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๐ŸŽ“ Grades 4-6๐Ÿ“„ Free PDF + Keysโ™พ๏ธ Dynamic Generator

Long DivisionFREEWorksheet Generator(Grades 4-6)

Long Division worksheets with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems for Grades 4โ€“6.

Count:
๐Ÿ“„ Sheet #1โ€ข6 Problems
PanMaths.comLong Division Worksheets โ€ข Worksheet #1
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 6
1.
5
8
8
9
Quotient:
2.
5
9
5
5
Quotient:
3.
9
7
5
6
Quotient:
4.
4
2
2
6
Quotient:
5.
6
4
3
2
Quotient:
6.
3
7
2
4
Quotient:
PanMaths.com โ€ข Free Math Worksheet GeneratorPage 1 of 2
PanMaths.comAnswer Key & Worked Solutions โ€ข Worksheet #1
Answer Key
Total Problems: 6
1.
5
1
7
7
R 4
8
8
9
Quotient:177 R 4
1. Divide 8 รท 5 = 1 (1 ร— 5 = 5), Subtract 8 - 5 = 3, Bring down 8 โ†’ 38
2. Divide 38 รท 5 = 7 (7 ร— 5 = 35), Subtract 38 - 35 = 3, Bring down 9 โ†’ 39
3. Divide 39 รท 5 = 7 (7 ร— 5 = 35), Remainder = 4
Final Quotient: 177 R 4 (Check: 177 ร— 5 + 4 = 889) โœ…
2.
5
1
9
1
9
5
5
Quotient:191
1. Divide 9 รท 5 = 1 (1 ร— 5 = 5), Subtract 9 - 5 = 4, Bring down 5 โ†’ 45
2. Divide 45 รท 5 = 9 (9 ร— 5 = 45), Subtract 45 - 45 = 0, Bring down 5 โ†’ 5
3. Divide 5 รท 5 = 1 (1 ร— 5 = 5), Remainder = 0
Final Quotient: 191 (Check: 191 ร— 5 = 955) โœ…
3.
9
8
4
7
5
6
Quotient:84
1. Divide 75 รท 9 = 8 (8 ร— 9 = 72), Subtract 75 - 72 = 3, Bring down 6 โ†’ 36
2. Divide 36 รท 9 = 4 (4 ร— 9 = 36), Remainder = 0
Final Quotient: 84 (Check: 84 ร— 9 = 756) โœ…
4.
4
5
6
R 2
2
2
6
Quotient:56 R 2
1. Divide 22 รท 4 = 5 (5 ร— 4 = 20), Subtract 22 - 20 = 2, Bring down 6 โ†’ 26
2. Divide 26 รท 4 = 6 (6 ร— 4 = 24), Remainder = 2
Final Quotient: 56 R 2 (Check: 56 ร— 4 + 2 = 226) โœ…
5.
6
7
2
4
3
2
Quotient:72
1. Divide 43 รท 6 = 7 (7 ร— 6 = 42), Subtract 43 - 42 = 1, Bring down 2 โ†’ 12
2. Divide 12 รท 6 = 2 (2 ร— 6 = 12), Remainder = 0
Final Quotient: 72 (Check: 72 ร— 6 = 432) โœ…
6.
3
2
4
1
R 1
7
2
4
Quotient:241 R 1
1. Divide 7 รท 3 = 2 (2 ร— 3 = 6), Subtract 7 - 6 = 1, Bring down 2 โ†’ 12
2. Divide 12 รท 3 = 4 (4 ร— 3 = 12), Subtract 12 - 12 = 0, Bring down 4 โ†’ 4
3. Divide 4 รท 3 = 1 (1 ร— 3 = 3), Remainder = 1
Final Quotient: 241 R 1 (Check: 241 ร— 3 + 1 = 724) โœ…
PanMaths.com โ€ข Answer Key & Worked SolutionsPage 2 of 2
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Worksheet Info

Categoryarithmetic
Grade LevelGrades 3-6
Difficultymedium
Time10-15 min

Skills Practiced

  • โœ“ Long Division fluency
  • โœ“ Mental math speed
  • โœ“ Step-by-step problem solving

Key Strategies

  • DMSB Cycle Discipline: Follow Divide, Multiply, Subtract, Bring Down sequentially on grid lines to eliminate place-value drift.
  • Remainder Invariant Check: Always ensure the subtraction difference is strictly less than the divisor before bringing down.
  • Multiplication Verification: Multiply the quotient by the divisor and add remainder to verify the original dividend.
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Related Worksheets

Strategies

  • DMSB Cycle Discipline: Follow Divide, Multiply, Subtract, Bring Down sequentially on grid lines to eliminate place-value drift.
  • Remainder Invariant Check: Always ensure the subtraction difference is strictly less than the divisor before bringing down.
  • Multiplication Verification: Multiply the quotient by the divisor and add remainder to verify the original dividend.

Mastering Long Division: Core Concepts & Mental Models

Long Division worksheets with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems for Grades 4โ€“6.

๐Ÿ’ก Essential Strategies for Long Division

DMSB Cycle Discipline

Follow Divide, Multiply, Subtract, Bring Down sequentially on grid lines to eliminate place-value drift.

Remainder Invariant Check

Always ensure the subtraction difference is strictly less than the divisor before bringing down.

Multiplication Verification

Multiply the quotient by the divisor and add remainder to verify the original dividend.

โš ๏ธ Common Mistakes & Teacher Fixes

โš ๏ธForgetting to Bring Down the Next Digit

Why students stumble: Students subtract the product and stop, writing the difference as the remainder rather than dropping the next place-value column.

Teacher Fix: Follow the DMSB cycle (Divide โž” Multiply โž” Subtract โž” Bring Down) strictly until every column of the dividend is evaluated.
Example: In 374 รท 5: 37 - 35 = 2. You MUST bring down 4 to make 24 before concluding.
โš ๏ธWriting a Remainder Larger Than the Divisor

Why students stumble: Underestimating the quotient digit leaves a difference equal to or greater than the divisor.

Teacher Fix: Verify after every subtraction step: the remaining difference MUST be strictly less than the divisor.
Example: If dividing by 6 and your subtraction gives 7, your quotient digit was too small. Increase the quotient by 1.
โš ๏ธMisaligning Place-Value Columns in the Quotient

Why students stumble: Writing quotient digits above the wrong dividend place values causes missing zeros in multi-digit answers.

Teacher Fix: Always write each quotient digit directly above the last digit of the current working dividend segment.
Example: In 412 รท 4: 4 goes into 4 once (1), 4 goes into 1 zero times (0), 4 goes into 12 three times (3) โž” 103, not 13.

โ“ Frequently Asked Questions

Are these long division worksheets free for classroom use?

Yes! Every worksheet generated on PanMaths is completely free to print and photocopy for schools, tutors, and homeschooling families โ€” no sign-up needed.

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?

The default generator produces 100% exact whole-number division with no remainders. Click "Generate New Worksheet" to get fresh problems every time.

What paper size is the PDF optimized for?

Worksheets format automatically for standard 8.5"ร—11" Letter and A4 paper with zero web margin bloat.

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. 1. Divide (D): Determine how many times the divisor fits into the current dividend segment. Write this digit in the quotient on top.
  2. 2. Multiply (M): Multiply that quotient digit by the divisor and write the resulting product directly below the working segment.
  3. 3. Subtract (S): Subtract the product from the working segment. Check: The difference must be less than the divisor!
  4. 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 ร— Quotient) + Remainder

For example, if 374 รท 5 = 74 R 4, we verify: (5 ร— 74) + 4 = 370 + 4 = 374 โœ….

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 รท 24 by thinking 14 รท 2 = 7).
  • Trial Multiplication: Test your estimate on scratch paper. If the product is larger than the segment, reduce the quotient digit by 1.

Worksheet Facts by Grade Level

Grade LevelCommon Core StandardTarget Divisors & ComplexityRecommended Drills
Grade 3CCSS.MATH.CONTENT.3.OA.C.7Single-digit division facts within 100 (No remainders)Set D (Timed Sprint 15 Problems)
Grade 4CCSS.MATH.CONTENT.4.NBT.B.6Find whole-number quotients up to 4-digit dividends and 1-digit divisorsSet A (Standard) & Set B (Remainders)
Grade 5CCSS.MATH.CONTENT.5.NBT.B.6Multi-digit division with 2-digit divisors and up to 4-digit dividendsSet C (Challenging 8 Problems)
Grade 6CCSS.MATH.CONTENT.6.NS.B.2Fluently divide multi-digit numbers using the standard algorithmSet 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. 1. Divide (D): Determine how many times the divisor fits into the current dividend segment. Write this digit in the quotient on top.
  2. 2. Multiply (M): Multiply that quotient digit by the divisor and write the resulting product directly below the working segment.
  3. 3. Subtract (S): Subtract the product from the working segment. Check: The difference must be less than the divisor!
  4. 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 ร— Quotient) + Remainder

For example, if 374 รท 5 = 74 R 4, we verify: (5 ร— 74) + 4 = 370 + 4 = 374 โœ….

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 รท 24 by thinking 14 รท 2 = 7).
  • Trial Multiplication: Test your estimate on scratch paper. If the product is larger than the segment, reduce the quotient digit by 1.
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Benefits of Mastery

๐Ÿ“ Place-Value Fluency

Builds deep conceptual intuition for columns, carries, and multi-digit subtraction.

โšก Standardized Exam Success

Directly targets Common Core standard 4.NBT.B.6 for state exams and middle school algebra.

๐Ÿง  Scratchpad Analytical Rigor

Develops disciplined step-by-step problem-solving habits with dedicated pencil workspaces.

๐Ÿ–จ๏ธ 100% Free Classroom Photocopying

All sets print cleanly with verified intermediate solution keys for instant grading.