Free Long Division Worksheets (Grades 4-6)
Practice long division (Grades 4-6) with free printable PDF worksheets. 4 pre-packaged classroom sets with 100% verified step-by-step answer keys, plus an unlimited live customizer for teachers and homeschoolers.
PDF + Answer KeysLong Division & Remainders 50-Worksheet Master Workbook
- ✓50 curated printable worksheets in 1 PDF
- ✓100% verified step-by-step answer keys
- ✓Unlimited classroom & homeschool print license
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How to Create & Print Custom Worksheets in 3 Steps
Every generated sheet includes student name, date, score lines, and a complete answer key!
1. Set Options & Count
Select difficulty (Easy, Medium, Hard) and choose your exact problem count (8, 12, 16, or 20 problems per sheet).
2. Generate & Review
Click "Shuffle" to generate fresh randomized questions. Student name, date, and score blanks are added automatically.
3. Print with Answer Key
Print clean 8.5"×11" pages. Includes a detachable verified answer key for 1-minute grading or student self-checking!
Recommended Classroom & Homeschool Uses
Versatile math practice formats designed for busy educators and parents.
Explore Interactive Tools for Long Division Worksheets
Master this math concept across all PanMaths learning verticals:
Worksheet Facts by Grade Level
| Grade Level | Common Core Standard | Target Divisors & Complexity | Recommended Drills |
|---|---|---|---|
| Grade 3 | CCSS.MATH.CONTENT.3.OA.C.7 | Single-digit division facts within 100 (No remainders) | Set D (Timed Sprint 15 Problems) |
| Grade 4 | CCSS.MATH.CONTENT.4.NBT.B.6 | Find whole-number quotients up to 4-digit dividends and 1-digit divisors | Set A (Standard) & Set B (Remainders) |
| Grade 5 | CCSS.MATH.CONTENT.5.NBT.B.6 | Multi-digit division with 2-digit divisors and up to 4-digit dividends | Set C (Challenging 8 Problems) |
| Grade 6 | CCSS.MATH.CONTENT.6.NS.B.2 | Fluently divide multi-digit numbers using the standard algorithm | Set C & Unlimited Studio custom counts |
Mastering Long Division: The DMSB Four-Step Algorithm
Long division is the foundational arithmetic algorithm that bridges basic single-digit division facts with multi-digit algebraic fractions and polynomial division. To solve any long division problem accurately, students memorize the four-step DMSB cycle:
- 1. Divide (D): Determine how many times the divisor fits into the current dividend segment. Write this digit in the quotient on top.
- 2. Multiply (M): Multiply that quotient digit by the divisor and write the resulting product directly below the working segment.
- 3. Subtract (S): Subtract the product from the working segment. Check: The difference must be less than the divisor!
- 4. Bring Down (B): Drop the next place-value digit of the dividend beside the difference and repeat the cycle.
Classroom Mnemonic: Daddy, Mommy, Sister, Brother (Divide, Multiply, Subtract, Bring down).
How to Handle Remainders & Verification Invariants
When the final subtraction yields a number that cannot be divided further and there are no remaining digits to bring down, that number is the Remainder (R).
The Euclidean Division Theorem (Checking Your Work)
Every long division calculation can be verified with 100% mathematical certainty using the Euclidean invariant equation:
Dividend = (Divisor × Quotient) + Remainder
For example, if 374 ÷ 5 = 74 R 4, we verify: (5 × 74) + 4 = 370 + 4 = 374 ✅.
Transitioning from 1-Digit to 2-Digit Divisors
When advancing from Grade 4 to Grades 5 and 6, dividing by 2-digit numbers (like 12, 18, 25) requires estimation strategies:
- Leading-Digit Rounding: Round the divisor to the nearest 10 (e.g. estimate
1452 ÷ 24by thinking14 ÷ 2 = 7). - Trial Multiplication: Test your estimate on scratch paper. If the product is larger than the segment, reduce the quotient digit by 1.
Benefits of Mastery
📐 Place-Value Fluency
Builds deep conceptual intuition for columns, carries, and multi-digit subtraction.
⚡ Standardized Exam Success
Directly targets Common Core standard 4.NBT.B.6 for state exams and middle school algebra.
🧠 Scratchpad Analytical Rigor
Develops disciplined step-by-step problem-solving habits with dedicated pencil workspaces.
🖨️ 100% Free Classroom Photocopying
All sets print cleanly with verified intermediate solution keys for instant grading.
Frequently Asked Questions
Are these long division worksheets free for classroom use?
Yes! All 4 pre-packaged classroom sets and the live customizer generator are completely free to print and photocopy for schools, tutors, and homeschooling families.
Do the answer keys show step-by-step intermediate work?
Yes. Every generated answer key provides the complete DMSB breakdown (Divide, Multiply, Subtract, Bring Down) alongside the final quotient and remainder for 1-minute teacher grading.
How do I generate worksheets with no remainders?
Set A on the showcase page defaults to 100% exact whole-number division with no remainders. You can also customize difficulty in the Studio.
What paper size is the PDF optimized for?
Worksheets format automatically for standard 8.5"×11" Letter and A4 paper with zero web margin bloat.