Long Division Calculator
Perform long division with complete step-by-step solution. Get quotient, remainder, decimal result, fraction form, and mixed number representation.
The number you want to divide
The number you are dividing by
Number of decimal places in result
What is long division and when do you use it?
Long division is a method to divide large numbers step-by-step. Parts: Dividend (number being divided), Divisor (dividing by), Quotient (result), Remainder (leftover). Example: 157 ÷ 12 → Quotient = 13, Remainder = 1 (because 12×13 + 1 = 157). Use when: Dividing large numbers without calculator, teaching division concepts, finding exact quotients and remainders, converting fractions to decimals. Algorithm: Divide, Multiply, Subtract, Bring down (repeat). Essential for: Elementary math, fraction simplification, modular arithmetic, programming.
How do you perform long division step by step?
Steps using 456 ÷ 12: 1) Divide: 12 into 45 goes 3 times (write 3 above). 2) Multiply: 3 × 12 = 36 (write below 45). 3) Subtract: 45 - 36 = 9. 4) Bring down: Next digit (6) → 96. 5) Repeat: 12 into 96 goes 8 times. 6) Multiply: 8 × 12 = 96. 7) Subtract: 96 - 96 = 0. Result: 456 ÷ 12 = 38 remainder 0. If remainder ≠ 0: Either leave as remainder or continue dividing for decimals. Check: Divisor × Quotient + Remainder = Dividend (12 × 38 + 0 = 456).
What is the difference between quotient and remainder?
Quotient: How many times divisor goes into dividend (whole number part). Remainder: What is left over (must be less than divisor). Example: 17 ÷ 5 → Quotient = 3, Remainder = 2 (because 5×3 = 15, and 17-15 = 2). Mathematical notation: 17 = 5 × 3 + 2 or 17 ÷ 5 = 3 R 2. As decimal: 17 ÷ 5 = 3.4 (quotient with decimal). As fraction: 17/5 = 3 2/5 (mixed number). Remainder is always: 0 ≤ remainder < divisor. Division with remainder is exact when remainder = 0.
How do you convert division with remainder to a decimal or fraction?
To decimal: Continue long division, adding decimal point. Example: 7 ÷ 4 = 1.75 (1 remainder 3 → 30 ÷ 4 = 7.5 → 20 ÷ 4 = 5). To mixed number: Quotient becomes whole part, remainder/divisor becomes fraction. Example: 17 ÷ 5 = 3 2/5. To improper fraction: Just write dividend/divisor. Example: 17/5. Repeating decimals: If division never ends, use bar notation. Example: 1 ÷ 3 = 0.333... = 0.3̄. Terminating vs repeating: Terminates if denominator has only factors of 2 and 5 (after simplification).
What are common mistakes in long division and how to avoid them?
Mistake 1: Wrong placement - Write quotient digits directly above dividend digits being divided. Mistake 2: Bringing down too early - Complete multiply and subtract before bringing down next digit. Mistake 3: Remainder > divisor - If remainder ≥ divisor, quotient digit is too small (increase it). Mistake 4: Forgetting to check - Verify: divisor × quotient + remainder = dividend. Mistake 5: Decimal point errors - Align decimal points when bringing down. Tips: Estimate first (40 ÷ 5 ≈ 8), work neatly with columns aligned, check each step, practice with smaller numbers first.