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Complete Chapter 6 answer key

Full answers and reasoning for every chapter lesson and assessment.

Print this separately when students work on assessment pages. These are publicly available explanatory solutions, not secure school answers.

Lesson 1: Dividing Tens and Hundreds

Entry

  1. 8 — 8 equal groups contain 64 counters: 64÷8=8; verify 8×8=64.
  2. 11 — 9 equal groups contain 99 counters: 99÷9=11; verify 11×9=99.

Worked checks

  1. 900 — Group 1,800 into 2 equal parts using place-value exchanges. Each group has 900. Verify 900×2=1,800.
  2. 40 — Group 120 into 3 equal parts using place-value exchanges. Each group has 40. Verify 40×3=120.
  3. 700 — Group 2,800 into 4 equal parts using place-value exchanges. Each group has 700. Verify 700×4=2,800.

Guided

  1. 400 — Group 800 into 2 equal parts using place-value exchanges. Each group has 400. Verify 400×2=800.
  2. 70 — Group 210 into 3 equal parts using place-value exchanges. Each group has 70. Verify 70×3=210.
  3. 200 — Group 800 into 4 equal parts using place-value exchanges. Each group has 200. Verify 200×4=800.
  4. 50 — Group 250 into 5 equal parts using place-value exchanges. Each group has 50. Verify 50×5=250.

Independent

  1. 600 — Group 1,200 into 2 equal parts using place-value exchanges. Each group has 600. Verify 600×2=1,200.
  2. 90 — Group 270 into 3 equal parts using place-value exchanges. Each group has 90. Verify 90×3=270.
  3. 400 — Group 1,600 into 4 equal parts using place-value exchanges. Each group has 400. Verify 400×4=1,600.
  4. 70 — Group 350 into 5 equal parts using place-value exchanges. Each group has 70. Verify 70×5=350.
  5. 200 — Group 400 into 2 equal parts using place-value exchanges. Each group has 200. Verify 200×2=400.
  6. 50 — Group 150 into 3 equal parts using place-value exchanges. Each group has 50. Verify 50×3=150.
  7. 800 — Group 3,200 into 4 equal parts using place-value exchanges. Each group has 800. Verify 800×4=3,200.
  8. 30 — Group 150 into 5 equal parts using place-value exchanges. Each group has 30. Verify 30×5=150.

Challenge

  1. 120 — 360 is 36 tens. 36 tens ÷3=12 tens = 120 ones.
  2. 120 per group — 480=48 tens, and 48 tens÷4=12 tens = 120 ones.

Exit

  1. 300 — Group 600 into 2 equal parts using place-value exchanges. Each group has 300. Verify 300×2=600.
  2. 60 — Group 180 into 3 equal parts using place-value exchanges. Each group has 60. Verify 60×3=180.
  3. 900 — Group 3,600 into 4 equal parts using place-value exchanges. Each group has 900. Verify 900×4=3,600.

Lesson 2: Dividing a 2-digit Number by 2 — Part 1

Entry

  1. 700 — Group 1,400 into 2 equal parts using place-value exchanges. Each group has 700. Verify 700×2=1,400.
  2. 20 — Group 60 into 3 equal parts using place-value exchanges. Each group has 20. Verify 20×3=60.

Worked checks

  1. 42 — Group 84 into 2 equal parts using place-value exchanges. Each group has 42. Verify 42×2=84.
  2. 13 — Group 26 into 2 equal parts using place-value exchanges. Each group has 13. Verify 13×2=26.
  3. 23 — Group 46 into 2 equal parts using place-value exchanges. Each group has 23. Verify 23×2=46.

Guided

  1. 12 — Group 24 into 2 equal parts using place-value exchanges. Each group has 12. Verify 12×2=24.
  2. 22 — Group 44 into 2 equal parts using place-value exchanges. Each group has 22. Verify 22×2=44.
  3. 32 — Group 64 into 2 equal parts using place-value exchanges. Each group has 32. Verify 32×2=64.
  4. 42 — Group 84 into 2 equal parts using place-value exchanges. Each group has 42. Verify 42×2=84.

Independent

  1. 13 — Group 26 into 2 equal parts using place-value exchanges. Each group has 13. Verify 13×2=26.
  2. 23 — Group 46 into 2 equal parts using place-value exchanges. Each group has 23. Verify 23×2=46.
  3. 33 — Group 66 into 2 equal parts using place-value exchanges. Each group has 33. Verify 33×2=66.
  4. 43 — Group 86 into 2 equal parts using place-value exchanges. Each group has 43. Verify 43×2=86.
  5. 14 — Group 28 into 2 equal parts using place-value exchanges. Each group has 14. Verify 14×2=28.
  6. 24 — Group 48 into 2 equal parts using place-value exchanges. Each group has 24. Verify 24×2=48.
  7. 34 — Group 68 into 2 equal parts using place-value exchanges. Each group has 34. Verify 34×2=68.
  8. 44 — Group 88 into 2 equal parts using place-value exchanges. Each group has 44. Verify 44×2=88.

Challenge

  1. 42 — Because 84=80+4 and equal halving distributes over the sum: 40+2=42.
  2. 43 — (80+6)÷2 = 40+3=43; both parts are split into the same two groups.

Exit

  1. 11 — Group 22 into 2 equal parts using place-value exchanges. Each group has 11. Verify 11×2=22.
  2. 21 — Group 42 into 2 equal parts using place-value exchanges. Each group has 21. Verify 21×2=42.
  3. 31 — Group 62 into 2 equal parts using place-value exchanges. Each group has 31. Verify 31×2=62.

Lesson 3: Dividing a 2-digit Number by 2 — Part 2

Entry

  1. 31 — Group 62 into 2 equal parts using place-value exchanges. Each group has 31. Verify 31×2=62.
  2. 41 — Group 82 into 2 equal parts using place-value exchanges. Each group has 41. Verify 41×2=82.

Worked checks

  1. 35 — Group 70 into 2 equal parts using place-value exchanges. Each group has 35. Verify 35×2=70.
  2. 45 — Group 90 into 2 equal parts using place-value exchanges. Each group has 45. Verify 45×2=90.
  3. 16 — Group 32 into 2 equal parts using place-value exchanges. Each group has 16. Verify 16×2=32.

Guided

  1. 15 — Group 30 into 2 equal parts using place-value exchanges. Each group has 15. Verify 15×2=30.
  2. 25 — Group 50 into 2 equal parts using place-value exchanges. Each group has 25. Verify 25×2=50.
  3. 35 — Group 70 into 2 equal parts using place-value exchanges. Each group has 35. Verify 35×2=70.
  4. 45 — Group 90 into 2 equal parts using place-value exchanges. Each group has 45. Verify 45×2=90.

Independent

  1. 16 — Group 32 into 2 equal parts using place-value exchanges. Each group has 16. Verify 16×2=32.
  2. 26 — Group 52 into 2 equal parts using place-value exchanges. Each group has 26. Verify 26×2=52.
  3. 36 — Group 72 into 2 equal parts using place-value exchanges. Each group has 36. Verify 36×2=72.
  4. 46 — Group 92 into 2 equal parts using place-value exchanges. Each group has 46. Verify 46×2=92.
  5. 17 — Group 34 into 2 equal parts using place-value exchanges. Each group has 17. Verify 17×2=34.
  6. 27 — Group 54 into 2 equal parts using place-value exchanges. Each group has 27. Verify 27×2=54.
  7. 37 — Group 74 into 2 equal parts using place-value exchanges. Each group has 37. Verify 37×2=74.
  8. 47 — Group 94 into 2 equal parts using place-value exchanges. Each group has 47. Verify 47×2=94.

Challenge

  1. 27 — Share four tens as two tens each, exchange the remaining ten to get 14 ones, and share seven ones each: 27.
  2. 37 — Share 6 tens as 3 tens each; exchange the remaining ten into 10 ones, combining with 4 ones to make 14 ones. Share 7 ones each: 37.

Exit

  1. 18 — Group 36 into 2 equal parts using place-value exchanges. Each group has 18. Verify 18×2=36.
  2. 28 — Group 56 into 2 equal parts using place-value exchanges. Each group has 28. Verify 28×2=56.
  3. 38 — Group 76 into 2 equal parts using place-value exchanges. Each group has 38. Verify 38×2=76.

Lesson 4: Dividing a 2-digit Number by 3, 4, and 5

Entry

  1. 7 — 6 equal groups contain 42 counters: 42÷6=7; verify 7×6=42.
  2. 10 — 7 equal groups contain 70 counters: 70÷7=10; verify 10×7=70.

Worked checks

  1. 29 — Group 87 into 3 equal parts using place-value exchanges. Each group has 29. Verify 29×3=87.
  2. 16 — Group 64 into 4 equal parts using place-value exchanges. Each group has 16. Verify 16×4=64.
  3. 16 — Group 80 into 5 equal parts using place-value exchanges. Each group has 16. Verify 16×5=80.

Guided

  1. 9 — Group 36 into 4 equal parts using place-value exchanges. Each group has 9. Verify 9×4=36.
  2. 10 — Group 50 into 5 equal parts using place-value exchanges. Each group has 10. Verify 10×5=50.
  3. 29 — Group 87 into 3 equal parts using place-value exchanges. Each group has 29. Verify 29×3=87.
  4. 7 — Group 28 into 4 equal parts using place-value exchanges. Each group has 7. Verify 7×4=28.

Independent

  1. 11 — Group 33 into 3 equal parts using place-value exchanges. Each group has 11. Verify 11×3=33.
  2. 16 — Group 64 into 4 equal parts using place-value exchanges. Each group has 16. Verify 16×4=64.
  3. 14 — Group 70 into 5 equal parts using place-value exchanges. Each group has 14. Verify 14×5=70.
  4. 26 — Group 78 into 3 equal parts using place-value exchanges. Each group has 26. Verify 26×3=78.
  5. 13 — Group 52 into 4 equal parts using place-value exchanges. Each group has 13. Verify 13×4=52.
  6. 16 — Group 80 into 5 equal parts using place-value exchanges. Each group has 16. Verify 16×5=80.
  7. 15 — Group 45 into 3 equal parts using place-value exchanges. Each group has 15. Verify 15×3=45.
  8. 11 — Group 44 into 4 equal parts using place-value exchanges. Each group has 11. Verify 11×4=44.

Challenge

  1. 24 — 24 groups of 4 total 96; equivalently 20×4=80 and 4×4=16.
  2. 29 trays — 87÷3=29, and 29×3=87. No cookies remain.

Exit

  1. 18 — Group 90 into 5 equal parts using place-value exchanges. Each group has 18. Verify 18×5=90.
  2. 33 — Group 99 into 3 equal parts using place-value exchanges. Each group has 33. Verify 33×3=99.
  3. 8 — Group 40 into 5 equal parts using place-value exchanges. Each group has 8. Verify 8×5=40.

Lesson 5: Dividing a 3-digit Number by 2

Entry

  1. 37 — Group 74 into 2 equal parts using place-value exchanges. Each group has 37. Verify 37×2=74.
  2. 47 — Group 94 into 2 equal parts using place-value exchanges. Each group has 47. Verify 47×2=94.

Worked checks

  1. 167 — Group 334 into 2 equal parts using place-value exchanges. Each group has 167. Verify 167×2=334.
  2. 204 — Group 408 into 2 equal parts using place-value exchanges. Each group has 204. Verify 204×2=408.
  3. 241 — Group 482 into 2 equal parts using place-value exchanges. Each group has 241. Verify 241×2=482.

Guided

  1. 95 — Group 190 into 2 equal parts using place-value exchanges. Each group has 95. Verify 95×2=190.
  2. 132 — Group 264 into 2 equal parts using place-value exchanges. Each group has 132. Verify 132×2=264.
  3. 169 — Group 338 into 2 equal parts using place-value exchanges. Each group has 169. Verify 169×2=338.
  4. 206 — Group 412 into 2 equal parts using place-value exchanges. Each group has 206. Verify 206×2=412.

Independent

  1. 175 — Group 350 into 2 equal parts using place-value exchanges. Each group has 175. Verify 175×2=350.
  2. 212 — Group 424 into 2 equal parts using place-value exchanges. Each group has 212. Verify 212×2=424.
  3. 249 — Group 498 into 2 equal parts using place-value exchanges. Each group has 249. Verify 249×2=498.
  4. 286 — Group 572 into 2 equal parts using place-value exchanges. Each group has 286. Verify 286×2=572.
  5. 323 — Group 646 into 2 equal parts using place-value exchanges. Each group has 323. Verify 323×2=646.
  6. 360 — Group 720 into 2 equal parts using place-value exchanges. Each group has 360. Verify 360×2=720.
  7. 67 — Group 134 into 2 equal parts using place-value exchanges. Each group has 67. Verify 67×2=134.
  8. 104 — Group 208 into 2 equal parts using place-value exchanges. Each group has 104. Verify 104×2=208.

Challenge

  1. 204 — Four hundreds shared in two groups give 2 hundreds each. Zero tens remain zero, and 8 ones give 4 each; the quotient is 204.
  2. 303 — Six hundreds make 3 hundreds per group; zero tens makes 0 tens; six ones make 3 ones. The zero placeholder is necessary: 303.

Exit

  1. 335 — Group 670 into 2 equal parts using place-value exchanges. Each group has 335. Verify 335×2=670.
  2. 372 — Group 744 into 2 equal parts using place-value exchanges. Each group has 372. Verify 372×2=744.
  3. 79 — Group 158 into 2 equal parts using place-value exchanges. Each group has 79. Verify 79×2=158.

Lesson 6: Dividing a 3-digit Number by 3, 4, and 5

Entry

  1. 13 — Group 52 into 4 equal parts using place-value exchanges. Each group has 13. Verify 13×4=52.
  2. 18 — Group 90 into 5 equal parts using place-value exchanges. Each group has 18. Verify 18×5=90.

Worked checks

  1. 138 — Group 414 into 3 equal parts using place-value exchanges. Each group has 138. Verify 138×3=414.
  2. 149 — Group 596 into 4 equal parts using place-value exchanges. Each group has 149. Verify 149×4=596.
  3. 160 — Group 800 into 5 equal parts using place-value exchanges. Each group has 160. Verify 160×5=800.

Guided

  1. 115 — Group 575 into 5 equal parts using place-value exchanges. Each group has 115. Verify 115×5=575.
  2. 126 — Group 378 into 3 equal parts using place-value exchanges. Each group has 126. Verify 126×3=378.
  3. 137 — Group 548 into 4 equal parts using place-value exchanges. Each group has 137. Verify 137×4=548.
  4. 148 — Group 740 into 5 equal parts using place-value exchanges. Each group has 148. Verify 148×5=740.

Independent

  1. 65 — Group 260 into 4 equal parts using place-value exchanges. Each group has 65. Verify 65×4=260.
  2. 76 — Group 380 into 5 equal parts using place-value exchanges. Each group has 76. Verify 76×5=380.
  3. 87 — Group 261 into 3 equal parts using place-value exchanges. Each group has 87. Verify 87×3=261.
  4. 98 — Group 392 into 4 equal parts using place-value exchanges. Each group has 98. Verify 98×4=392.
  5. 109 — Group 545 into 5 equal parts using place-value exchanges. Each group has 109. Verify 109×5=545.
  6. 120 — Group 360 into 3 equal parts using place-value exchanges. Each group has 120. Verify 120×3=360.
  7. 131 — Group 524 into 4 equal parts using place-value exchanges. Each group has 131. Verify 131×4=524.
  8. 142 — Group 710 into 5 equal parts using place-value exchanges. Each group has 142. Verify 142×5=710.

Challenge

  1. 117 — 400÷4=100 and 68÷4=17. Their sum is 117, checked by 117×4=468.
  2. 156 — 400÷4=100; 200÷4=50; 24÷4=6. Add 100+50+6=156.

Exit

  1. 159 — Group 477 into 3 equal parts using place-value exchanges. Each group has 159. Verify 159×3=477.
  2. 170 — Group 680 into 4 equal parts using place-value exchanges. Each group has 170. Verify 170×4=680.
  3. 181 — Group 905 into 5 equal parts using place-value exchanges. Each group has 181. Verify 181×5=905.

Lesson 7: Dividing a 3-digit Number, Quotient is 2 Digits

Entry

  1. 115 — Group 575 into 5 equal parts using place-value exchanges. Each group has 115. Verify 115×5=575.
  2. 126 — Group 378 into 3 equal parts using place-value exchanges. Each group has 126. Verify 126×3=378.

Worked checks

  1. 94 — Group 282 into 3 equal parts using place-value exchanges. Each group has 94. Verify 94×3=282.
  2. 48 — Group 192 into 4 equal parts using place-value exchanges. Each group has 48. Verify 48×4=192.
  3. 57 — Group 285 into 5 equal parts using place-value exchanges. Each group has 57. Verify 57×5=285.

Guided

  1. 73 — Group 292 into 4 equal parts using place-value exchanges. Each group has 73. Verify 73×4=292.
  2. 82 — Group 410 into 5 equal parts using place-value exchanges. Each group has 82. Verify 82×5=410.
  3. 91 — Group 273 into 3 equal parts using place-value exchanges. Each group has 91. Verify 91×3=273.
  4. 46 — Group 184 into 4 equal parts using place-value exchanges. Each group has 46. Verify 46×4=184.

Independent

  1. 44 — Group 132 into 3 equal parts using place-value exchanges. Each group has 44. Verify 44×3=132.
  2. 53 — Group 212 into 4 equal parts using place-value exchanges. Each group has 53. Verify 53×4=212.
  3. 62 — Group 310 into 5 equal parts using place-value exchanges. Each group has 62. Verify 62×5=310.
  4. 71 — Group 213 into 3 equal parts using place-value exchanges. Each group has 71. Verify 71×3=213.
  5. 80 — Group 320 into 4 equal parts using place-value exchanges. Each group has 80. Verify 80×4=320.
  6. 90 — Group 450 into 5 equal parts using place-value exchanges. Each group has 90. Verify 90×5=450.
  7. 89 — Group 445 into 5 equal parts using place-value exchanges. Each group has 89. Verify 89×5=445.
  8. 43 — Group 129 into 3 equal parts using place-value exchanges. Each group has 43. Verify 43×3=129.

Challenge

  1. 42 — Four groups of 100 would require 400, more than 168. Instead 168÷4=42, which is two-digit.
  2. 42 pencils — 100 per table would require 400 pencils, which is too many. 168÷4=42, checked 42×4=168.

Exit

  1. 40 — Group 160 into 4 equal parts using place-value exchanges. Each group has 40. Verify 40×4=160.
  2. 49 — Group 245 into 5 equal parts using place-value exchanges. Each group has 49. Verify 49×5=245.
  3. 59 — Group 177 into 3 equal parts using place-value exchanges. Each group has 59. Verify 59×3=177.

Practice A

Solutions

  1. 200 — Group 400 into 2 equal parts using place-value exchanges. Each group has 200. Verify 200×2=400.
  2. 50 — Group 150 into 3 equal parts using place-value exchanges. Each group has 50. Verify 50×3=150.
  3. 800 — Group 3,200 into 4 equal parts using place-value exchanges. Each group has 800. Verify 800×4=3,200.
  4. 13 — Group 26 into 2 equal parts using place-value exchanges. Each group has 13. Verify 13×2=26.
  5. 23 — Group 46 into 2 equal parts using place-value exchanges. Each group has 23. Verify 23×2=46.
  6. 33 — Group 66 into 2 equal parts using place-value exchanges. Each group has 33. Verify 33×2=66.
  7. 15 — Group 30 into 2 equal parts using place-value exchanges. Each group has 15. Verify 15×2=30.
  8. 25 — Group 50 into 2 equal parts using place-value exchanges. Each group has 25. Verify 25×2=50.
  9. 35 — Group 70 into 2 equal parts using place-value exchanges. Each group has 35. Verify 35×2=70.
  10. 17 — Group 68 into 4 equal parts using place-value exchanges. Each group has 17. Verify 17×4=68.
  11. 12 — Group 60 into 5 equal parts using place-value exchanges. Each group has 12. Verify 12×5=60.
  12. 19 — Group 57 into 3 equal parts using place-value exchanges. Each group has 19. Verify 19×3=57.

Practice B

Solutions

  1. 17 — Group 68 into 4 equal parts using place-value exchanges. Each group has 17. Verify 17×4=68.
  2. 12 — Group 60 into 5 equal parts using place-value exchanges. Each group has 12. Verify 12×5=60.
  3. 19 — Group 57 into 3 equal parts using place-value exchanges. Each group has 19. Verify 19×3=57.
  4. 335 — Group 670 into 2 equal parts using place-value exchanges. Each group has 335. Verify 335×2=670.
  5. 372 — Group 744 into 2 equal parts using place-value exchanges. Each group has 372. Verify 372×2=744.
  6. 79 — Group 158 into 2 equal parts using place-value exchanges. Each group has 79. Verify 79×2=158.
  7. 115 — Group 575 into 5 equal parts using place-value exchanges. Each group has 115. Verify 115×5=575.
  8. 126 — Group 378 into 3 equal parts using place-value exchanges. Each group has 126. Verify 126×3=378.
  9. 137 — Group 548 into 4 equal parts using place-value exchanges. Each group has 137. Verify 137×4=548.
  10. 72 — Group 288 into 4 equal parts using place-value exchanges. Each group has 72. Verify 72×4=288.
  11. 81 — Group 405 into 5 equal parts using place-value exchanges. Each group has 81. Verify 81×5=405.
  12. 90 — Group 270 into 3 equal parts using place-value exchanges. Each group has 90. Verify 90×3=270.

Chapter Review

Solutions

  1. 65 — Three groups of 100 would require 300, which is more than 195. 195÷3=65.
  2. 210 — 84 tens divided into 4 equal groups gives 21 tens in each group=210.
  3. 24 — Group 48 into 2 equal parts using place-value exchanges. Each group has 24. Verify 24×2=48.
  4. 76 — Group 228 into 3 equal parts using place-value exchanges. Each group has 76. Verify 76×3=228.
  5. 57 — Group 228 into 4 equal parts using place-value exchanges. Each group has 57. Verify 57×4=228.
  6. 26 — Group 78 into 3 equal parts using place-value exchanges. Each group has 26. Verify 26×3=78.
  7. 75 — Group 225 into 3 equal parts using place-value exchanges. Each group has 75. Verify 75×3=225.
  8. 16 — Group 64 into 4 equal parts using place-value exchanges. Each group has 16. Verify 16×4=64.
  9. 28 — Group 56 into 2 equal parts using place-value exchanges. Each group has 28. Verify 28×2=56.
  10. 80 — Group 400 into 5 equal parts using place-value exchanges. Each group has 80. Verify 80×5=400.
  11. 14 — Group 28 into 2 equal parts using place-value exchanges. Each group has 14. Verify 14×2=28.
  12. 72 — Group 144 into 2 equal parts using place-value exchanges. Each group has 72. Verify 72×2=144.
  13. 365 — Group 730 into 2 equal parts using place-value exchanges. Each group has 365. Verify 365×2=730.
  14. 66 — Group 330 into 5 equal parts using place-value exchanges. Each group has 66. Verify 66×5=330.
  15. 400 — Group 800 into 2 equal parts using place-value exchanges. Each group has 400. Verify 400×2=800.
  16. 11 — Group 33 into 3 equal parts using place-value exchanges. Each group has 11. Verify 11×3=33.
  17. 47 — Group 94 into 2 equal parts using place-value exchanges. Each group has 47. Verify 47×2=94.
  18. 97 — Group 485 into 5 equal parts using place-value exchanges. Each group has 97. Verify 97×5=485.
  19. 500 — Group 2,000 into 4 equal parts using place-value exchanges. Each group has 500. Verify 500×4=2,000.
  20. 34 — Group 68 into 2 equal parts using place-value exchanges. Each group has 34. Verify 34×2=68.
  21. 108 — Group 324 into 3 equal parts using place-value exchanges. Each group has 108. Verify 108×3=324.
  22. 304 — 6 hundreds ÷2=3 hundreds; zero tens stays zero; 8 ones÷2=4, so 304.
  23. 70 — Group 210 into 3 equal parts using place-value exchanges. Each group has 70. Verify 70×3=210.
  24. 18 — Group 36 into 2 equal parts using place-value exchanges. Each group has 18. Verify 18×2=36.
  25. 109 — Group 218 into 2 equal parts using place-value exchanges. Each group has 109. Verify 109×2=218.
  26. 37 — Group 74 into 2 equal parts using place-value exchanges. Each group has 37. Verify 37×2=74.
  27. 147 — 735÷5=147; 147×5=735.
  28. 44 — Group 88 into 2 equal parts using place-value exchanges. Each group has 44. Verify 44×2=88.
  29. 86 — Group 344 into 4 equal parts using place-value exchanges. Each group has 86. Verify 86×4=344.
  30. 48 — Group 144 into 3 equal parts using place-value exchanges. Each group has 48. Verify 48×3=144.
  31. 146 — Group 292 into 2 equal parts using place-value exchanges. Each group has 146. Verify 146×2=292.
  32. 13 — Group 65 into 5 equal parts using place-value exchanges. Each group has 13. Verify 13×5=65.

Practice Exam

Solutions

  1. 216 — Since 4×200=800, quotient is above 200. Exact 864÷4=216.
  2. 120 — 360 is 36 tens. Divide 36 tens by 3 = 12 tens = 120.
  3. Because 168 < 4×100 — Four hundreds would require at least 400. The quotient must be smaller than 100; 168÷4=42.
  4. 195 — Group 390 into 2 equal parts using place-value exchanges. Each group has 195. Verify 195×2=390.
  5. 37 — Group 74 into 2 equal parts using place-value exchanges. Each group has 37. Verify 37×2=74.
  6. 204 — 4 hundreds÷2=2 hundreds; 0 tens÷2=0 tens; 8 ones÷2=4 ones.
  7. 232 — Group 464 into 2 equal parts using place-value exchanges. Each group has 232. Verify 232×2=464.
  8. 168 — Share 5 hundreds among three groups: 1 hundred each, 2 hundreds remain. Exchange 2 hundreds for 20 tens, share 6 tens per group with 2 tens left, then exchange the remaining 2 tens for 20 ones. Add 4 more ones and share 24 ones as 8 each. Each share is 1 hundred + 6 tens + 8 ones = 168.
  9. 37 — Seven tens: give three to each class, exchange the remaining one ten for ten ones, making 14 ones; give seven ones each.
  10. 102 — 3 hundreds÷3=1 hundred; 0 tens÷3=0 tens; 6 ones÷3=2 ones. Answer 102.
  11. 40 — Group 200 into 5 equal parts using place-value exchanges. Each group has 40. Verify 40×5=200.
  12. 94 — 282÷3=94, checked 94×3=282.
  13. 24 — Group 48 into 2 equal parts using place-value exchanges. Each group has 24. Verify 24×2=48.
  14. 54 — Group 270 into 5 equal parts using place-value exchanges. Each group has 54. Verify 54×5=270.
  15. 900 — Group 3,600 into 4 equal parts using place-value exchanges. Each group has 900. Verify 900×4=3,600.
  16. 156 — 624÷4=156; 156×4=624.
  17. 13 — Group 52 into 4 equal parts using place-value exchanges. Each group has 13. Verify 13×4=52.
  18. 125 — Group 500 into 4 equal parts using place-value exchanges. Each group has 125. Verify 125×4=500.
  19. 14 — Group 28 into 2 equal parts using place-value exchanges. Each group has 14. Verify 14×2=28.
  20. 17 — Group 85 into 5 equal parts using place-value exchanges. Each group has 17. Verify 17×5=85.
  21. 45 — Group 180 into 4 equal parts using place-value exchanges. Each group has 45. Verify 45×4=180.
  22. 47 — Group 94 into 2 equal parts using place-value exchanges. Each group has 47. Verify 47×2=94.
  23. 136 — Group 680 into 5 equal parts using place-value exchanges. Each group has 136. Verify 136×5=680.
  24. 19 — 95÷5=19; 19×5=95.