Long Division Calculator Perform step-by-step long division with remainders, decimals, and detailed explanations — perfec...

Long Division Calculator

Perform step-by-step long division with remainders, decimals, and detailed explanations — perfect for learning and verification.

Dividend (Numerator)

Divisor (Denominator)

Decimal Places

13

Quotient

0

Remainder

13.00

Decimal Result

13

Fraction Result

Long Division Formula

Basic Division

Dividend = Divisor × Quotient + Remainder

Fraction to Decimal

a/b = a ÷ b

Remainder

Remainder = Dividend - (Divisor × Quotient)

Verification

(Divisor × Quotient) + Remainder = Dividend

Step-by-Step Explanation

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Long Division Fundamentals

Long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand.

Key Components**:

• Dividend**: The number being divided (numerator)
• Divisor**: The number you are dividing by (denominator)
• Quotient**: The result of the division
• Remainder**: What's left over after division

Basic Formula**:

Dividend = Divisor × Quotient + Remainder

✅ Example**: 156 ÷ 12 = 13 with remainder 0, because 156 = 12 × 13 + 0.

Common Long Division Mistakes

⚠️ Avoid these frequent errors:

• Incorrect place value alignment**: Misaligning digits in the quotient
• Subtraction errors**: Incorrect subtraction during the division process
• Forgetting to bring down digits**: Skipping the "bring down" step
• Division by zero**: Divisor cannot be zero
• Decimal point placement**: Incorrect positioning when calculating decimals

✅ Best Practices**:

• Always align digits properly in columns
• Double-check each subtraction step
• Remember to bring down the next digit after each step
• For decimal division, add zeros to the dividend as needed
• Verify your answer using the basic division formula

Real-World Applications

Long division is essential in:

• Education**: Teaching fundamental arithmetic skills to students
• Budgeting**: Dividing expenses among multiple people or categories
• Cooking**: Scaling recipes up or down based on serving sizes
• Construction**: Calculating materials needed for projects
• Time Management**: Dividing time among different tasks or activities

📊 Example Use Cases**:

• Restaurant Bill**: $156 total ÷ 12 people = $13 per person
• Project Timeline**: 156 days ÷ 12 phases = 13 days per phase
• Baking Recipe**: 156 cookies ÷ 12 batches = 13 cookies per batch

How to Perform Long Division

Step-by-Step Process**:

1. Set up the problem**: Write dividend inside the division bracket, divisor outside
2. Divide**: Determine how many times the divisor goes into the first digit(s) of the dividend
3. Multiply**: Multiply the divisor by the quotient digit and write the result below
4. Subtract**: Subtract to find the remainder for this step
5. Bring down**: Bring down the next digit of the dividend
6. Repeat**: Continue the process until all digits are used
7. Handle remainder**: If there's a remainder, you can express it as a fraction or continue with decimals

Example**: 156 ÷ 12

• 12 goes into 15 once (12 × 1 = 12)
• Subtract: 15 - 12 = 3
• Bring down 6 → 36
• 12 goes into 36 three times (12 × 3 = 36)
• Subtract: 36 - 36 = 0
• Result: Quotient = 13, Remainder = 0