4th Grade Dividing with Remainders Test Answer Key and Scoring Guide (PDF)

4th grade long division test answer key – Maths PDF

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This 4th grade long division test answer key 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 see how each point on the division test was earned.

Topic: Dividing with Remainders (4th grade)
Content: Worked solutions and a scoring guide for 9 questions
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 see how each point on the division test was earned. Also, it gives complete solutions to all nine questions, with the remainder, a multiplication check, and the reasoning for the three part word problems and the error question.

The key models two ways to divide, area models and long division, so students can compare with their own method. Add your points out of 20, then spend about 15 minutes redoing every question that lost credit. Then, for a missed remainder question, write the multiplication check and make sure it matches the dividend.

Use this answer key to score the test. Each solution shows the partial quotients and a check, and the scoring note tells how the points are awarded. Total: 20 points.

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

4th grade long division test answer key: worked solutions

1 – Mental math [2 pts]

36 tens ÷ 6 = 6 tens. 60
40 hundreds ÷ 5 = 8 hundreds. 800

Scoring: 1 point for each answer.

2 – Two-digit dividends [2 pts]

\(80 \div 4 = 20\) and \(16 \div 4 = 4\). 24
\(6 \times 14 = 84\) and \(87 – 84 = 3\). 14 R 3

Scoring: 1 point for each answer.

3 – Three-digit dividend [2 pts]

\(500 \div 5 = 100\); \(125 \div 5 = 25\). Quotient \(100 + 25 = 125\).

Check: \(125 \times 5 = 625\).

125

Scoring: 1 point for 125. 1 point for the check.

4 – Remainder in the tens place [2 pts]

700 + 56 = 756, with 2 left.

\(758 – 700 = 58\); \(7 \times 8 = 56\); \(58 – 56 = 2\).

Also, check: \(108 \times 7 + 2 = 758\).

108 R 2

Scoring: 1 point for 108. 1 point for the remainder 2.

5 – Four-digit dividend [2 pts]

\(6 \times 800 = 4{,}800\); \(4{,}872 – 4{,}800 = 72\); \(72 \div 6 = 12\).

\(800 + 12 = 812\)

Check: \(812 \times 6 = 4{,}872\).

\(812\)

Scoring: 1 point for correct partial quotients. 1 point for 812.

6 – Read the area model [2 pts]

200 + 40 + 7 = 247.

\(1{,}000 \div 5 = 200\), \(200 \div 5 = 40\), \(35 \div 5 = 7\).

\(200 + 40 + 7 = 247\)

247

Scoring: 1 point for the three widths. 1 point for 247.

Question 7 and after

7 – School vans [3 pts]

\(83 \div 6 = 13 \text{ R } 5\) because \(13 \times 6 = 78\) and \(83 – 78 = 5\). 13 vans
5 students
The 5 students need one more van. 14 vans

Scoring: 1 point for each part.

8 – Find the mistake [3 pts]

\(14 \times 5 + 3 = 70 + 3 = 73\), which is not 523.
\(5 \times 100 = 500\); \(523 – 500 = 23\); \(5 \times 4 = 20\); \(23 – 20 = 3\). 104 R 3
There are 0 tens left after taking 500, but Liam skipped the zero and wrote 14 instead of 104.

Scoring: 1 point for each part.

9 – Photo album pages [2 pts]

\(7 \times 60 = 420\); \(458 – 420 = 38\); \(7 \times 5 = 35\); \(38 – 35 = 3\).

Check: \(65 \times 7 + 3 = 455 + 3 = 458\).

65 full pages; 3 photos left

Scoring: 1 point for 65. 1 point for 3 left.

Total score

Total

20 points

Key facts behind this 4th grade long division test answer key

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 test answer key

Students assume a quotient is wrong when the key uses another method. Check that your answer matches, since area models and long division give the same result.
Students overlook that question 7 has three separate answers. Instead, full vans, leftover students, and vans needed are each scored.
Students copy the explanation in question 8 without understanding it. Also, say why 14 times 5 plus 3 does not make 523.
Students forget to include the remainder in the check for question 9. Instead, the photos left over are part of the original total.

How to learn from your test

Sort lost points into basic facts, long division steps, and word problem reading. Practice the group with the most lost points first.
Redo question 5 with a different four digit number. Finally, changing one number shows whether you understand the steps or only the answer.
Teachers can ask students to compare the key’s area model with their own work and explain which parts match.

Download the 4th grade long division test answer key as a PDF with the button below and keep it with your notes.

4th grade long division test answer key: frequently asked questions

How do I show that Liam’s division is wrong?

Multiply his quotient by the divisor and add his remainder. Also, if 14 times 5 plus 3 is 73, not 523, his answer cannot be right. The correct quotient is 104 with a remainder of 3, since 104 times 5 plus 3 gives 523.

Why do the key’s area model widths add up to the quotient?

Each rectangle has the same height, which is the divisor, and a width that is a partial quotient. So, the total width is the sum of the partial quotients. Also, for a height of 5, widths of 200, 40, and 7 give a quotient of 247.

What if my remainder is correct but my quotient is off by one?

Check the multiplication step. A quotient that is one too small leaves a remainder at least as big as the divisor, and one that is too large needs a negative remainder. Both signal that you should try the neighbor of your quotient.

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