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Long Division with RemaindersFREEWorksheet Generator(Grade 4)

Long Division with Remainders worksheets (Grade 4) with step-by-step answer keys. Generate unlimited unique practice sheets with fresh problems.

Level:
Set:
Format:
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Set A โ€ข 6 Qs
PanMaths.comLong Division with Remainders Worksheets โ€ข Set A (Medium)
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 6
1.
9
5
1
5
Quotient:
2.
3
7
9
5
Quotient:
3.
7
9
4
0
Quotient:
4.
2
9
9
5
Quotient:
5.
2
9
3
1
Quotient:
6.
6
4
8
1
Quotient:
PanMaths.com โ€ข Free Math Worksheet Generator โ€ข Set A (Medium)Page 1 of 2
PanMaths.comAnswer Key & Worked Solutions โ€ข Set A (Medium)
Answer Key
Total Problems: 6
1.
9
5
7
R 2
5
1
5
Quotient:57 R 2
1. Divide 51 รท 9 = 5 (5 ร— 9 = 45), Subtract 51 - 45 = 6, Bring down 5 โ†’ 65
2. Divide 65 รท 9 = 7 (7 ร— 9 = 63), Remainder = 2
Final Quotient: 57 R 2 (Check: 57 ร— 9 + 2 = 515) โœ…
2.
3
2
6
5
7
9
5
Quotient:265
1. Divide 7 รท 3 = 2 (2 ร— 3 = 6), Subtract 7 - 6 = 1, Bring down 9 โ†’ 19
2. Divide 19 รท 3 = 6 (6 ร— 3 = 18), Subtract 19 - 18 = 1, Bring down 5 โ†’ 15
3. Divide 15 รท 3 = 5 (5 ร— 3 = 15), Remainder = 0
Final Quotient: 265 (Check: 265 ร— 3 = 795) โœ…
3.
7
1
3
4
R 2
9
4
0
Quotient:134 R 2
1. Divide 9 รท 7 = 1 (1 ร— 7 = 7), Subtract 9 - 7 = 2, Bring down 4 โ†’ 24
2. Divide 24 รท 7 = 3 (3 ร— 7 = 21), Subtract 24 - 21 = 3, Bring down 0 โ†’ 30
3. Divide 30 รท 7 = 4 (4 ร— 7 = 28), Remainder = 2
Final Quotient: 134 R 2 (Check: 134 ร— 7 + 2 = 940) โœ…
4.
2
4
9
7
R 1
9
9
5
Quotient:497 R 1
1. Divide 9 รท 2 = 4 (4 ร— 2 = 8), Subtract 9 - 8 = 1, Bring down 9 โ†’ 19
2. Divide 19 รท 2 = 9 (9 ร— 2 = 18), Subtract 19 - 18 = 1, Bring down 5 โ†’ 15
3. Divide 15 รท 2 = 7 (7 ร— 2 = 14), Remainder = 1
Final Quotient: 497 R 1 (Check: 497 ร— 2 + 1 = 995) โœ…
5.
2
4
6
5
R 1
9
3
1
Quotient:465 R 1
1. Divide 9 รท 2 = 4 (4 ร— 2 = 8), Subtract 9 - 8 = 1, Bring down 3 โ†’ 13
2. Divide 13 รท 2 = 6 (6 ร— 2 = 12), Subtract 13 - 12 = 1, Bring down 1 โ†’ 11
3. Divide 11 รท 2 = 5 (5 ร— 2 = 10), Remainder = 1
Final Quotient: 465 R 1 (Check: 465 ร— 2 + 1 = 931) โœ…
6.
6
8
0
R 1
4
8
1
Quotient:80 R 1
1. Divide 48 รท 6 = 8 (8 ร— 6 = 48), Subtract 48 - 48 = 0, Bring down 1 โ†’ 1
2. Divide 1 รท 6 = 0 (0 ร— 6 = 0), Remainder = 1
Final Quotient: 80 R 1 (Check: 80 ร— 6 + 1 = 481) โœ…
PanMaths.com โ€ข Answer Key & Worked SolutionsPage 2 of 2
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Worksheet Info

Categorygrade-4
Grade LevelGrade 4
DifficultyEasy, Medium, Hard, Sprint
Time5-10 min
CCSS CodeCCSS.MATH.CONTENT.4.NBT.B.6

Skills Practiced

  • โœ“ Long Division with Remainders

Key Strategies

  • ๐Ÿ”„ The DMSB Mnemonic (Does McDonald's Serve Burgers?): Memorize the 4-step loop: 1. Divide (estimate how many times divisor fits into current working value), 2. Multiply (quotient digit ร— divisor), 3. Subtract (find leftover difference), 4. Bring Down (drop next dividend digit).
  • โš–๏ธ The Remainder Invariant (R < Divisor): After every subtraction step, the difference MUST be strictly less than the divisor. If it is equal or greater, the estimated quotient digit was too low!
  • 0๏ธโƒฃ Placeholders in the Quotient: If the divisor does not fit into the brought-down working value, record a 0 in the quotient before bringing down the next digit.
  • โœ… The Inverse Check Equation: Check every answer using: (Quotient ร— Divisor) + Remainder = Dividend. If the sum does not match the original dividend, recheck subtraction steps.
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Related Worksheets

๐Ÿ“œ Standard: CCSS.MATH.CONTENT.4.NBT.B.6๐Ÿ”— CCSS.MATH.CONTENT.3.OA.A.3

Mastering Long Division with Remainders: Core Concepts & Mental Models

Long division with remainders equips Grade 4 students with the standard algorithm for dividing larger dividends by single-digit divisors. Students master the rhythmic four-stage cycle: Divide, Multiply, Subtract, and Bring Down (DMSB), interpreting leftover amounts as remainders that are strictly less than the divisor.

Worked Example & SolutionTeacher Step-by-Step Method
๐Ÿ“ Problem: Divide: 746 รท 5
Worked Solution: 1. Divide 7 รท 5 = 1. Multiply 1 ร— 5 = 5. Subtract 7 - 5 = 2. Bring down 4 โ†’ 24. 2. Divide 24 รท 5 = 4. Multiply 4 ร— 5 = 20. Subtract 24 - 20 = 4. Bring down 6 โ†’ 46. 3. Divide 46 รท 5 = 9. Multiply 9 ร— 5 = 45. Subtract 46 - 45 = 1 (Remainder = 1). 4. Quotient = 149 R 1. Check: (149 ร— 5) + 1 = 745 + 1 = 746. โœ…

๐Ÿ’ก Essential Strategies for Long Division with Remainders

๐Ÿ”„ The DMSB Mnemonic (Does McDonald's Serve Burgers?)

Memorize the 4-step loop: 1. Divide (estimate how many times divisor fits into current working value), 2. Multiply (quotient digit ร— divisor), 3. Subtract (find leftover difference), 4. Bring Down (drop next dividend digit).

โš–๏ธ The Remainder Invariant (R < Divisor)

After every subtraction step, the difference MUST be strictly less than the divisor. If it is equal or greater, the estimated quotient digit was too low!

0๏ธโƒฃ Placeholders in the Quotient

If the divisor does not fit into the brought-down working value, record a 0 in the quotient before bringing down the next digit.

โœ… The Inverse Check Equation

Check every answer using: (Quotient ร— Divisor) + Remainder = Dividend. If the sum does not match the original dividend, recheck subtraction steps.

โš ๏ธ Common Mistakes & Teacher Fixes

โš ๏ธLeaving a remainder that is greater than or equal to the divisor

Why students stumble: Underestimating the quotient digit in a division step.

Teacher Fix: Always verify after subtraction: Remainder must be strictly LESS than the divisor. If diff โ‰ฅ divisor, increase quotient digit by 1.
Example: In 38 รท 5, writing 6 R 8 is incorrect because 8 > 5; correct quotient is 7 R 3.
โš ๏ธSkipping the quotient zero when the divisor doesn't fit into the brought-down digit

Why students stumble: Bringing down a second digit immediately without recording 0 in the quotient first.

Teacher Fix: Every 'bring down' must produce a quotient digit. If divisor > working number, write 0 before bringing down again.
Example: In 612 รท 3: 6 รท 3 = 2; bring down 1 (3 into 1 is 0 times โ†’ write 0); bring down 2 (12 รท 3 = 4) โ†’ 204, not 24.
โš ๏ธSubtracting incorrectly during intermediate DMSB steps

Why students stumble: Mental arithmetic slips when carrying down remainders.

Teacher Fix: Write out intermediate subtractions clearly in columns and check each step with inverse addition.
Example: Subtract 24 - 20 = 4 clearly before dropping the next digit.

๐Ÿ“– Key Mathematical Vocabulary

Dividend

The total number being divided into smaller equal groups.

Divisor

The number of equal groups, or the size of each group.

Quotient

The whole number of times the divisor completely divides into the dividend.

Remainder

The leftover amount that cannot be evenly grouped into the divisor (always Remainder < Divisor).

โ“ Frequently Asked Questions

How do you solve a long division with remainders problem step by step?

Here is a worked example: "Divide: 746 รท 5". Solution: 1. Divide 7 รท 5 = 1. Multiply 1 ร— 5 = 5. Subtract 7 - 5 = 2. Bring down 4 โ†’ 24. 2. Divide 24 รท 5 = 4. Multiply 4 ร— 5 = 20. Subtract 24 - 20 = 4. Bring down 6 โ†’ 46. 3. Divide 46 รท 5 = 9. Multiply 9 ร— 5 = 45. Subtract 46 - 45 = 1 (Remainder = 1). 4. Quotient = 149 R 1. Check: (149 ร— 5) + 1 = 745 + 1 = 746. โœ…

What is the core learning objective for long division with remainders?

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value, the DMSB long division algorithm, and area models. This directly aligns with Common Core Standard CCSS.MATH.CONTENT.4.NBT.B.6.

What is the most common mistake students make with long division with remainders?

A frequent pitfall is: "Leaving a remainder that is greater than or equal to the divisor". Why students stumble: Underestimating the quotient digit in a division step. How to fix it: Always verify after subtraction: Remainder must be strictly LESS than the divisor. If diff โ‰ฅ divisor, increase quotient digit by 1. (Example: In 38 รท 5, writing 6 R 8 is incorrect because 8 > 5; correct quotient is 7 R 3.)

How does the unlimited long division with remainders worksheet generator work?

Every click of 'Generate New Worksheet' creates a completely fresh set of long division with remainders problems with unique numbers. No two worksheets are ever the same โ€” perfect for daily practice, homework variety, and preventing student copying. You can also customize the problem count (6, 8, 10, 12, 15, or 20 problems per sheet).

Are these long division with remainders worksheets free to print with answer keys?

Yes! Every single worksheet on PanMaths is 100% free with no sign-up needed. Each sheet includes a dedicated Answer Key on Page 2 with step-by-step intermediate evaluation lines for 1-minute grading.