How to Do Long Division: Complete Step-by-Step Guide

Master long division with our comprehensive guide. Learn the process, practice with examples, and discover helpful tips and tricks.

Understanding Long Division

Long division is a method for dividing large numbers that might be difficult to compute mentally. It breaks down complex division problems into a series of simpler steps, making it easier to find accurate answers.

The Four Basic Steps of Long Division

  1. Divide: Determine how many times the divisor goes into the current digits
  2. Multiply: Multiply the quotient digit by the divisor
  3. Subtract: Subtract the product from the current digits
  4. Bring Down: Bring down the next digit and repeat

Remember: "Does McDonald's Sell Burgers?" - Divide, Multiply, Subtract, Bring down!

Step-by-Step Long Division Process

Example 1: 156 ÷ 12

Let's work through this example together:

Step 1: Set Up the Problem

Write the dividend (156) inside the division bracket and the divisor (12) outside:

      _______
12 | 156

Step 2: Divide the First Part

Look at the first digit or digits of the dividend that are greater than or equal to the divisor.

  • 12 doesn't go into 1, so look at 15
  • 12 goes into 15 once (12 × 1 = 12)
  • Write 1 above the 5 in 156

Step 3: Multiply and Subtract

  • Multiply: 1 × 12 = 12
  • Write 12 below 15
  • Subtract: 15 - 12 = 3

Step 4: Bring Down the Next Digit

  • Bring down the 6 to make 36
  • 12 goes into 36 three times (12 × 3 = 36)
  • Write 3 next to the 1 in the quotient
  • Subtract: 36 - 36 = 0

Final Answer

156 ÷ 12 = 13

Verification: 13 × 12 = 156 ✓

Example 2: Division with Remainders (847 ÷ 7)

Step-by-step solution:

  1. 7 goes into 8 once: 1 × 7 = 7, subtract: 8 - 7 = 1
  2. Bring down 4 to make 14
  3. 7 goes into 14 twice: 2 × 7 = 14, subtract: 14 - 14 = 0
  4. Bring down 7 to make 07
  5. 7 goes into 7 once: 1 × 7 = 7, subtract: 7 - 7 = 0

Answer: 847 ÷ 7 = 121 with remainder 0

Example 3: Division with Remainder (235 ÷ 6)

  1. 6 goes into 23 three times: 3 × 6 = 18, subtract: 23 - 18 = 5
  2. Bring down 5 to make 55
  3. 6 goes into 55 nine times: 9 × 6 = 54, subtract: 55 - 54 = 1

Answer: 235 ÷ 6 = 39 remainder 1

As a decimal: 235 ÷ 6 = 39.166...

Converting Remainders to Decimals

To continue division past a remainder and get a decimal answer:

  1. Add a decimal point to the quotient
  2. Add a zero to the remainder
  3. Continue dividing as normal
  4. Repeat until you get 0 or a repeating pattern

Example: 17 ÷ 4

  • 4 goes into 17 four times: 4 × 4 = 16, remainder 1
  • Add decimal point: 4.
  • Add 0 to remainder: 10
  • 4 goes into 10 twice: 2 × 4 = 8, remainder 2
  • Add another 0: 20
  • 4 goes into 20 five times: 5 × 4 = 20, remainder 0

Answer: 17 ÷ 4 = 4.25

Common Long Division Mistakes to Avoid

❌ Mistake #1: Wrong Placement

Make sure to write each quotient digit directly above the last digit you used from the dividend.

❌ Mistake #2: Skipping Zeros

If the divisor doesn't go into a number, write 0 in the quotient. Don't skip it!

❌ Mistake #3: Subtraction Errors

Double-check your subtraction. This is where most errors occur.

❌ Mistake #4: Forgetting to Bring Down

Always remember to bring down the next digit before continuing.

Tips for Mastering Long Division

💡 Pro Tips

  • Memorize multiplication tables: Knowing your times tables up to 12 makes long division much faster
  • Estimate first: Before starting, estimate what the answer should be (e.g., 156 ÷ 12 is about 150 ÷ 10 = 15)
  • Check your work: Multiply your answer by the divisor and add any remainder - you should get the original dividend
  • Use graph paper: This helps keep your numbers aligned properly
  • Practice regularly: Start with simple problems and gradually increase difficulty
  • Stay organized: Keep your work neat and aligned - it reduces errors

Practice Problems

Try these problems on your own, then check with our calculator:

Beginner Level

  1. 84 ÷ 7 = ?
  2. 144 ÷ 12 = ?
  3. 96 ÷ 8 = ?

Intermediate Level

  1. 456 ÷ 19 = ?
  2. 789 ÷ 13 = ?
  3. 1024 ÷ 16 = ?

Advanced Level

  1. 9876 ÷ 234 = ?
  2. 15625 ÷ 125 = ?
  3. 99999 ÷ 37 = ?

When to Use Long Division vs. Calculator

Use Long Division When:

  • Learning the concept
  • Showing your work for homework
  • No calculator available
  • Practicing math skills
  • Understanding the process

Use Our Calculator When:

  • Need quick answers
  • Checking your work
  • Working with large numbers
  • Need step-by-step verification
  • Learning from examples

Historical Context

Long division has been taught for centuries and remains a fundamental mathematical skill. The method we use today was developed in Europe during the Renaissance period and has remained largely unchanged because of its effectiveness and reliability.

Beyond Basic Division

Once you master long division, you can apply these skills to:

  • Polynomial division: Used in algebra
  • Fraction operations: Dividing fractions
  • Decimal division: Working with decimal numbers
  • Ratio and proportion: Real-world applications

Ready to Practice?

Use our free calculator to check your answers and see step-by-step solutions!

Try the Calculator

Conclusion

Long division is a valuable skill that builds mathematical understanding and problem-solving abilities. With practice and patience, anyone can master this technique. Remember to:

  • Take your time and work carefully
  • Check your work by multiplying back
  • Practice regularly with different problems
  • Use our calculator to verify your answers
  • Don't get discouraged - everyone makes mistakes while learning!

Have questions? Check our FAQ section or try our interactive calculator with step-by-step solutions.