# Long Division Word Problems: Easy, Medium & Hard Examples with Real-World Practice

Practice long division with real-world word problems graded from easy to hard, learn how to handle decimal answers, know when to round remainders up or down, and check your work against every answer.

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- **Canonical URL:** https://dothecalculation.com/blog/math/long-division-word-problems-guide
- **Category:** Math
- **Author:** Do The Calculation Team
- **Published:** 2026-08-03
- **Last updated:** 2026-08-03
- **Reading time:** 16 min read
- **Publisher:** Do The Calculation (https://dothecalculation.com)
- **Methodology:** https://dothecalculation.com/methodology

---

## Long Division Word Problems: Easy, Medium & Hard Examples with Real-World Practice

Knowing the steps of long division is one thing — recognizing when and how to use it in a real problem is another. This guide is built entirely around worked, real-world word problems, graded from easy to hard, so you can practice applying long division the way it actually shows up on homework, tests, and in everyday life.

New to long division itself? Start with our [complete step-by-step long division guide](/blog/math/long-division-examples-step-by-step-guide) first, which covers the 5-step method and an advanced mental-math technique in full detail. This guide picks up from there and focuses on applying it.

In this article, you'll find:

- A quick recap of long division terms and the 5-step method
- Easy, medium, and hard long division word problems with full worked solutions
- How to handle decimal (non-whole-number) answers
- When to round a remainder up vs. down in a word problem
- Common mistakes and how to avoid them
- Practice questions with answers

Tool: [Try the Long Division Calculator](https://dothecalculation.com/calculators/long-division-calculator) — Solve any long division problem step-by-step with remainders, decimals, and an interactive walkthrough.

## Quick Recap: Terms and the 5-Step Method

**Key Terms (Example: 175 ÷ 3)**
| Term | Definition | Example (175 ÷ 3) |
| --- | --- | --- |
| Dividend | The number being divided | 175 |
| Divisor | The number you divide by | 3 |
| Quotient | The answer (whole number part) | 58 |
| Remainder | The amount left over | 1 |

**The 5 Steps of Long Division**

```
Divide → Multiply → Subtract → Bring Down → Repeat
```
- Divide: how many times does the divisor go into the current digit(s)?
- Multiply: multiply the divisor by the digit you just wrote.
- Subtract: subtract that product from the current digit(s).
- Bring Down: bring down the next digit from the dividend.
- Repeat: start again from Divide until there are no more digits.

> **Always Check Your Work** — Dividend = (Divisor × Quotient) + Remainder. For 175 ÷ 3 = 58 R1: 3 × 58 + 1 = 174 + 1 = 175 ✓. Use this on every problem below.

## Easy Long Division Word Problems

### Example 1: 180 ÷ 12 — Eggs in Trays

Question: eggs are put in trays of 12. Each box contains 180 eggs. How many trays are in each box?

**Solution: 180 ÷ 12**
| Step | Action | Calculation |
| --- | --- | --- |
| 1 | Set up | 12 ) 180 |
| 2 | 12 goes into 18? | 1 time (1 × 12 = 12) |
| 3 | Subtract | 18 − 12 = 6 |
| 4 | Bring down 0 | 60 |
| 5 | 12 goes into 60? | 5 times (5 × 12 = 60) |
| 6 | Subtract | 60 − 60 = 0 |

> **Answer** — 15 trays in each box. Check: 15 × 12 = 180 ✓.

### Example 2: 504 ÷ 21 — Charity Donation

Question: a lottery donates £504 to 21 different charities, split equally. How much does each charity get?

**Solution: 504 ÷ 21**
| Step | Action | Calculation |
| --- | --- | --- |
| 1 | Set up | 21 ) 504 |
| 2 | 21 goes into 50? | 2 times (2 × 21 = 42) |
| 3 | Subtract | 50 − 42 = 8 |
| 4 | Bring down 4 | 84 |
| 5 | 21 goes into 84? | 4 times (4 × 21 = 84) |
| 6 | Subtract | 84 − 84 = 0 |

> **Answer** — Each charity gets £24. Check: 24 × 21 = 504 ✓.

## Medium Long Division Word Problems

### Example 3: 8,051 ÷ 83 — A Classic Exam-Style Question

Question: this type of question often appears on standardized math tests. Calculate 8,051 ÷ 83.

> **Tip: List the Multiples First** — Before you start a division with a 2-digit divisor, jot down its first 9 multiples: 83, 166, 249, 332, 415, 498, 581, 664, 747. It turns guesswork into a quick lookup.

**Solution: 8,051 ÷ 83**
| Step | Action | Calculation |
| --- | --- | --- |
| 1 | Set up | 83 ) 8051 |
| 2 | 83 goes into 8? | No (0) → write 0 above the 8 |
| 3 | 83 goes into 80? | No (0) → write 0 above the 0 |
| 4 | 83 goes into 805? | 9 times (9 × 83 = 747) |
| 5 | Subtract | 805 − 747 = 58 |
| 6 | Bring down 1 | 581 |
| 7 | 83 goes into 581? | 7 times (7 × 83 = 581) |
| 8 | Subtract | 581 − 581 = 0 |

> **Answer** — 8,051 ÷ 83 = 97. Check: 97 × 83 = 8,051 ✓.

### Example 4: 1,000 ÷ 34 — Booklets from Paper Packets

Question: Adam is making booklets. Each booklet needs 34 sheets of paper. He has 2 packets of paper, with 500 sheets in each packet. How many complete booklets can Adam make?

**Step 1 — Total Sheets Available**

```
2 packets × 500 sheets = 1,000 sheets
```

**Step 2 — Solution: 1,000 ÷ 34**
| Step | Action | Calculation |
| --- | --- | --- |
| 1 | Set up | 34 ) 1000 |
| 2 | 34 goes into 100? | 2 times (2 × 34 = 68) |
| 3 | Subtract | 100 − 68 = 32 |
| 4 | Bring down 0 | 320 |
| 5 | 34 goes into 320? | 9 times (9 × 34 = 306) |
| 6 | Subtract | 320 − 306 = 14 |

> **Answer** — Adam can make 29 complete booklets, with 14 sheets left over (29 R14). Notice the leftover 14 sheets are not enough for a 34-sheet booklet, so the remainder is simply left over — this word problem rounds down.

## Hard Long Division Word Problems

### Example 5: 4,923 ÷ 37 — Leftover Teddy Bears

Question: a factory makes 4,923 teddy bears, packed in boxes of 37. How many bears are left over after filling as many full boxes as possible?

**Solution: 4,923 ÷ 37**
| Step | Action | Calculation |
| --- | --- | --- |
| 1 | Set up | 37 ) 4923 |
| 2 | 37 goes into 49? | 1 time (1 × 37 = 37) |
| 3 | Subtract | 49 − 37 = 12 |
| 4 | Bring down 2 | 122 |
| 5 | 37 goes into 122? | 3 times (3 × 37 = 111) |
| 6 | Subtract | 122 − 111 = 11 |
| 7 | Bring down 3 | 113 |
| 8 | 37 goes into 113? | 3 times (3 × 37 = 111) |
| 9 | Subtract | 113 − 111 = 2 |

> **Answer** — 4,923 ÷ 37 = 133 R2, so 2 teddy bears are left over.

### Example 6: 427 ÷ 15 — Chaperones for a School Trip

Question: 427 children visit a castle. They travel in groups of 15, and every group — even a partial one — needs one adult chaperone. How many adults need to go?

**Solution: 427 ÷ 15**
| Step | Action | Calculation |
| --- | --- | --- |
| 1 | Set up | 15 ) 427 |
| 2 | 15 goes into 42? | 2 times (2 × 15 = 30) |
| 3 | Subtract | 42 − 30 = 12 |
| 4 | Bring down 7 | 127 |
| 5 | 15 goes into 127? | 8 times (8 × 15 = 120) |
| 6 | Subtract | 127 − 120 = 7 |

> **Answer** — 427 ÷ 15 = 28 R7 — that is 28 full groups of 15, plus one partial group of 7 children. Because every group (even the partial one) needs its own adult, this word problem rounds up: 28 + 1 = 29 groups, so 29 adults are needed.

### Example 7: 1,176 ÷ 392 — Ordering Boxes of Apples

Question: a grocer needs to order 1,176 apples. Apples are sold in boxes containing 28 trays, with 14 apples on each tray. How many boxes does the grocer need to order?

**Step 1 — Apples per Box**

```
28 trays × 14 apples = 392 apples per box
```

**Step 2 — Solution: 1,176 ÷ 392**
| Step | Action | Calculation |
| --- | --- | --- |
| 1 | Set up | 392 ) 1176 |
| 2 | 392 goes into 1176? | 3 times (3 × 392 = 1176) |
| 3 | Subtract | 1176 − 1176 = 0 |

> **Answer** — The grocer needs to order 3 boxes of apples. Check: 3 × 392 = 1,176 ✓ — this one divides exactly, with no remainder to round at all.

## Long Division with Decimal Answers

Not every word problem wants a remainder — sometimes you need a precise decimal instead. After you reach a remainder, add a decimal point to the quotient, bring down a 0, and keep dividing.

### Example 8: 22 ÷ 4

**Solution**

```
4 goes into 22: 5 times (5 × 4 = 20), remainder 2
```
- Add a decimal point: 22.0 ÷ 4 → bring down 0 → 20
- 4 goes into 20: 5 times (5 × 4 = 20), remainder 0
- Answer: 22 ÷ 4 = 5.5 — check: 5.5 × 4 = 22 ✓

### Example 9: 10 ÷ 3

**Solution**

```
3 goes into 10: 3 times (3 × 3 = 9), remainder 1
```
- Add a decimal point: 10.0 ÷ 3 → bring down 0 → 10
- 3 goes into 10: 3 times (3 × 3 = 9), remainder 1 — and it keeps repeating
- Answer: 10 ÷ 3 = 3.333... (a repeating decimal)

> **Why Some Decimals Repeat Forever** — When the remainder starts repeating (like the 1 in 10 ÷ 3), the decimal digits repeat too — some divisions genuinely never terminate. In practice, you round to however many decimal places the problem needs.

## When to Round a Remainder Up vs. Down

This is the single most common place students lose marks on word problems — the division itself is correct, but the final answer is rounded the wrong way. The rule depends on what the remainder actually represents:

- Round DOWN (keep the whole-number quotient, ignore the remainder as leftover) when the remainder cannot form another complete unit of whatever you are counting — like Example 4, where 14 leftover sheets are not enough for another 34-sheet booklet, so the answer stays at 29 booklets.
- Round UP (add 1 to the quotient) when the remainder still needs its own full unit of something else — like Example 6, where a partial group of 7 children still needs its own adult chaperone, so 28 full groups becomes 29 groups that each need an adult.
- Report the remainder as-is when the question specifically asks "how many are left over," rather than asking for a rounded count of groups or units — like Example 5, where the answer is simply "2 bears are left over," not a rounded number of boxes.

> **The Question Text Is the Clue** — Read exactly what is being asked. "How many complete X" or "how many full X" is a signal to round down. "How many X are needed to cover everyone/everything" is a signal to round up. "How many are left over" means report the remainder itself.

## Common Long Division Mistakes in Word Problems

_[Figure: Common Long Division Mistakes & Correct Fixes — These are the mistakes that show up most often once long division is applied to a real word problem, not just a bare equation.]_

## Top Tips for Long Division Success

- List 9 multiples of the divisor before you start — this saves time and reduces mistakes on larger divisors.
- Line up place values carefully — each quotient digit goes directly above the correct dividend digit.
- Write clearly and neatly — messy layouts lead to messy, error-prone calculations.
- Always include the 0 when needed — if the divisor will not fit, write 0 in the quotient and move on.
- Double-check subtraction — it is the single most common source of errors.
- Use the inverse to check your answer — multiply the quotient by the divisor (and add the remainder) to confirm it matches the dividend.
- Do not rush — long division is a repeatable process; take each step in order.
- Practice regularly with real word problems, not just bare equations, since that is where the rounding rules actually get tested.

## Practice Questions (With Answers)

**Practice Problems**
| # | Problem | Answer |
| --- | --- | --- |
| 1 | Divide 256 ÷ 7 | 36 R4 (or 36.571...) |
| 2 | Divide 1,024 ÷ 8 | 128 |
| 3 | Divide 3,456 ÷ 12 | 288 |
| 4 | Divide 5,000 ÷ 25 | 200 |
| 5 | Divide 10,000 ÷ 13 | 769 R3 (or 769.23...) |
| 6 | A school has 1,000 students, divided into groups of 24. How many groups are there, and how many students are left over? | 41 groups, 16 students left over |
| 7 | A factory produces 2,500 widgets per day. Each box holds 48 widgets. How many boxes are filled per day, and how many widgets are left over? | 52 boxes, 4 widgets left over |

## Frequently Asked Questions

**How do I know whether to round a long division answer up or down in a word problem?**

Round down if the remainder cannot form another complete unit of what you are counting. Round up if the remainder still needs its own full unit of something else (like an extra container or chaperone). Report the remainder directly if the question asks how many are "left over."

**How do I do long division with decimals?**

After reaching a remainder, add a decimal point to the quotient, bring down a 0, and keep dividing until you reach the precision the problem needs.

**Why do some long division answers have repeating decimals?**

Some divisions never resolve to zero remainder. For example, 10 ÷ 3 = 3.333... because the remainder of 1 keeps reappearing at every step.

**What happens if the divisor is larger than the current digit?**

Write 0 above that digit and move to the next one. For example, in 3 ) 175, 3 does not go into 1, so you write 0 above the 1 and continue with 17.

**What if the divisor is 0?**

Division by zero is undefined. A correctly built calculator, including ours, should show an error rather than a result if the divisor is 0.

**Should I always list multiples of the divisor before starting?**

It is not required, but it helps a lot with 2-digit or larger divisors — listing the first 9 multiples turns repeated guessing into a quick lookup and reduces mistakes.

**How can I practice long division word problems?**

Work through the graded examples in this guide, try the practice questions above, and use our Long Division Calculator to check your work step by step.

**What age group is long division typically taught to?**

Long division is typically introduced around Year 6 (ages 10-11) in the UK and 4th-6th grade in the US, though it varies by curriculum.

**Is long division still relevant if I have a calculator?**

Yes — understanding long division builds number sense and helps you sanity-check calculator results, and it remains part of most math curricula and standardized tests.

**Is this long division word problems guide free?**

Yes — completely free, with no registration required.

## Related Math Calculators & Guides

- [Long Division Calculator](/calculators/long-division-calculator) — Calculate long division step-by-step with remainders and decimals.
- [Long Division: A Complete Guide for Students & Mental Math Enthusiasts](/blog/math/long-division-examples-step-by-step-guide) — the full 5-step method plus an advanced mental-math cross-division technique.
- [Long Division in Real Life: Bills, Recipes, Budgets, Sports & More](/blog/math/long-division-real-world-applications-guide) — eight everyday scenarios worked out step by step.
- [Long Division Answers: Remainder, Decimal, or Fraction?](/blog/math/long-division-remainder-decimal-fraction-guide) — a deeper look at converting between all three answer forms once you have decided whether to round.
- [Long Division with 2-Digit, 3-Digit & Decimal Divisors](/blog/math/long-division-multi-digit-decimal-divisors-guide) — advanced techniques for bigger and decimal divisors.
- [Long Division with Zeros: A Step-by-Step Guide](/blog/math/long-division-with-zeros-guide) — the three places zeros trip people up, isolated and fully worked.
- [Fraction Calculator](/calculators/fraction-calculator) — Add, subtract, multiply, and divide fractions easily.
- [Fraction to Decimal Calculator](/calculators/fraction-to-decimal-calculator) — Convert fractions into decimal form, including repeating decimals.
- [Prime Factorization & Divisors Calculator](/calculators/prime-factorization-calculator) — Find all divisors, GCD, and LCM for a number.
- [Rounding Calculator](/calculators/rounding-calculator) — Round numbers to the nearest whole number, tenth, or hundredth.

## Final Summary

Long division stops feeling abstract once you have worked through it in real contexts — trays of eggs, boxes of apples, school trips, and factory orders all use exactly the same 5-step process. The math never changes; what changes is how you interpret the remainder once you get there.

**Remember**

```
Dividend = (Divisor × Quotient) + Remainder
```
- Round down when the remainder cannot form another full unit
- Round up when the remainder still needs its own full unit
- Report the remainder directly when the question asks how many are left over

Start practicing now — use our Long Division Calculator above to check every answer, step by step, completely free.

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_Source: [Do The Calculation](https://dothecalculation.com/blog/math/long-division-word-problems-guide). Quote freely with attribution and a link to this page._