Long Division with & without Remainders Worksheet Generator
Standard long division with single-digit divisors, remainders, and decimal quotients terminating to hundredths. Generate unlimited practice worksheets with answer keys for home or school.
Tip: in the print dialog, choose 'Save as PDF' to keep a copy.
Long Division with & without Remainders
Divide using long division steps: Divide, Multiply, Subtract, Bring down (DMSB). Write remainders as R r.
Long Division with & without Remainders — Answer Key
Divide using long division steps: Divide, Multiply, Subtract, Bring down (DMSB). Write remainders as R r.
Answer each card and click Check or press Enter
Ways to Use This Sheet
Immediate desk work following direct instruction to verify individual concept mastery.
A clean, predictable practice sheet students can complete at home without adult coaching.
Self-contained station work for small groups rotating on 15-minute timers.
How to Use This Worksheet Generator
In the Classroom
Long division is one of the most multi-step algorithms in elementary school, synthesizing division, multiplication, subtraction, and place-value estimation. In the classroom, spacious worksheets with generous vertical workspace are essential to prevent students from misaligning columns. This generator formats problems with standard long-division brackets.
At Home & Homeschool
At home, parents often find that long division errors are actually minor subtraction or multiplication slips rather than conceptual division misunderstandings. Using worksheets with clear answer keys that display quotients and remainders (formatted as "q R r") allows parents and students to pinpoint the exact step where an error occurred.
Step-by-Step Worked Example
- 1
Divide Hundreds and Tens (47 ÷ 6)
6 does not divide into 4. Divide into 47: 6 goes into 47 seven times (7 × 6 = 42). Write 7 above the 7 on the quotient line.
- 2
Multiply and Subtract (47 - 42 = 5)
Multiply 7 × 6 = 42. Subtract 47 - 42 = 5. Check that the remainder 5 is less than the divisor 6.
- 3
Bring Down and Divide (58 ÷ 6)
Bring down the 8 to make 58. 6 goes into 58 nine times (9 × 6 = 54). Write 9 in the quotient. Subtract: 58 - 54 = 4. Since 4 < 6, the remainder is 4.
Difficulty Progression: Easy vs. Standard vs. Challenge
| Preset Level | Target Grade | Configuration & Range | Skill Focus & Mastery |
|---|---|---|---|
| Easy | Grade 4 | 12 problems, 2-digit dividend by 1-digit divisor, no remainders | Mastering the DMSB four-step cycle (Divide, Multiply, Subtract, Bring down) without remainders. |
| Standard | Grades 4–5 | 12 problems, 3-digit dividend by 1-digit divisor, remainders allowed | Multi-step division across hundreds, tens, and ones with optional remainders. |
| Challenge | Grades 5–6 | 9 problems, 4-digit dividend by 1-digit divisor, remainders guaranteed | Extensive multi-digit division requiring persistent place value alignment and remainder notation. |
Frequently Asked Questions
What does the DMSB mnemonic stand for in long division?
DMSB stands for Divide, Multiply, Subtract, Bring down. Many teachers use the memory hook "Does McDonalds Sell Burgers?" or "Dad, Mom, Sister, Brother" to help students remember the repeating cycle.
How do I know if a remainder is mathematically valid?
A remainder must always be strictly less than the divisor. For example, if you divide by 6, the only possible remainders are 0, 1, 2, 3, 4, and 5. If your remainder is 6 or larger, you can divide at least one more time.
How are remainders formatted on the answer key?
When a remainder exists, our answer keys format the result as "q R r" (e.g. "79 R 4"). When division is exact, only the whole quotient is displayed.
Understanding Your Unique Worksheet Code
Every worksheet generated on this site includes a unique 6-character alphanumeric Worksheet Code (such as 432VPD) printed in the header and footer.
This code represents the mathematical pseudo-random seed used to create your exact problem set. If you ever need to reprint the identical worksheet for absent students or retrieve the matching answer key at a later date, simply enter the code into the Worksheet Code box and click Load Code. All problems will instantly regenerate in identical order.