Free long division calculator with step-by-step work. Shows quotient, remainder, decimal, mixed number, and visual division layout.
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Learning long division? Our free long division calculator shows you exactly how to solve any division problem with step-by-step work. Whether you're a student checking homework, a parent helping with math, or a teacher demonstrating the process, this calculator displays the complete long division procedure including quotient, remainder, decimal conversion, and mixed number form. See the traditional long division layout and verify your answers with the division relationship formula.
Long division is a method for dividing large numbers that breaks the problem into smaller, manageable steps. It involves dividing digit by digit, multiplying, subtracting, and bringing down the next digit repeatedly until all digits have been processed. The result includes a quotient (the answer) and sometimes a remainder (the leftover). Long division is fundamental in mathematics and helps develop understanding of place value, multiplication, and subtraction.
Division Equation
Dividend = Divisor × Quotient + RemainderSee every step of the long division process—divide, multiply, subtract, bring down—just like you'd write it on paper.
Get results as quotient with remainder, decimal, mixed number, and fraction—all at once.
View the traditional division bracket notation that matches textbook format.
Every answer is verified using the division equation: Dividend = Divisor × Quotient + Remainder.
Identifies repeating patterns in decimal results, like 1÷3 = 0.333...
Understand why each step happens with clear explanations alongside the math.
Works with multi-digit dividends and divisors, decimals, and negative numbers.
No signup required, solve as many division problems as you need at no cost.
Check your division homework and understand where you made mistakes by comparing step-by-step work.
Demonstrate the long division algorithm to students with clear, visual step-by-step examples.
Practice for math tests and exams by working through example problems and verifying your answers.
Split bills, divide quantities evenly, or allocate resources among groups.
Confirm integer division and modulo operation results when debugging code.
Convert improper fractions to decimals by dividing numerator by denominator.
Manual verification of computed division results for critical calculations.
Scale recipes up or down by dividing ingredient quantities.
Follow the DMSB method: (1) Divide - how many times does the divisor go into the current digits; (2) Multiply - multiply divisor by quotient digit; (3) Subtract - subtract product from current number; (4) Bring down - bring down the next digit. Repeat until no digits remain.
The fundamental formula is: Dividend = (Divisor × Quotient) + Remainder, or a = b × q + r. This also serves as your verification check to confirm your answer is correct.
Remainders can be expressed four ways: (1) as a remainder (25 ÷ 4 = 6 R1); (2) as a fraction (6¼); (3) as a decimal (6.25 by continuing division); or (4) as a mixed number. The remainder must always be less than the divisor.
The dividend is the number being divided (numerator). The divisor is what you divide by (denominator). The quotient is the answer. The remainder is what's left over after division. For example, in 25 ÷ 4 = 6 R1: 25 is dividend, 4 is divisor, 6 is quotient, 1 is remainder.
Multiply your quotient by the divisor, then add the remainder. If you get the original dividend, your answer is correct: (Quotient × Divisor) + Remainder = Dividend. For example: (6 × 4) + 1 = 25 ✓
Add zeros after the decimal point in the dividend and continue the division process. Place the decimal in the quotient directly above its position in the dividend. Keep dividing until you reach your desired precision or the remainder becomes zero.
A repeating decimal is a decimal that has a pattern of digits that repeats forever, like 1/3 = 0.333... (written as 0.3̄). This happens when the division produces a remainder that appeared before, creating an infinite loop.
When the divisor is larger, the whole number quotient is 0, and the entire dividend becomes the remainder. As a decimal, this gives a result less than 1. For example, 3 ÷ 7 = 0 R3 = 0.428...
Bringing down combines the remainder with the next digit to create a new number to divide. This is equivalent to dividing place values from left to right, working with hundreds, then tens, then ones.
Long division is typically introduced in 4th grade with single-digit divisors, then expanded in 5th-6th grade to multi-digit divisors and decimal dividends.
Short division writes remainders above the dividend and works faster for small divisors. Long division shows all work below the dividend in a structured layout, making it better for larger divisors or for learning the process.
Yes. Apply sign rules: positive ÷ positive = positive, negative ÷ positive = negative, positive ÷ negative = negative, negative ÷ negative = positive. Work with absolute values, then apply the correct sign to the result.