What is the formula for long division?

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.

How do you handle remainders in long division?

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.

What do dividend, divisor, quotient, and remainder mean?

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.

How do you check if long division is correct?

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 ✓

How do you do long division with decimals?

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.

What is a repeating decimal?

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 is the divisor larger than the dividend?

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...

Why do we 'bring down' the next digit?

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.

What grade is long division taught?

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.

What is the difference between short division and long division?

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.

Can you divide negative numbers with long division?

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.

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Long Division Calculator

Free long division calculator with step-by-step work. Shows quotient, remainder, decimal, mixed number, and visual division layout.

Example Problems

Dividend (number being divided)*

Divisor (number dividing by)*

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How to Do Long Division Step by Step

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.

What Is Long Division?

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 + Remainder

Why Use Our Long Division Calculator?

Complete Step-by-Step Work

See every step of the long division process—divide, multiply, subtract, bring down—just like you'd write it on paper.

Multiple Answer Formats

Get results as quotient with remainder, decimal, mixed number, and fraction—all at once.

Visual Long Division Layout

View the traditional division bracket notation that matches textbook format.

Automatic Verification

Every answer is verified using the division equation: Dividend = Divisor × Quotient + Remainder.

Repeating Decimal Detection

Identifies repeating patterns in decimal results, like 1÷3 = 0.333...

Educational Explanations

Understand why each step happens with clear explanations alongside the math.

Handles Any Numbers

Works with multi-digit dividends and divisors, decimals, and negative numbers.

Free and Unlimited

No signup required, solve as many division problems as you need at no cost.

How to Use the Long Division Calculator

When to Use Long Division

Homework Help

Check your division homework and understand where you made mistakes by comparing step-by-step work.

Teaching Tool

Demonstrate the long division algorithm to students with clear, visual step-by-step examples.

Test Preparation

Practice for math tests and exams by working through example problems and verifying your answers.

Real-World Calculations

Split bills, divide quantities evenly, or allocate resources among groups.

Programming Verification

Confirm integer division and modulo operation results when debugging code.

Fraction Conversion

Convert improper fractions to decimals by dividing numerator by denominator.

Engineering Calculations

Manual verification of computed division results for critical calculations.

Cooking and Recipes

Scale recipes up or down by dividing ingredient quantities.

Frequently Asked Questions

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.

How to Do Long Division Step by Step

What Is Long Division?

Division Equation

Dividend = Divisor × Quotient + Remainder