIC TO ALGEBRA no yes yes; no n n n n 80 5 60 25 18. 20. 22. 24. n n n n 8. 10. 12. 14. 16. 18. 20. no no n n n n n 4 3 360 240 Page 47 1. Add 5. 2. Subtract 9. 3. Add 1. 4. Subtract 6. 5. Subtract 7. 6. Add 10. Page 42 4. 5 12 5. 20 4 6. 15 20 7. 4 8 8. 8 ÷ 4 9. 300 20 10. 5 n 11. 5n 12. 16 n or n 16 13. 3t 14. 2(n 3) 15. 2n 3 16. (n 5)/2 or n + 5/2 17. 5n 6 18. m d 19. np Page 43 1. subtract 3. add 13. 14. 15. 16. 17. 19. 21. 23. 3 4 9 9 24 16 2 20 4 4 Page 49 1. 3(17) 24 27 51 51 2. 5(6) 20 10 30 30 3. 2(13) 12 14 26 26 4. 6(13) 54 24 78 78 Page 50 5. 5(7) 25 10 35 35 6. 8(9) 72 0 72 72 7. 2(10) 8 12 20 20 8. 6(13) 30 48 78 78 9. y 8 10. 11. y 8 12. 13. y 7 14. 15. y 2 16. 17. y 4 18. 19. y 4 20. 21. y 3 22. y y y y y y y 4 3 5 3 8 5 6 © CSL Associates, Inc. (877) 790-7915 Answer Key Page 52 1. 5 d 22 2. 3n 6 3. m/2 9 4. t 2 5 5. 5s 80; 16 stamps 6. c 8 22; 14 candles 7. m 2.2 4.5; 2.3 miles 8. t/3 2; 6 hours 9. 2c 80; $40 10. 85 m 140; $55 Page 54 1. 2. 3. 4. 5. 6. x y 0 1 2 3 5 6 7 8 x y 0 1 2 3 1 0 1 2 x y 0 1 2 3 0 3 6 9 x y 0 1 2 3 1 3 5 7 x y 0 1 2 3 0 1 112 x y 0 1 2 3 3 0 3 6 1 2 © CSL Associates, Inc. (877) 790-7915 7. (0, 7), (2, 9), (4, 11), (6, 13) 8. (0, 2), (2, 0), (4, 2), (6, 4) 9. (0, 0), (2, 10), (4, 20), (6, 30) 10. (0, 0), (2, 2/3), (4, 1 1/3), (6, 2) 11. (0, 1), (2, 3), (4, 7), (6, 11) 12. (0, 2), (2, 6), (4, 10), (6, 14) 13. yes 14. yes 15. no 16. no 17. yes 18. yes 19. no 20. yes Page 55 1. 8 7 6 5 4 3 2 1 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 y 8 7 6 5 4 3 2 1 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 x 2. no 3. yes Page 56 4. 8 5. yes 6. no 7. x 11. no 12. yes Page 57 1. 150 miles 2. 35 square inches y 7 6 5 4 3 2 1 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 x 8. no 9. yes 10. y 6 5 4 3 2 1 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 y x Page 58 3. 600 miles per hour 4. 220 miles 5. 5 hours 6. 24 square feet 7. 32 inches 8. 4.25 square centimeters 9. 13.95 square meters 10. 2 inches 11. 12 inches 12. 6 feet 13. 10 inches 14. 2 ARITHMETIC TO ALGEBRA 3 16 square inches IL Workbook R 63