# 4th Grade Long Division: Introduction, Visual Models, and Easy Worksheets

How 4th graders learn division by 1-digit numbers: area models, bar models, partial quotients and the DMSB steps, with worked examples and worksheets with answers.

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- **Canonical URL:** https://dothecalculation.com/blog/math/4th-grade-long-division-visual-models
- **Category:** Math
- **Author:** Do The Calculation Team
- **Published:** 2026-10-07
- **Reading time:** 12 min read
- **Publisher:** Do The Calculation (https://dothecalculation.com)
- **Methodology:** https://dothecalculation.com/methodology

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Fourth grade is when most children meet division with bigger numbers, and for many parents it is also when homework suddenly looks unfamiliar. Your child may bring home boxes, bars and lists of "partial quotients" instead of the long division layout you remember.

Those models are not a detour. They show why long division works, and they lead straight into the step-by-step method. This guide explains what 4th graders are expected to learn, walks through each visual model with a picture, then shows the standard layout and gives practice sets with answers.

In this guide:

- What 4th grade division covers (and what waits until 5th and 6th grade)
- The area model, the bar model and partial quotients, with diagrams
- The DMSB steps of long division, worked through in full
- Three worksheets with answers, from easy to challenge
- How to help at home, and the mistakes to watch for

## Quick Answer

In 4th grade, students divide numbers up to four digits by a one-digit number, with or without a remainder. Under the Common Core standard 4.NBT.B.6 they are expected to use strategies based on place value and the link between multiplication and division, and to explain them with equations, arrays or area models. Many classes also teach the standard long division layout, but full fluency with it is a 6th grade goal (6.NS.B.2).

_[Figure: The DMSB steps of long division - A common memory trick is "Dad, Mom, Sister, Brother" (some classes add "Rover" for the remainder).]_

Quick example, 48 ÷ 4: 4 goes into 4 once (write 1); 1 × 4 = 4; 4 − 4 = 0; bring down 8; 4 goes into 8 twice (write 2); 2 × 4 = 8; 8 − 8 = 0. Answer: 12.

## What 4th Graders Learn About Division

**Division vocabulary, using 148 ÷ 4 = 37**
| Term | Meaning | In 148 ÷ 4 |
| --- | --- | --- |
| Dividend | The number being divided | 148 |
| Divisor | The number you divide by | 4 |
| Quotient | The answer | 37 |
| Remainder | What is left over when the divisor does not fit exactly | 0 |

**How division builds from 3rd to 6th grade (Common Core)**
| Grade | What students do | Standard |
| --- | --- | --- |
| 3rd | Learn division facts within 100 and link them to multiplication | 3.OA.C.7 |
| 4th | Divide up to 4-digit numbers by 1-digit numbers, with remainders, using place value strategies and models | 4.NBT.B.6 |
| 5th | Divide up to 4-digit numbers by 2-digit numbers | 5.NBT.B.6 |
| 6th | Divide multi-digit numbers fluently with the standard algorithm | 6.NS.B.2 |

The [grade-by-grade guide to when long division is taught](/blog/math/when-is-long-division-taught) covers each year in more detail, including decimals in 5th and 6th grade.

## Visual Models for 4th Grade Division

### 1. The area model (box method)

The area model treats division as a missing side of a rectangle. The divisor is one side, the dividend is the total area, and the quotient is the other side. Your child splits the area into friendly chunks they can divide easily, finds each chunk's side, and adds the sides.

_[Figure: Area model for 148 ÷ 4 - Split 148 into 100 + 40 + 8. Each part divides easily by 4, and the side lengths add up to the quotient.]_

- Why it helps: it shows the dividend broken up by place value.
- It shows the distributive property: 148 ÷ 4 = (100 ÷ 4) + (40 ÷ 4) + (8 ÷ 4).
- The chunks are flexible. 120 + 28 works just as well: 30 + 7 = 37.

### 2. The bar model (equal sharing)

The bar model shows division as sharing a total into equal groups. Draw a bar for the total, split it into as many equal parts as the divisor, and find the size of each part.

_[Figure: Bar model for 55 ÷ 5 - Share 55 equally into 5 parts. Each part is 11.]_

### 3. Partial quotients (the "big chunks" method)

Partial quotients is the written version of the area model. Your child takes away easy multiples of the divisor (10 times, 20 times, 5 times) until nothing useful is left, then adds up how many times they took it away. It is forgiving: a small chunk is never wrong, it just takes an extra step.

**Partial quotients for 148 ÷ 4**
| Start with | Take away | Times 4 | Left over |
| --- | --- | --- | --- |
| 148 | 4 × 30 = 120 | 30 | 28 |
| 28 | 4 × 7 = 28 | 7 | 0 |
| Total |  | 30 + 7 = 37 | Remainder 0 |

_[Figure: Models vs the standard layout]_

## How to Do Long Division, Step by Step

Here is 176 ÷ 4 in the standard layout. The digits on top are the quotient, and the brought-down digit is shown in orange.

_[Figure: Long division layout for 176 ÷ 4 - Each pass through Divide, Multiply, Subtract and Bring down puts one digit on top.]_

Tool: [Check homework with the Long Division Calculator](https://dothecalculation.com/calculators/long-division-calculator): Shows every Divide, Multiply, Subtract and Bring down step, so you can find exactly where your child's working went off track.

### Worked example 1: 237 ÷ 5 (with a remainder)

- Divide: 5 does not go into 2, so use 23. 23 ÷ 5 = 4. Write 4 above the 3.
- Multiply: 4 × 5 = 20. Subtract: 23 − 20 = 3.
- Bring down 7 to make 37. Divide: 37 ÷ 5 = 7. Write 7 above the 7.
- Multiply: 7 × 5 = 35. Subtract: 37 − 35 = 2. No digits left.
- Answer: 47 R2. Check: 47 × 5 + 2 = 235 + 2 = 237.

### Worked example 2: 851 ÷ 3

- 8 ÷ 3 = 2 (write 2); 2 × 3 = 6; 8 − 6 = 2; bring down 5 to make 25.
- 25 ÷ 3 = 8 (write 8); 8 × 3 = 24; 25 − 24 = 1; bring down 1 to make 11.
- 11 ÷ 3 = 3 (write 3); 3 × 3 = 9; 11 − 9 = 2.
- Answer: 283 R2. Check: 283 × 3 + 2 = 849 + 2 = 851.

### Worked example 3: 6,249 ÷ 3 (a zero in the quotient)

- 6 ÷ 3 = 2 (write 2); 2 × 3 = 6; 6 − 6 = 0; bring down 2.
- 2 ÷ 3 = 0. Write 0 on top. This is the step children most often skip. Bring down 4 to make 24.
- 24 ÷ 3 = 8 (write 8); 8 × 3 = 24; 24 − 24 = 0; bring down 9.
- 9 ÷ 3 = 3 (write 3); 3 × 3 = 9; 9 − 9 = 0.
- Answer: 2,083. Check: 2,083 × 3 = 6,249.

Zeros in the middle of a quotient cause more wrong answers than anything else at this level. The [long division with zeros guide](/blog/math/long-division-with-zeros-guide) has more examples.

## Easy Worksheets (With Answers)

Print or copy these onto squared paper. Cover the answer column, work each problem, then check by multiplying the quotient by the divisor and adding the remainder.

**Worksheet 1: 2-digit and 3-digit dividends, no remainder**
| Problem | Answer | Check |
| --- | --- | --- |
| 48 ÷ 4 | 12 | 12 × 4 = 48 |
| 75 ÷ 3 | 25 | 25 × 3 = 75 |
| 96 ÷ 4 | 24 | 24 × 4 = 96 |
| 126 ÷ 6 | 21 | 21 × 6 = 126 |
| 176 ÷ 4 | 44 | 44 × 4 = 176 |
| 365 ÷ 5 | 73 | 73 × 5 = 365 |

**Worksheet 2: with remainders**
| Problem | Answer | Check |
| --- | --- | --- |
| 237 ÷ 5 | 47 R2 | 47 × 5 + 2 = 237 |
| 851 ÷ 3 | 283 R2 | 283 × 3 + 2 = 851 |
| 500 ÷ 8 | 62 R4 | 62 × 8 + 4 = 500 |
| 813 ÷ 9 | 90 R3 | 90 × 9 + 3 = 813 |

**Worksheet 3: 4-digit dividends (challenge)**
| Problem | Answer | Check |
| --- | --- | --- |
| 6,249 ÷ 3 | 2,083 | 2,083 × 3 = 6,249 |
| 1,234 ÷ 6 | 205 R4 | 205 × 6 + 4 = 1,234 |
| 2,507 ÷ 9 | 278 R5 | 278 × 9 + 5 = 2,507 |
| 4,086 ÷ 7 | 583 R5 | 583 × 7 + 5 = 4,086 |

> **Working for 2,507 ÷ 9**: 9 goes into 25 twice (18), 25 − 18 = 7; bring down 0 to make 70; 9 goes into 70 seven times (63), 70 − 63 = 7; bring down 7 to make 77; 9 goes into 77 eight times (72), 77 − 72 = 5. Answer: 278 R5.

When your child is ready for story problems, the [long division word problems guide](/blog/math/long-division-word-problems-guide) has easy, medium and hard sets, including problems where the remainder decides the answer (30 children in vans that seat 8 is 3 R6, so you need 4 vans).

## How to Help Your Child at Home

**Tips that make the biggest difference**
| Tip | Why it helps |
| --- | --- |
| Practise times tables first | Every Divide step is a multiplication fact in reverse |
| Use squared or graph paper | One digit per square keeps place values lined up |
| Ask "about how big?" before starting | 148 ÷ 4 must be between 30 (120) and 40 (160) |
| Let them use the model their teacher uses | Mixing methods at home can confuse more than help |
| Always check by multiplying | Quotient × divisor + remainder must equal the dividend |
| Keep sessions short | Ten focused minutes beats an hour of frustration |

For a one-page reminder of the steps and vocabulary to keep next to the homework, see the [long division cheat sheet for parents](/blog/math/long-division-cheat-sheet-for-parents).

## Common Mistakes Kids Make (and How to Help)

**What goes wrong and what to do**
| Mistake | Why it happens | How to help |
| --- | --- | --- |
| Forgetting to bring down | Rushing through the steps | Say D-M-S-B out loud for each digit |
| Skipping a zero in the quotient | The divisor "does not fit", so nothing gets written | Every digit brought down needs a digit on top, even 0 |
| Remainder bigger than the divisor | The quotient digit was too small | After subtracting, check the result is less than the divisor |
| Multiplication slips | Times tables not yet automatic | Practise the facts for that divisor first |
| Digits drifting out of line | Messy layout | Use squared paper |
| Writing the first quotient digit too far left | Place value not clear | The first digit goes above the last digit you used |
| Not checking | Rushing to finish | Make "multiply back" the last step every time |

## Frequently Asked Questions

**What kind of division do 4th graders learn?**

Dividing numbers up to four digits by a one-digit number, with remainders, using place value strategies such as the area model and partial quotients. Two-digit divisors come in 5th grade.

**Is long division taught in 4th grade?**

Usually it is introduced in 4th grade alongside the visual models, practised with two-digit divisors in 5th grade, and expected to be fluent with the standard algorithm by the end of 6th grade (6.NS.B.2).

**What is the area model for division?**

A rectangle whose area is the dividend and whose one side is the divisor. You split the area into easy parts, find each part's other side, and add those sides to get the quotient.

**What is the DMSB method?**

The repeating steps of long division: Divide, Multiply, Subtract, Bring down. Children often remember it as "Dad, Mom, Sister, Brother".

**How do I check a long division answer?**

Multiply the quotient by the divisor and add the remainder. If you get the dividend, the answer is right. For 237 ÷ 5 = 47 R2: 47 × 5 + 2 = 237.

**Why is my child struggling with long division?**

The most common reasons are times tables that are not yet automatic, digits that drift out of line, and skipped zeros. Fix the times tables first; the rest usually follows with squared paper and checking.

## Final Summary

- 4th graders divide up to 4-digit numbers by 1-digit numbers, with remainders (4.NBT.B.6).
- The area model, bar model and partial quotients show why division works.
- The standard layout repeats Divide, Multiply, Subtract, Bring down.
- Every brought-down digit needs a digit on top, even a zero.
- Check every answer: quotient × divisor + remainder = dividend.

Curious how a calculator does the same job? It uses a version of long division in binary, explained in [how calculators arrive at the answer](/blog/math/how-calculators-arrive-at-the-answer).

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_Source: [Do The Calculation](https://dothecalculation.com/blog/math/4th-grade-long-division-visual-models). Quote freely with attribution and a link to this page._