Division with Remainders: Grade 4 Math Worksheet Answer Key – PDF Download

Grade 4 Division Worksheet Answer Key: problems 1–5

Problem 1: Groups of 5

Make groups of 5: three full groups use 15 dots, and 2 dots are left. Check: \(5 \times 3 = 15\text{, then }15 + 2 = 17\).

Answer: 3 R 2

Problem 2: Sharing 29 by 6

Count by 6: 6, 12, 18, 24. The next count, 30, is too big. So \(6 \times 4 = 24\) and \(29 – 24 = 5\). Check: \(6 \times 4 = 24\text{, then }24 + 5 = 29\).

Answer: 4 R 5

Problem 3: Check by multiplying

\(8 \times 5 = 40\) and \(43 – 40 = 3\). Check: \(8 \times 5 = 40\text{, then }40 + 3 = 43\).

Answer: 5 R 3

Problem 4: Area model for 72

\(60 : 3 = 20\) and \(12 : 3 = 4\). Add the partial quotients: \(20 + 4 = 24\). Check: \(3 \times 24 = 72\).

Answer: 24

Problem 5: Two digits, one left

\(3 \times 30 = 90\), and \(94 – 90 = 4\). Another group fits: \(3 \times 1 = 3\), and \(4 – 3 = 1\). The quotient is \(30 + 1 = 31\). Check: \(3 \times 31 = 93\text{, then }93 + 1 = 94\).

Answer: 31 R 1

Grade 4 Division Worksheet Answer Key: problems 6–10

Problem 6: Remainder of 5

\(7 \times 10 = 70\), and \(96 – 70 = 26\). \(7 \times 3 = 21\), and \(26 – 21 = 5\). The quotient is \(10 + 3 = 13\). Check: \(7 \times 13 = 91\text{, then }91 + 5 = 96\).

Answer: 13 R 5

Problem 7: Area model for 348

\(300 : 6 = 50\) and \(48 : 6 = 8\). The quotient is \(50 + 8 = 58\). Check: \(6 \times 58 = 348\).

Answer: 58

Problem 8: Hundreds place

1. \(5 : 5 = 1\) with \(1 \times 5 = 5\); \(5 – 5 = 0\). Write 1 in the quotient.
2. Bring down the 2 to make 2.
3. \(2 : 5 = 0\) with \(0 \times 5 = 0\); \(2 – 0 = 2\). Write 0 in the quotient.
4. Bring down the 7 to make 27.
5. \(27 : 5 = 5\) with \(5 \times 5 = 25\); \(27 – 25 = 2\). Write 5 in the quotient.
6. No digits are left. The quotient is 105 and the remainder is 2.

Check: \(5 \times 105 = 525\text{, then }525 + 2 = 527\).

Answer: 105 R 2

Problem 9: Zero in the quotient

1. \(6 : 3 = 2\) with \(2 \times 3 = 6\); \(6 – 6 = 0\). Write 2 in the quotient.
2. Bring down the 1 to make 1.
3. \(1 : 3 = 0\) with \(0 \times 3 = 0\); \(1 – 0 = 1\). Write 0 in the quotient.
4. Bring down the 4 to make 14.
5. \(14 : 3 = 4\) with \(4 \times 3 = 12\); \(14 – 12 = 2\). Write 4 in the quotient.
6. No digits are left. The quotient is 204 and the remainder is 2.

The 1 left after the first step is less than 3, so the tens place of the quotient is 0. Check: \(3 \times 204 = 612\text{, then }612 + 2 = 614\).

Answer: 204 R 2

Problem 10: Missing parts

\(800 : 4 = 200\), \(160 : 4 = 40\), and \(32 : 4 = 8\). Add: \(200 + 40 + 8 = 248\). Check: \(4 \times 248 = 992\).

Answer: 248

Grade 4 Division Worksheet Answer Key: problems 11–15

Problem 11: Four-digit, no remainder

1. Since 1 is less than 4, start with the first 2 digits: 12.
2. \(12 : 4 = 3\) with \(3 \times 4 = 12\); \(12 – 12 = 0\). Write 3 in the quotient.
3. Bring down the 3 to make 3.
4. \(3 : 4 = 0\) with \(0 \times 4 = 0\); \(3 – 0 = 3\). Write 0 in the quotient.
5. Bring down the 6 to make 36.
6. \(36 : 4 = 9\) with \(9 \times 4 = 36\); \(36 – 36 = 0\). Write 9 in the quotient.
7. No digits are left. The quotient is 309 with no remainder.

Check: \(4 \times 309 = 1,236\).

Answer: 309

Problem 12: Four digits, remainder 4

1. Since 2 is less than 6, start with the first 2 digits: 24.
2. \(24 : 6 = 4\) with \(4 \times 6 = 24\); \(24 – 24 = 0\). Write 4 in the quotient.
3. Bring down the 5 to make 5.
4. \(5 : 6 = 0\) with \(0 \times 6 = 0\); \(5 – 0 = 5\). Write 0 in the quotient.
5. Bring down the 8 to make 58.
6. \(58 : 6 = 9\) with \(9 \times 6 = 54\); \(58 – 54 = 4\). Write 9 in the quotient.
7. No digits are left. The quotient is 409 and the remainder is 4.

Check: \(6 \times 409 = 2,454\text{, then }2,454 + 4 = 2,458\).

Answer: 409 R 4

Problem 13: Equal groups of 5

1. Since 3 is less than 5, start with the first 2 digits: 30.
2. \(30 : 5 = 6\) with \(6 \times 5 = 30\); \(30 – 30 = 0\). Write 6 in the quotient.
3. Bring down the 7 to make 7.
4. \(7 : 5 = 1\) with \(1 \times 5 = 5\); \(7 – 5 = 2\). Write 1 in the quotient.
5. Bring down the 5 to make 25.
6. \(25 : 5 = 5\) with \(5 \times 5 = 25\); \(25 – 25 = 0\). Write 5 in the quotient.
7. No digits are left. The quotient is 615 with no remainder.

Check: \(5 \times 615 = 3,075\).

Answer: 615

Problem 14: Dividing by 7

1. Since 5 is less than 7, start with the first 2 digits: 53.
2. \(53 : 7 = 7\) with \(7 \times 7 = 49\); \(53 – 49 = 4\). Write 7 in the quotient.
3. Bring down the 0 to make 40.
4. \(40 : 7 = 5\) with \(5 \times 7 = 35\); \(40 – 35 = 5\). Write 5 in the quotient.
5. Bring down the 9 to make 59.
6. \(59 : 7 = 8\) with \(8 \times 7 = 56\); \(59 – 56 = 3\). Write 8 in the quotient.
7. No digits are left. The quotient is 758 and the remainder is 3.

Check: \(7 \times 758 = 5,306\text{, then }5,306 + 3 = 5,309\).

Answer: 758 R 3

Problem 15: Zeros in the dividend

1. Since 8 is less than 9, start with the first 2 digits: 80.
2. \(80 : 9 = 8\) with \(8 \times 9 = 72\); \(80 – 72 = 8\). Write 8 in the quotient.
3. Bring down the 0 to make 80.
4. \(80 : 9 = 8\) with \(8 \times 9 = 72\); \(80 – 72 = 8\). Write 8 in the quotient.
5. Bring down the 0 to make 80.
6. \(80 : 9 = 8\) with \(8 \times 9 = 72\); \(80 – 72 = 8\). Write 8 in the quotient.
7. No digits are left. The quotient is 888 and the remainder is 8.

Check: \(9 \times 888 = 7,992\text{, then }7,992 + 8 = 8,000\).

Answer: 888 R 8

Grade 4 Division Worksheet Answer Key: problems 16–20

Problem 16: Find the mistake

Check his answer: \(8 \times 57 = 456\), and \(456 + 5 = 461\), which is not 457. The remainder should be \(457 – 456 = 1\).

Answer: 57 R 1; Ethan subtracted incorrectly.

Problem 17: Find the dividend

Multiply the divisor by the quotient: \(7 \times 45 = 315\). Add the remainder: \(315 + 6 = 321\). Check: \(321 : 7 = 45\) R 6.

Answer: 321

Problem 18: Boxes of cookies

\(47 : 6 = 7\text{ R }5\). Only full boxes count, so the remainder is not used for the boxes.

Answer: 7 full boxes with 5 cookies left

Problem 19: Vans for the field trip

\(38 : 8 = 4\text{ R }6\). The 6 extra students still need a ride, so one more van is needed: \(4 + 1 = 5\).

Answer: 5 vans

Problem 20: Sharing stickers

\(97 : 4 = 24\text{ R }1\). Check: \(4 \times 24 = 96\text{, then }96 + 1 = 97\).

Answer: 24 stickers each, with 1 left

Grade 4 Division Worksheet Answer Key: problems 21–23

Problem 21: Weeks and days

\(365 : 7 = 52\text{ R }1\). Check: \(7 \times 52 = 364\text{, then }364 + 1 = 365\). The remainder is the answer to the second question.

Answer: 52 weeks and 1 day

Problem 22: Beads for bracelets

Step 1: \(2,450 : 8 = 306\text{ R }2\). She can finish 306 bracelets and has 2 beads left.

Step 2: \(306 \times 3 = 918\).

Answer: 306 bracelets and $918

Problem 23: Apples at the market

Step 1: \(1,000 : 6 = 166\text{ R }4\). He fills 166 bags and has 4 apples left. Check: \(6 \times 166 = 996\text{, then }996 + 4 = 1,000\).

Step 2: \(166 \times 4 = 664\).

Answer: 166 bags, 4 apples left, and $664

How to use this grade 4 division worksheet answer key

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