Comprehensive long division calculator with detailed step-by-step solutions and long division with decimals. Learn how to do long division through interactive practice, long division examples, and printable long division worksheets. Perfect long division tool for students, teachers, and anyone mastering division algorithms.
Input the dividend (number to be divided) and divisor (number to divide by) into the long division calculator
Click "Calculate" to see the long division method applied with detailed step-by-step solutions
Learn from the detailed long division steps, understand the long division method, and master the concepts
Use long division practice mode and generate long division worksheets to improve your skills
Start with simple long division examples like 84 ÷ 4 = 21. Understanding each step of the long division method is key to mastering more complex long division problems.
Long division is a method for dividing large numbers by breaking the division process into a sequence of easier steps. It's called "long" because of the lengthy process and notation used.
The long division method follows these steps: Divide, Multiply, Subtract, Bring down. This process repeats until completion.
Master long division through detailed examples ranging from simple to complex problems. Each example demonstrates the complete long division method with step-by-step explanations.
Example 1: 84 ÷ 4 = ?
Step-by-step: 8÷4=2, 4÷4=1, answer is 21
Example 2: 96 ÷ 3 = ?
Step-by-step: 9÷3=3, 6÷3=2, answer is 32
Example 3: 144 ÷ 12 = ?
Step-by-step: 144÷12=12, using multiplication tables
Example 4: 156 ÷ 13 = ?
Long division steps: 15÷13=1 remainder 2, bring down 6, 26÷13=2
Example 5: 246 ÷ 6 = ?
Long division method: 24÷6=4, 6÷6=1, answer is 41
Example 6: 378 ÷ 14 = ?
Step-by-step: 37÷14=2 remainder 9, bring down 8, 98÷14=7
Example 7: 1248 ÷ 24 = ?
Long division: 124÷24=5 remainder 4, bring down 8, 48÷24=2
Example 8: 3456 ÷ 32 = ?
Multi-step: 345÷32=10 remainder 25, 256÷32=8, answer is 108
Example 9: 12.6 ÷ 3 = ?
Decimal division: 12÷3=4, 6÷3=2, place decimal correctly
Example 10: 15.75 ÷ 2.5 = ?
Convert to whole numbers: 1575÷25=63, adjust decimal place
Example 11: 85 ÷ 7 = ?
Complete long division: 7×12=84, 85-84=1 remainder
Example 12: 157 ÷ 11 = ?
Long division process: 11×14=154, 157-154=3 remainder
Use the long division method when dividing large numbers that cannot be easily divided mentally, for exact decimal results, and when teaching division concepts step by step.
Dividing profits, calculating averages, budget allocation
Teaching division concepts, homework problems, test preparation
Algorithm verification, precision calculations, decimal analysis
The long division method has evolved significantly throughout history. Ancient civilizations used various division techniques, from Egyptian doubling methods to Babylonian algorithms. The modern long division algorithm we use today was standardized during the Renaissance period.
Beyond the standard long division method, several alternative approaches exist. These include the chunking method, short division for simple cases, and the galley method used in medieval times.
Subtracts multiples of the divisor from the dividend
Simplified method for single-digit divisors
Medieval lattice-based division technique
Our long division calculator maintains high precision throughout calculations, ensuring accurate results for both simple and complex division problems. This precision is especially important when working with decimals.
Example: Precise decimal division
The long division algorithm is based on the division algorithm theorem: For any integers a and b (b ≠ 0), there exist unique integers q and r such that a = bq + r, where 0 ≤ r < |b|.
This fundamental equation underlies all long division calculations
Understanding the historical development and mathematical foundations of long division enhances appreciation for this fundamental algorithm. Whether using traditional long division method, long division calculator, or practicing with decimals, the core principles remain consistent across all applications.
Common Error:
Writing quotient digits in wrong positions during long division steps
Solution:
Always align quotient digits directly above the last digit of the dividend group being divided. Use our long division calculator to verify proper placement.
Common Error:
Stopping the long division process without bringing down all remaining digits
Solution:
Remember the long division method: Divide, Multiply, Subtract, Bring down. Continue until all digits are processed.
Common Error:
Making basic multiplication mistakes during long division calculations
Solution:
Review multiplication tables regularly. Use our multiplication chart tool to strengthen foundational skills before attempting complex long division.
Common Error:
Incorrectly placing decimal points in long division with decimals
Solution:
Place decimal point in quotient directly above decimal point in dividend. For decimal divisors, convert to whole numbers first.
Common Error:
Choosing quotient digits that are too large, requiring multiple corrections
Solution:
Start with smaller estimates and adjust up. Practice estimation skills with our interactive long division calculator.
Common Error:
Incorrect remainder calculations or forgetting to check if remainder is less than divisor
Solution:
Always verify: remainder must be less than divisor. Use multiplication to check: quotient × divisor + remainder = dividend.
Common Error:
Getting overwhelmed by large numbers or losing track of place values
Solution:
Break down large numbers systematically. Use our long division calculator to practice with different sized numbers and build confidence.
Common Error:
Not checking long division answers, leading to undetected errors
Solution:
Always verify by multiplying: quotient × divisor + remainder should equal original dividend.
The long division method is a systematic way to divide large numbers using the steps: divide, multiply, subtract, and bring down. Our long division calculator demonstrates each step clearly.
Follow these long division steps: 1) Divide the first digit(s), 2) Multiply quotient by divisor, 3) Subtract from dividend, 4) Bring down next digit, 5) Repeat until complete.
Start with simple long division examples: 84÷4, 96÷3, 144÷12. Then progress to long division with decimals and longer numbers for more challenging practice.
Long division with decimals follows the same steps but continues past the decimal point. Add zeros as needed and place the decimal point in the quotient directly above the dividend's decimal point.
Always verify your long division results by multiplying: quotient × divisor + remainder should equal the original dividend. Our calculator shows this verification for every calculation.
Our long division calculator includes a worksheet generator for creating printable long division practice problems with various difficulty levels and answer keys.
Enter dividend (number to divide) and divisor (number to divide by). Supports whole numbers, decimals, and negative numbers.
Shows complete long division method with each step clearly labeled: divide, multiply, subtract, bring down.
Automatically checks answers using multiplication: quotient × divisor + remainder = dividend.
Handles long division with decimals automatically, showing proper decimal placement in quotient.
Processes multi-digit numbers efficiently, perfect for complex long division problems.
Displays remainders as fractions when applicable, showing both forms of the answer.
Practice long division problems with timer functionality to improve speed and accuracy.
Choose from beginner, intermediate, and advanced long division problems matching your skill level.
Monitor accuracy rates and improvement over time with detailed performance statistics.
Generate long division worksheets with specific number ranges and problem types.
Automatic answer key generation with step-by-step solutions for teacher convenience.
Professional formatting optimized for printing, perfect for classroom use.
Efficiently handles very large numbers and complex decimal calculations.
Maintains high precision throughout calculations for accurate results.
Displays results in decimal form, with remainders, and as mixed numbers when appropriate.
Fully optimized for mobile devices, tablets, and desktop computers.
Efficient keyboard navigation for faster input and calculation.
Accessible design with proper ARIA labels for assistive technologies.
When to use: Single-digit divisors, simple calculations
Example: 246 ÷ 6 = 41 (can be done mentally)
Advantage: Faster for simple problems
When to use: Quick results, complex numbers
Example: 1357.89 ÷ 47.23 = 28.746...
Limitation: Doesn't show the process or build understanding
When to use: Approximate results, quick verification
Example: 198 ÷ 21 ≈ 200 ÷ 20 = 10
Use case: Checking if long division results are reasonable
Begin with easy long division examples like 84÷4 or 96÷3. Master these before moving to long division with larger numbers or decimals.
Remember: Divide, Multiply, Subtract, Bring down. This long division method sequence is the foundation for all long division problems.
Use our long division calculator's visual layout feature to see proper formatting. Neat organization prevents errors in long division steps.
Our practice mode offers timed long division problems with immediate feedback. Regular practice improves speed and accuracy in long division.
Before solving, estimate the answer. For 84÷4, think "4×20=80, so answer is about 21." This helps verify your long division result.
Use our worksheet generator to create customized long division practice sheets. Focus on specific difficulty levels for targeted learning.
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