Dividing Whole Numbers: math test solutions, Grade 5 – download the PDF

1 Mental division with zeros / 3 pts

1. \(450 \div 5 = 90\) (1 pt)
2. \(630 \div 9 = 70\) (1 pt)
3. \(56 \div 8 = 7\) (1 pt)

2 Estimating quotients / 3 pts

1. \(6{,}218 \approx 6{,}300\); \(6{,}300 \div 7 = 900\). About 900. (1 pt)
2. \(2{,}950 \approx 3{,}000\); \(3{,}000 \div 6 = 500\). About 500. (1 pt)
3. \(1{,}985 \approx 2{,}000\); \(2{,}000 \div 4 = 500\). About 500. (1 pt)

Any reasonable compatible numbers earn the points.

3 Partial quotients and area model / 4 pts

1. \(4 \times 200 = 800\), remainder \(292\). \(4 \times 70 = 280\), remainder \(12\). \(4 \times 3 = 12\). The quotient is \(200 + 70 + 3 = 273\). (2 pts)
2. \(12 \times 80 = 960\), and \(972 - 960 = 12\); \(12 \times 1 = 12\). The missing side is \(80 + 1 = 81\), so \(972 \div 12 = 81\). (2 pts)

4 Long division / 4 pts

1. \(54 \div 7 = 7\) R 5; \(58 \div 7 = 8\) R 2; \(27 \div 7 = 3\) R 6. The result is \(783\) R 6. Check: \(7 \times 783 + 6 = 5{,}487\). (2 pts)
2. \(86 \div 38 = 2\) R 10; \(109 \div 38 = 2\) R 33; \(334 \div 38 = 8\) R 30. The result is \(228\) R 30. Check: \(38 \times 228 + 30 = 8{,}694\). (2 pts)

5 Field trip remainders / 3 pts

1. \(9 \times 14 = 126\), and \(134 - 126 = 8\), so \(134 \div 9 = 14\) R 8. (1 pt)
2. The last 8 students still need a van, so we round up: 15 vans. (1 pt)
3. 14 whole pieces and 8 centimeters left over. (1 pt)

6 Seats in a theater / 3 pts

1. \(2{,}340 \div 36 = 65\), because \(36 \times 60 = 2{,}160\), \(2{,}340 - 2{,}160 = 180\) and \(36 \times 5 = 180\). Each row has 65 seats. (2 pts)
2. \(4 \times 65 = 260\). Four rows have 260 seats. (1 pt)