5th Grade Dividing by Two-Digit Divisors Test with Answer Key (Free PDF)

5th grade long division test – Maths PDF

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This 5th grade long division test covers dividing by two-digit divisors (Common Core 5.NBT.B.6), with a free PDF to print.

Key takeaway: This test helps fifth grade students show that they can divide by two digit divisors, write remainders, and explain their thinking.

Topic: Dividing by Two-Digit Divisors (5th grade)
Content: 8 questions with point values, about 45 minutes
Standards: 5.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 fifth grade students show that they can divide by two digit divisors, write remainders, and explain their thinking. Also, it is worth 20 points and takes 45 minutes.

The eight questions begin with short quotients, then divide four digit numbers and write a remainder. Then, later questions use an area model, estimate with compatible numbers, and find a classmate’s mistake. Also, two questions are three part word problems about vans and pencil boxes. Then, show every step for partial credit.

This test covers dividing whole numbers by two-digit divisors for Grade 5 (5.NBT.B.6). It has 8 questions worth 20 points. You have 45 minutes. Show your partial quotients or your area model. Calculators are not allowed. Check each answer by multiplying.

Time and points

About this test

Grade: Grade 5
Chapter: Dividing by Two-Digit Divisors
Standards: 5.NBT.B.6
Time: 45 minutes
Total: 20 points

5th grade long division test: questions

1 – Short quotients [2 pts]

First, find each quotient.

\(168\div12\) (1 point)
\(5{,}400\div90\) (1 point)

2 – Divide 1,404 [3 pts]

Next, find the quotient: \(1{,}404\div26\).

3 – Division with a remainder [3 pts]

Then, divide: \(3{,}816\div47\). Write the answer with a remainder.

4 – Area model [2 pts]

Now, the area model shows \(2{,}016\div32\). Find the missing widths and the quotient.

Area model.

5 – Estimate and solve [2 pts]

Also, use compatible numbers to estimate \(2{,}982\div42\). Then find the exact quotient.

6 – Diego's work [2 pts]

Diego says that \(1{,}260\div18=7\) because \(18\times7=126\). Explain his mistake and find the correct quotient.

7 – Field trip vans [3 pts]

Next, there are 389 students on a field trip. Each van holds 15 students.

Each van holds 15 students.

Find the quotient and remainder for \(389\div15\). (2 points)
How many vans does the school need? (1 point)

8 – Pencil boxes [3 pts]

Priya packs 1,440 pencils equally into 36 boxes.

Equal boxes.

How many pencils go in each box? (2 points)
Each box is shared equally by 8 students. How many pencils does each student get? (1 point)

Key facts behind this 5th grade long division test

Key facts

The dividend is divided by the divisor to give the quotient.
Partial quotients break the answer into easy pieces that add up to the quotient.
An area model shows the dividend as an area with the divisor as one side.
Then, a remainder is always smaller than the divisor.
Check by multiplying the quotient by the divisor and adding the remainder.

Common mistakes with this 5th grade long division test

Students explain a classmate’s mistake without checking with multiplication. Instead, multiply the wrong quotient by the divisor and compare with the dividend.
Students give only the quotient and remainder when a question asks how many vans are needed. Also, decide whether to round up.
Students skip the estimate. Instead, compatible numbers show whether an exact answer is in the right range. Slow down at that step and check it twice.
Students stop at a partial quotient. Also, keep dividing until the leftover is smaller than the divisor. Slow down at that step and check it twice.

Test-taking strategy

Do the short quotients first. Finally, quick points give you time for the three part stories. Repeat this habit on every problem for the best results.
Write a multiples list for each divisor. Also, it makes each step fast and accurate. Repeat this habit on every problem for the best results.
Parents can review the night before by asking the child to solve one problem two ways. Repeat this habit on every problem for the best results.

Download the 5th grade long division test as a PDF with the button below and keep it with your notes.

5th 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. Also, a correct setup with a small arithmetic slip often earns partial credit. Show every partial quotient so the work is clear. A quick check like this takes only a few seconds and prevents most errors.

Can I use partial quotients on the test?

Yes, unless the question names a method. Partial quotients, area models, and the standard algorithm are all accepted. Use the one you can do accurately, and show enough steps for the teacher to follow.

How do I check a long division answer?

Multiply the quotient by the divisor and add the remainder. For 150 divided by 12, the quotient 12 times 12 is 144, and adding the remainder 6 gives 150. A match confirms the answer.

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