This answer key gives a full worked solution for each of the 10 long division problems, including each divide, multiply, subtract, and bring down step. Use the check lines to confirm every quotient by multiplying back to the dividend.
Problem 1: Divide by one digit
6 goes into 7 once: \(1 \times 6 = 6\), \(7 – 6 = 1\). Bring down 5 to get 15. 6 goes into 15 twice: \(2 \times 6 = 12\), \(15 – 12 = 3\). Bring down 6 to get 36. \(6 \times 6 = 36\), remainder 0.
Check: \(6 \times 126 = 756\).
126
Problem 2: Four-digit dividend
8 goes into 21 twice: \(16\), \(21 – 16 = 5\). Bring down 8 to get 58. 8 goes into 58 seven times : \(56\), \(58 – 56 = 2\). Bring down 4 to get 24. \(8 \times 3 = 24\), remainder 0.
Check: \(8 \times 273 = 2{,}184\).
273
Problem 3: Two-digit divisor
24 does not go into 9, so use 93. 24 goes into 93 three times : \(3 \times 24 = 72\), \(93 – 72 = 21\). Bring down 6 to get 216. \(9 \times 24 = 216\), remainder 0.
Check: \(24 \times 39 = 936\).
39
Problem 4: Larger dividend
Use 43. 17 goes into 43 twice: \(34\), \(43 – 34 = 9\). Bring down 5 to get 95. \(5 \times 17 = 85\), \(95 – 85 = 10\). Bring down 2 to get 102. \(6 \times 17 = 102\), remainder 0.
Check: \(17 \times 256 = 4{,}352\).
256
Problem 5: Repeated subtraction steps
Use 84. 33 goes into 84 twice: \(66\), \(84 – 66 = 18\). Bring down 1 to get 181. \(5 \times 33 = 165\), \(181 – 165 = 16\). Bring down 5 to get 165. \(5 \times 33 = 165\), remainder 0.
Check: \(33 \times 255 = 8{,}415\).
255
Problem 6: Quotient with a remainder
Use 73. 45 goes into 73 once: \(45\), \(73 – 45 = 28\). Bring down 5 to get 285. \(6 \times 45 = 270\), \(285 – 270 = 15\). Bring down 9 to get 159. \(3 \times 45 = 135\), \(159 – 135 = 24\).
Check: \(45 \times 163 + 24 = 7{,}335 + 24 = 7{,}359\).
163 R 24
Problem 7: Estimate then divide
Estimate: \(6{,}123 \approx 6{,}000\) and \(29 \approx 30\), so \(6{,}000 : 30 = 200\).
Exact: use 61. 29 goes into 61 twice: \(58\), \(61 – 58 = 3\). Bring down 2 to get 32. \(1 \times 29 = 29\), \(32 – 29 = 3\). Bring down 3 to get 33. \(1 \times 29 = 29\), \(33 – 29 = 4\).
Check: \(29 \times 211 + 4 = 6{,}119 + 4 = 6{,}123\). The answer is close to the estimate of 200.
211 R 4
Problem 8: Bake sale boxes
Divide \(1{,}248 : 24\). Use 124: \(5 \times 24 = 120\), \(124 – 120 = 4\). Bring down 8 to get 48. \(2 \times 24 = 48\), remainder 0.
Check: \(24 \times 52 = 1{,}248\).
Sofia fills 52 boxes.
Problem 9: Field trip buses
Divide \(275 : 48\). 48 goes into 275 five times : \(5 \times 48 = 240\), \(275 – 240 = 35\). The quotient is 5 R 35.
Five buses seat only 240 students, so 35 students would be left without a seat. One more bus is needed.
The school needs 6 buses.
Problem 10: Egg cartons
Divide \(3{,}650 : 12\). Use 36: \(3 \times 12 = 36\), remainder 0. Bring down 5: 12 does not go into 5, so write 0. Bring down 0 to get 50. \(4 \times 12 = 48\), \(50 – 48 = 2\). The quotient is 304 R 2.
Check: \(12 \times 304 + 2 = 3{,}648 + 2 = 3{,}650\).
Money: \(304 \times \$3 = \$912\).
304 full cartons, 2 eggs left over, and \$912 earned.
See every chapter on the Grade 6 math page.