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.
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 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
Quick Recap: Terms and the 5-Step Method
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| 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 |
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?
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| 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 |
Example 2: 504 ÷ 21 — Charity Donation
Question: a lottery donates £504 to 21 different charities, split equally. How much does each charity get?
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| 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 |
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.
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| 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 |
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?
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| 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 |
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?
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| 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 |
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?
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| 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 |
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?
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| Step | Action | Calculation |
|---|---|---|
| 1 | Set up | 392 ) 1176 |
| 2 | 392 goes into 1176? | 3 times (3 × 392 = 1176) |
| 3 | Subtract | 1176 − 1176 = 0 |
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
Example 9: 10 ÷ 3
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.
Common Long Division Mistakes in Word Problems
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.
Common Mistakes to Avoid
Traps that break an otherwise correct division
- Forgetting to bring down the next digit after subtracting
- Choosing a quotient digit that is too large or too small
- Making a small subtraction error that changes the entire answer
- Misplacing a quotient digit over the wrong place value
- Stopping at a remainder when the question asks for a decimal
- Forgetting to write a 0 in the quotient when the divisor does not fit a digit
- Skipping the final check, so an arithmetic slip goes unnoticed
- Rounding the final answer the wrong way for what the word problem is actually asking
Correct Strategies to Follow
Fixes that keep the answer accurate and correctly rounded
- After every subtraction, check whether another digit is waiting to be brought down
- Make sure the product of divisor × digit stays less than or equal to the current number
- Double-check every subtraction step individually, not just the final total
- Keep each quotient digit aligned directly above the correct dividend digit
- Continue past the remainder into decimals whenever the problem calls for one
- Always write the 0 above the dividend digit when the divisor does not fit
- Verify every answer with Dividend = (Divisor × Quotient) + Remainder before moving on
- Reread the question and match it to the round-up, round-down, or report-the-remainder rule above
Most of these mistakes are caught immediately by checking: Dividend = (Divisor × Quotient) + Remainder.
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)
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| # | 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 — Calculate long division step-by-step with remainders and decimals.
- Long Division: A Complete Guide for Students & Mental Math Enthusiasts — the full 5-step method plus an advanced mental-math cross-division technique.
- Long Division in Real Life: Bills, Recipes, Budgets, Sports & More — eight everyday scenarios worked out step by step.
- Long Division with 2-Digit, 3-Digit & Decimal Divisors — advanced techniques for bigger and decimal divisors.
- Fraction Calculator — Add, subtract, multiply, and divide fractions easily.
- Fraction to Decimal Calculator — Convert fractions into decimal form, including repeating decimals.
- Prime Factorization & Divisors Calculator — Find all divisors, GCD, and LCM for a number.
- 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.
Start practicing now — use our Long Division Calculator above to check every answer, step by step, completely free.
Written by
Do The Calculation Team
Do The Calculation Editorial Board
The Do The Calculation Editorial Board is comprised of software engineers, finance analysts, and technical contributors focused on building clean, accurate, and easy-to-use calculator tools.
Reviewed & Verified By
Dr. Elena Rostova, PhD
Mathematics Advisor
Professor of mathematics with 20+ years of teaching experience. Dr. Rostova oversees the formulas, proofs, and algorithms behind our math division tools, fractions, logarithms, and scientific equations.