One important step in building a strong foundation in mathematics is mastering long division. Whether dividing multi-digit numbers or understanding how remainder works, long division builds children’s logical thinking and number sense.
In this blog, let’s explore long division worksheets designed for classes 3-6. These worksheets contain long division questions with key answers to strengthen accuracy and confidence. Students also learn how to solve long division sums using Vedic Maths division tricks, which help students in fast calculation, reducing calculation time.
Key Takeaways
- Long Division Builds Logical Thinking: Mastering long division strengthens number sense, accuracy, and problem-solving skills — essential for higher math like fractions, decimals, and algebra.
- Step-by-Step Learning Approach: The D–M–S–B (Divide–multiply–subtract–bring down) method helps students solve long division problems easily and confidently.
- Vedic Maths Makes Division Faster: Vedic Maths division tricks, such as the Nikhilam Sutra and the Paravartya Yojayet Sutra, allow students to perform divisions mentally, reduce errors, and boost speed.
- Class-Wise Worksheets for Progressive Learning: These free printable long division worksheets for Classes 3–6 include problems ranging from basic single-digit to complex multi-digit, decimal, and word problems — with answer keys.
- Real-Life Application of Math: Worksheets use everyday examples (money, distance, sharing, time) to make math relatable and meaningful.
- Error-Free Learning Through Practice: The blog highlights common student mistakes and simple self-correction tips — ensuring clarity in divisors, dividends, remainders, and place values.
- Perfect for Home and School Learning: Parents, teachers, and students can use these worksheets for daily practice — with free downloadable PDFs and answer keys for self-assessment.
- Free Resources & Live Learning Options: Students can download free long division worksheets or join Live Vedic Maths Classes and the Vedic Maths Bundle Kit to learn quick division techniques anytime.
1. Introduction: Why Long Division Matters
Long division is the backbone of understanding advanced math concepts such as fractions, decimals, ratios, and algebra. When children understand the concept of long division clearly, they understand how numbers break down through division, which helps them boost logical thinking, accuracy, and confidence.
For example, whenever we divide money among friends, divide a recipe into portions, or measure equal distances, we apply long division without knowing it in everyday life.
According to the National Education Policy (NEP 2020), developing problem-solving and logical reasoning boosts children's cognitive abilities and confidence. We created long division worksheets aligned with the NCERT/CBSE mathematics curriculum and NEP 2020 guidelines, which boost conceptual clarity and are suitable for every level of learners.
2. What Is Long Division? A Step-by-Step Breakdown
Long division is a step-wise method for dividing large numbers into smaller numbers. Students divide step-by-step by bringing down numbers and dividing the dividend digit by digit. This long division method can also be applied to multi-digit division problems.
With the help of worksheets, practice the long division questions consistently. This will help students with place value alignment, subtraction checks, remainders, and re-checking answers, which will build accuracy and confidence in problem-solving.
For every stage in the long division, follow the steps below in a cycle:
1. Divide - How many times does the divisor go into the given number
2. Multiply - multiply the quotient number by the divisor
3. Subtract - Subtract the result from the current number
4. Bring Down - Bring down the next digit of the dividend and repeat the same process until the Remainder is zero or non-divisible.
After finishing, cross-check the answer using the DQRD technique, i.e, Divisor x Quotient + Remainder = Dividend.
Let's see a few examples:
Example 1. 2-digit ÷ 1-digit
Problem: 84 ÷ 7
Step 1: Look at the first digit: does 7 go into 8 -> yes, 1 time
Step 2: Multiply: 1 x 7 = 7.
Step 3: Subtract 8-7 = 1.
Step 4: Bring down the next digit (4) -> 14 and repeat the steps.
Step 5: Divide: 7 goes into 14 -> Yes, 2 times
Step 6: Multiply 2 x 7 = 14
Step 7: Subtract: 14 - 14 = 0
Quotient: 12, and Remainder: 0.
Check: 7 x 12 + 0 = 84.
Example 2. 3-digit ÷ 2-digit (longer)
Problem: 432 ÷ 12
Step 1: Look at the first two digits (because 12 > 4): 43. How many times does 12 go into 43? → 3 times
Step 2: Multiply 3×12=36.
Step 3: Subtract: 43 − 36 = 7.
Step 4: Bring down the next digit (2) → 72 and repeat the steps.
Step 5: How many times does 12 go into 72? → 6 times
Step 6: Multiply 6×12=72
Step 7: Subtract: 72 − 72 = 0
Quotient = 36, Remainder 0.
Check: 12 × 36 + 0 = 432
3. How to Teach Long Division Easily Using Vedic Maths
Long division might be confusing, especially when you deal with larger numbers or decimals. But with Vedic Maths division tricks, division of any digit can be performed easily and quickly without any stress.
The Vedic Maths is derived from ancient scriptures called "The Vedas" and contains 16 sutras and 13-sub sutras (methods), which solve any math problem within seconds using mental math shortcuts.
At The Vedic Maths, we teach long division through concept-based techniques and shortcuts that simplify even complex division problems and build accuracy and confidence.
Vedic Maths Sutras that Simplify Division:
1. Nikhilam Sutra - All from 9 and last from 10.
Perfect for numbers close to the power of 10 — like 9, 99, 999, etc.
Nikhilam Sutra helps break down the division process into smaller complements, reducing calculation steps.
For example:
To divide 982 ÷ 9, instead of writing a long series of steps, we use 9's complement logic:
982 ÷ 9 = 109 remainder 1 (done mentally).
This saves time and enhances speed and accuracy.
2. Paravartya Yojayet Sutra - Transpose and Adjust
Useful when divisors are not near 10 (like 12, 23, 87).
It transposes the divisor into a simpler base (e.g., 12 → 10 + 2),
and then adjusts the quotient accordingly — a faster alternative to multi-step long division.
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Why learn with Mamta Rupesh?
Hear what students, parents, and teachers say about Mamta Rupesh’s teaching methodology. Her unique teaching method makes everyone fall in love with math and solve math problems smartly and clearly. Her real-world classroom insights help learners understand the concept easily and master it.
Testimonials from Students
Here are a few reviews from Parents
It has been wonderful experience for my granddaughter. Our brain is nothing but a number crunching machine. Vedic Maths sharpens the brain and improves this number crunching ability.
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Happy Grandfather, India
The most interesting and helpful class in the world,
The teacher always clears our doubts until we are clear about the concepts.
Her teaching style is very interactive. she keeps the class more fun also .Thank you mam for giving us a wonderful opportunity to learn with you.
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Happy Mother, UAE
I had enrolled my daughter for vedic math class with Miss Mamta and it was a good experience for her to learn the math concepts. Miss Mamta was patiently guiding through the course, helping out in case of doubts and flexible with kids. Thanks for sessions, it was really helpful.
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Ms Mamta is very warm and jovial. She made my child feel very comfortable. By sharing her own challenges in math in her early years and how she overcame these challenges she makes everything seem possible. During this short duration of the demo she showed atleast 5 tricks to solving problems there by piquing my daughter’s interest. We are very much looking forward to the classes with Ms Mamta.
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Happy Father, UAE
4. Free Printable Long Division Worksheets (Class-Wise)
Practice makes perfect; thus, consistent practice is the secret to mastering long division, so we created free printable class-wise long division worksheets with answers PDFs suitable for all levels of learners.
Each worksheet is created by certified Vedic Math educators and aligned with NCERT/CBSE learning outcomes, ensuring students practice what they learn according to the school curriculum.
These division worksheets, long division PDFs include practice problems, real-life word problems, and key answers suitable for home and classroom learning.
Let's see the Class-level long division worksheets:
1. Long Division Worksheets for Class 3
Perfect for beginners, these worksheets focus on:
- Basic division by single digits (e.g., 84 ÷ 7, 56 ÷ 8)
- Visual problems using pictures and groups to introduce the concept of division
- Real-life applications, such as sharing chocolates or candies equally among friends
2. Long Division Worksheets for Class 4
Class 4 worksheets include:
- 2-digit ÷ 1-digit and 3-digit ÷ 2-digit division problems
- Word problems (e.g., "If 432 candies are packed into 18 boxes, how many candies per box?")
- Answer key included for self-assessment.
These worksheets help students understand division of long numbers with a mix of long division sums.
3. Long Division Worksheets for Class 5
By Class 5, students are ready for complex problems involving:
- Division with remainders
- Decimal division (e.g., 56.4 ÷ 4)
- Multi-step division sums combining multiplication and subtraction
- Mixed word problems involving money, distance, and time
These worksheets include real-world logic-based challenges with answer keys for self-correction.
4. Long Division Worksheets for Class 6
Advanced learners can practice multi-digit and decimal division, fractions, and ratio-based questions.
Topics covered include:
- 4-digit ÷ 2-digit and 5-digit ÷ 3-digit long division
- Decimal and fractional division
- Applied problems (like dividing measurements or scaling quantities)
Each worksheet is designed for students with higher-order division problems, preparing them for Olympiads and other competitive exams.
These long division worksheet PDFs help students solve long division problems easily and learn the logic behind every step.
Each long division worksheet contains various long division questions, such as word problems, multiple-choice questions, etc., preparing children to answer any format of question they face.
They also contain key answers at the end, which help students check their answers independently, identify their mistakes, and correct them as soon as possible.
Download free long division worksheets with answers PDFs today and help your child master division easily and without stress.
5. Common Mistakes Students Make in Long Division
Even bright students sometimes stumble while solving division of long numbers, especially when dealing with multi-digit numbers and remainders.
Let's look at some common mistakes that Class 3-6 students make and find quick fixes.
1. Misplacing Digits in the Quotient
Many students write the quotient digit incorrectly, which shifts the entire calculation.
Fix: Always align the Quotient directly above the dividend digit you're dividing.
2. Forgetting to Bring Down the Next Digit
Students often stop too early after subtracting, missing the next step of bringing down the next number from the dividend.
Fix: Remember the smart rule — Divide → Multiply → Subtract → Bring Down → Repeat.
This sequence ensures no steps are skipped.
3. Ignoring or Misinterpreting the Remainder
Sometimes, students forget to include the Remainder or mistake it as part of the Quotient.
Fix: Always check:
Divisor × Quotient + Remainder = Dividend.
If this doesn't match, review the steps.
4. Confusing Divisor and Dividend
This is a very common error. Students may confuse numbers, dividing the smaller number by the larger one.
Fix:
Dividend ÷ Divisor = Quotient (with Remainder)
Example: In 84 ÷ 7 → 84 is the dividend, 7 is the divisor.
5. Skipping Zero in the Quotient
When a digit doesn't divide evenly, students skip writing "0" in the Quotient, throwing off the entire calculation.
Fix: Zeros hold place value importance — never skip them.
For example, 1,008 ÷ 12 → when dividing the "0" in the tens place, you must record a 0 in the Quotient.
Students can turn division errors into confident, accurate answers by understanding place value and stepwise calculation.
6. Long Division Word Problems (With Answers)
Real-world math helps students connect what they learn to what they experience in daily life. Practicing long division questions with answers helps students solve not only division problems but also think logically and apply their knowledge meaningfully.
Let's see a few word problems that strengthen reasoning and accuracy.
Question 1: Sharing Apples
A fruit seller has 96 apples. He wants to pack them equally into 8 boxes. How many apples will go in each box?
Solution: 96 ÷ 8 = 12
Answer: Each box will contain 12 apples.
Question 2: Dividing Money
Riya earned ₹2,160 from her art exhibition. She decided to share it equally among 6 friends.
How much money will each friend get?
Solution: 2160 ÷ 6 = 360
Answer: Each friend will receive ₹360.
Question 3: Distance Travelled
A car covers 1,125 km in 9 hours at a constant speed. What is the speed of the car per hour?
Solution: 1,125 ÷ 9 = 125
Answer: The car's speed is 125 km/hr.
Question 4: School Picnic Snacks
A school bought 1,296 cookies to distribute equally among 24 students.
How many cookies will each student receive?
Solution: 1,296 ÷ 24 = 54
Answer: Each student gets 54 cookies.
Question 5: Dividing Fabric Rolls
A tailor has 3,248 meters of cloth and wants to cut it into 8 equal pieces.
How long will each piece be?
Solution: 3,248 ÷ 8 = 406
Answer: Each piece will be 406 meters long.
Question 6: Sharing Chocolates
A box contains 2,730 chocolates. If each jar can hold 15 chocolates, how many jars are needed to pack all the chocolates?
Solution: 2,730 ÷ 15 = 182
Answer: 182 jars are needed.
Question 7: Travel Expenses
A family spent ₹18,540 on a trip for 6 days. What was their average expense per day?
Solution:
18,540 ÷ 6 = 3,090
Answer: The average daily expense was ₹3,090.
These long division questions with solutions suit students from Class 4 to 6. They help them apply long division to real-life situations such as shopping, sharing, travel, budgeting, measurement, etc.
Tip: Encourage students to write the division step: Dividend ÷ Divisor = Quotient before solving each problem, which builds clarity with no confusion.
7. Conclusion
Mastering long division is not just about performing division; it's about developing logical thinking and problem-solving ability that helps students learn math easily at any stage of life.
With the help of Vedic Maths techniques like Nikhilam sutra and Paravartya Yojayet Sutra and long division worksheets, students understand the long division concept clearly, with real-world problems, practice problems, key answers, and aligned as per NCERT/CBSE guidelines.
Every worksheet is designed to boost accuracy, confidence, and conceptual clarity, from basic single-digit division in Class 3 to complex multi-digit and decimal division in Class 6.
When children understand the concept clearly and the logic behind numbers and math operations, math becomes a life skill instead of a regular academic subject.
Join our Live Vedic Maths Classes or use our Vedic Maths Bundle Kit to learn quick division techniques using Vedic Maths from Mamta Rupesh.
Download your free long division worksheets with answers PDF today and help your child love math instead of feeling anxious.
8. FAQ's on Long Division Worksheets
1What is the easiest way to teach long division to students?
The easiest way to teach long division is to break it into simple steps: Divide, Multiply, Subtract, and Bring Down. Start with small numbers and use real-life examples, like sharing chocolates or apples. Once the child understands the concept clearly, gradually move to multi-digit division.
2How can Vedic Maths help in solving long division problems faster?
Vedic Maths simplifies long division using sutras like Nikhilam (All from 9 and the last from 10) and Paravartya Yojayet (Transpose and Adjust). These methods reduce multi-step calculations into quick mental calculations, helping students solve division problems more accurately.
3Are there free printable long division worksheets with answers?
Yes. The Vedic Maths offers free printable long division worksheets with answers for Classes 3 to 6. Each worksheet includes practice problems, word problems, and key answers for self-assessment, aligned with the NCERT/CBSE curriculum.
4What types of long division sums are included in these worksheets?
The worksheets contain problems ranging from single-digit division for beginners to multi-digit numbers, decimal numbers, and word problems for advanced learners. They include real-life math applications like sharing, distance, and money-based division problems.
5How often should students practice long division worksheets?
Students should practice at least 10–15 division questions daily. Regular practice builds speed, accuracy, and confidence, especially when paired with Vedic Maths techniques that make calculations faster and error-free.
6What’s the difference between short division and long division?
Short division is a quicker method used when divisors are small and the child can divide mentally. Long division, on the other hand, involves step-by-step division calculations — ideal for multi-digit numbers or when remainders are involved.
7How does long division help in higher mathematics?
Mastering long division builds a strong base for understanding fractions, decimals, ratios, and algebra. It also develops logical reasoning and problem-solving skills, which are essential for advanced math, Olympiads, and competitive exams.
8Can parents use these worksheets for home practice?
Absolutely. These worksheets are perfect for home learning. Parents can print them for daily practice, track progress using the answer keys, and help children confidently solve long division sums independently without a screen and stress.
9Are these long division worksheets suitable for CBSE and ICSE students?
Yes. The worksheets are designed according to NCERT/CBSE learning outcomes and are equally useful for ICSE or any other curriculum. They focus on conceptual clarity in mathematics.
10Where can I download free long division worksheets with answers?
You can download free Long Division Worksheets PDFs with Answers for Classes 3–6 from www.thevedicmaths.com. These include class-wise worksheets, real-world problems, and key answers for quick self-check.
