4th Grade Dividing with Remainders Worksheet Answer Key (PDF)

4th grade long division worksheet answers – Maths PDF

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This 4th grade long division worksheet answers covers dividing with remainders (Common Core 4.NBT.B.6), with a free PDF to print.

Key takeaway: This answer key helps fourth grade students and parents check division work with remainders and see every step.

Topic: Dividing with Remainders (4th grade)
Content: Step-by-step answers to 20 worksheet problems
Standards: 4.NBT.B.6
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fourth grade students and parents check division work with remainders and see every step. Each solution shows the partial quotients or the long division steps, the remainder, and a check by multiplication, so any error can be found quickly.

The key covers all 20 problems, including the area model completions in problems 5, 9, and 11. Also, word problem answers explain how the remainder is handled, whether it is dropped, kept, or rounded up. Then, plan about 15 minutes to compare your work, and redo any problem where your quotient or remainder differs.

Check your work with this answer key. Each solution shows the partial quotients and a multiplication check. Remainders are written with R and explained in the word problems. The final answer is in bold.

Grade 4 · Common Core State Standards: 4.NBT.B.6

4th grade long division worksheet answers: worksheet problems 1 to 10

1 – Divide tens

8 tens divided by 4 is 2 tens.

Check: \(20 \times 4 = 80\).

2 – Divide hundreds

6 hundreds divided by 3 is 2 hundreds.

Check: \(200 \times 3 = 600\).

200

3 – Two-digit quotient

\(30 \div 3 = 10\) and \(18 \div 3 = 6\).

\(10 + 6 = 16\)

4 – Break apart

\(50 \div 5 = 10\) and \(25 \div 5 = 5\).

\(10 + 5 = 15\)

5 – Area model: 156 ÷ 4

120 + 36 = 156.

Left over: \(156 – 120 = 36\). \(36 \div 4 = 9\).

\(30 + 9 = 39\)

6 – Remainder: 92 ÷ 6

\(6 \times 10 = 60\); \(92 – 60 = 32\). \(6 \times 5 = 30\); \(32 – 30 = 2\).

Quotient \(10 + 5 = 15\), remainder 2.

Check: \(15 \times 6 + 2 = 92\).

15 R 2

7 – Dots and remainders

9 groups of 5 and 2 left over.

There are 9 full groups of 5, and 2 dots are left over.

Check: \(9 \times 5 + 2 = 47\).

\(47 \div 5 = 9 \text{ R } 2\)

8 – Three-digit dividend

\(5 \times 50 = 250\); \(275 – 250 = 25\); \(25 \div 5 = 5\).

\(50 + 5 = 55\)

9 – Find partial quotients

70 + 3 = 73.

\(420 \div 6 = 70\) and \(18 \div 6 = 3\). The quotient is \(70 + 3 = 73\).

Also, check: \(73 \times 6 = 438\).

Worksheet problem 10 and after

10 – Zero in the quotient

\(4 \times 200 = 800\); \(817 – 800 = 17\). There are no whole tens in 17 that 4 can use except \(4 \times 4 = 16\), so the tens place is 0.

\(200 + 0 + 4 = 204\), and \(17 – 16 = 1\) is the remainder.

Check: \(204 \times 4 + 1 = 817\).

204 R 1

Worksheet problems 11 and up

11 – Area model: 2,736 ÷ 4

600 + 80 + 4 = 684.

\(2{,}400 \div 4 = 600\), \(320 \div 4 = 80\), \(16 \div 4 = 4\).

\(600 + 80 + 4 = 684\)

\(684\)

12 – Divide 1,500

\(1{,}200 \div 6 = 200\); \(1{,}500 – 1{,}200 = 300\); \(300 \div 6 = 50\).

\(200 + 50 = 250\)

250

13 – Four digits by seven

\(7 \times 400 = 2{,}800\); \(3{,}284 – 2{,}800 = 484\). \(7 \times 60 = 420\); \(484 – 420 = 64\). \(7 \times 9 = 63\); \(64 – 63 = 1\).

Quotient \(400 + 60 + 9 = 469\), remainder 1.

Check: \(469 \times 7 + 1 = 3{,}283 + 1 = 3{,}284\).

469 R 1

14 – Divide 5,000

\(8 \times 600 = 4{,}800\); \(5{,}000 – 4{,}800 = 200\). \(8 \times 25 = 200\).

\(600 + 25 = 625\)

Also, check: \(625 \times 8 = 5{,}000\).

625

15 – Cookie bags

\(138 \div 6\): \(6 \times 20 = 120\); \(138 – 120 = 18\); \(18 \div 6 = 3\).

\(20 + 3 = 23\)

Check: \(23 \times 6 = 138\).

23 cookies

16 – Soccer teams

\(83 \div 8\): \(8 \times 10 = 80\); \(83 – 80 = 3\).

The quotient is 10 and the remainder is 3. The remainder is dropped for full teams.

Check: \(10 \times 8 + 3 = 83\).

10 full teams; 3 players left

17 – Road trip days

\(1{,}260 \div 5\): \(5 \times 200 = 1{,}000\); \(1{,}260 – 1{,}000 = 260\); \(5 \times 50 = 250\); \(260 – 250 = 10\); \(5 \times 2 = 10\).

\(200 + 50 + 2 = 252\)

Check: \(252 \times 5 = 1{,}260\).

252 miles

Worksheet problem 18 and after

18 – Pencil boxes

\(8 \times 40 = 320\); \(365 – 320 = 45\); \(8 \times 5 = 40\); \(45 – 40 = 5\).

Quotient \(40 + 5 = 45\), remainder 5.

Check: \(45 \times 8 + 5 = 365\).

45 full boxes; 5 pencils left

19 – Vans for the field trip

\(94 \div 7\): \(7 \times 13 = 91\); \(94 – 91 = 3\). The quotient is 13 with remainder 3.

Thirteen vans carry 91 people, so 3 people still need a ride. One more van is needed.

14 vans

20 – Markers for classes

Total markers: \(3 \times 248 = 744\).

\(744 \div 9\): \(9 \times 80 = 720\); \(744 – 720 = 24\); \(9 \times 2 = 18\); \(24 – 18 = 6\).

Quotient \(80 + 2 = 82\), remainder 6. Check: \(82 \times 9 + 6 = 744\).

82 markers each; 6 left over

Key facts behind this 4th grade long division worksheet answers

Key facts

Dividend ÷ divisor = quotient with a remainder; the remainder is less than the divisor.
Partial quotients: divide easy parts of the dividend and add the results.
An area model for division starts with the area (dividend) and one side (divisor).
Then, check: quotient × divisor + remainder = dividend.
Think about the story to decide what to do with a remainder.

Common mistakes with this 4th grade long division worksheet answers

Students check only the quotient and ignore the remainder. A correct quotient with a wrong remainder is still a wrong answer, so check both.
Students copy the key for problem 19 without understanding why the answer is 14. Instead, read the reasoning about leftover people before moving on.
Students skip the multiplication checks. Also, those lines show the fastest way to verify any division answer on a test.
Students match area model answers by the total only. Check each partial width, since a correct total can hide an error in one part.

How to use these solutions

Mark each answer as quotient right, remainder right, or both. Then, most division errors are in one of the two, which tells you what to practice.
Redo problem 13 using partial quotients if you used long division, or the other way around. Finally, matching answers show that you understand both ways.
Parents can ask the child to explain why a remainder must be less than the divisor, using the cookie bags or the vans as an example.

Download the 4th grade long division worksheet answers as a PDF with the button below and keep it with your notes.

4th grade long division worksheet answers: frequently asked questions

Why is the answer to problem 19 not 13 R 3?

The question asks how many vans are needed, and the 3 leftover people still need a ride. Thirteen vans carry 91 people, so a fourteenth van is required. The division gives 13 R 3, but the real answer to the question is 14 vans.

How do I check 3,284 divided by 7?

Multiply the quotient by 7 and add the remainder. Since 469 times 7 is 3,283, adding the remainder of 1 gives 3,284. This matches the dividend, so the answer of 469 R 1 is correct. Always add the remainder in the check.

Why do some answers in the key have a zero in the quotient?

A zero keeps the place value correct when a place cannot make a full group. For 817 divided by 4, the tens place is left with too little after regrouping, so the quotient shows 204. Leaving out the zero would give 24, which is far too small.

All Grade 4 chapters: Grade 4 math.

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