4th Grade Dividing with Remainders Test with Answer Key (Free PDF)

4th grade long division test – Maths PDF

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

Key takeaway: This test helps fourth grade students show that they can divide numbers with up to four digits by a one digit divisor, interpret remainders, and check their work.

Topic: Dividing with Remainders (4th grade)
Content: 9 questions with point values, about 45 minutes
Standards: 4.NBT.B.6
Answers: On a separate page, so you can try every worksheet problem first
Format: Free printable PDF, US Letter, black and white

This test helps fourth grade students show that they can divide numbers with up to four digits by a one digit divisor, interpret remainders, and check their work. Also, it is worth 20 points and takes 45 minutes.

The nine questions begin with mental math, then move to two and three digit dividends, an area model with a remainder, and a four digit dividend. Then, one question reads an area model, two are word problems with remainders, and one asks students to find and explain an error. Show every step, since partial credit is given for correct work.

This 20-point test checks division with remainders (Common Core 4.NBT.B.6). Work alone, show your partial quotients, and check your answers with multiplication. You have 45 minutes.

Time and points

About this test

Grade: Grade 4
Chapter: Dividing with Remainders
Standards: 4.NBT.B.6
Time: 45 minutes
Total: 20 points

4th grade long division test: questions

1 – Mental math [2 pts]

Find \(360 \div 6\). (1 point)
Also, find \(4,000 \div 5\). (1 point)

2 – Two-digit dividends [2 pts]

Also, find \(96 \div 4\). (1 point)
Find \(87 \div 6\). Write the quotient with a remainder. (1 point)

3 – Three-digit dividend [2 pts]

Then, find \(625 \div 5\) and check your answer with multiplication.

4 – Remainder in the tens place [2 pts]

Use the area model to divide 758 by 7.

Now, the area model has height 7. Find \(758 \div 7\). Write the quotient with a remainder.

5 – Four-digit dividend [2 pts]

Also, find \(4,872 \div 6\).

6 – Read the area model [2 pts]

The areas are 1,000, 200, and 35.

First, the rectangle has height 5. The three partial areas are 1,000, 200, and 35. Find the three widths. Then find the quotient \(1,235 \div 5\).

7 – School vans [3 pts]

83 students in vans of 6.

Next, a school takes 83 students on a field trip. Each van seats 6 students.

How many vans will be completely full? (1 point)
Also, how many students are left over? (1 point)
How many vans are needed so every student has a seat? (1 point)

Question 8 and after

8 – Find the mistake [3 pts]

Liam says that 523 ÷ 5 = 14 R 3.

Use multiplication to show that his answer is wrong. (1 point)
Find the correct quotient with remainder. (1 point)
Explain what Liam did wrong. (1 point)

9 – Photo album pages [2 pts]

Sofia has 458 photos. She puts 7 photos on each album page. How many full pages can she fill, and how many photos are left?

Key facts behind this 4th grade long division test

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

Students correct an answer but do not show why it was wrong. Instead, multiply the wrong quotient by the divisor and add the remainder to show the mismatch.
Students answer only the first part of a three part question. Each part earns a point, so find full groups, leftovers, and groups needed.
Students write the remainder as a decimal in the quotient. Also, write a whole number, the letter R, and the leftover.
Students give a remainder as large as the divisor. Check that the remainder is smaller than the divisor, then divide again if it is not.

Test-taking strategy

Do the mental math first. Quick wins at the start give you time for the three part problems later.
Check every division by multiplying back. It takes ten seconds and catches most mistakes before you turn in your paper.
Parents can review the night before by asking for one division problem and one remainder story, then having the child check the answer.

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

4th grade long division test: frequently asked questions

How is a division test with remainders usually scored?

Teachers give points for the method, the quotient, and the remainder. A correct setup with a small arithmetic slip often earns partial credit. Word problems are worth more points, split across parts, so showing work for every part matters.

How can I check a division answer quickly?

Multiply the quotient by the divisor and add the remainder. For 840 divided by 4, the quotient 210 times 4 is 840, so it checks out. If the result does not equal the dividend, find the step where an error crept in.

Do I have to use the same method for every problem?

No. Partial quotients, area models, and standard long division are all accepted, as long as the work is clear. Use the method that you can do accurately, and show enough steps for a teacher to follow.

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