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Long Division Calculator

Perform long division with step-by-step solutions, visual representations, and comprehensive educational content. Calculate quotients, remainders, mixed numbers, and decimal results—the world's best long division calculator.

Calculate Long Division

Dividend

Divisor

Introduction to Division

Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. Division is the inverse operation of multiplication. If we multiply a number by another number and then divide the result by the same number, we get back the original number.

Division represents the number of times a given number goes into another number. For example, 8 divided by 4 equals 2, which means 4 goes into 8 exactly 2 times.

Division Notations:

8 ÷ 4 = 2

8/4 = 2

84= 2

Understanding the different parts of a division problem is essential for performing long division correctly and interpreting the results.

Components of Division

A division problem consists of three main components:

Dividend: The number being divided (the total amount).
Divisor: The number by which we divide (how many groups we're creating).
Quotient: The result of the division (how many times the divisor fits into the dividend).

Example: When dividing 9 objects into groups of 4:

9 ÷ 4 = 2 R1

This means we can make 2 complete groups of 4, with 1 object remaining. The quotient is 2, and the remainder is 1.

Visual Representation:

dividend8÷4=2

divisorquotient

division symbolequal sign

How to Perform Long Division?

Long division is a method for dividing large numbers by breaking the division into a series of simpler steps. Let's work through an example: 100 ÷ 7.

Step 1: Set up the problem

Write the dividend (100) under the division symbol and the divisor (7) outside. Start by looking at the first digit of the dividend.

7/1

Since 7 doesn't go into 1, we write 0 above and move to the next step.

Step 2: Bring down the next digit

Combine the first digit with the second digit to form a number that the divisor can divide into.

7/10

-7

Now we have 10, and 7 goes into 10 once (1 × 7 = 7).

Step 3: Subtract and bring down

Subtract 7 from 10 to get 3, then bring down the next digit (0) to make 30.

7/100

-7

10 - 7 = 3, bring down 0 to make 30.

Step 4: Continue the process

Determine how many times 7 goes into 30. 7 × 4 = 28, so we write 4 above and subtract 28 from 30 to get 2.

14 R2

7/100

-7

-28

At this point, we have a remainder of 2. For whole number division: 100 ÷ 7 = 14 R2

Step 5: Convert to decimal (optional)

To get a decimal result, add a decimal point and zeros to the dividend, then continue the division process.

14.285714...

7/100.000

Continue dividing: 20 ÷ 7 = 2 remainder 6, 60 ÷ 7 = 8 remainder 4, and so on.

Step 6: Final results

The division can result in:

Terminating decimal: The division ends with a remainder of 0 (e.g., 8 ÷ 4 = 2.0)
Repeating decimal: The remainder pattern repeats (e.g., 1 ÷ 3 = 0.333...)
Mixed number: A whole number with a fraction (e.g., 14 2/7)

100 ÷ 7 = 14 R2

= 14 2/7

= 14.285714285714...

Division Formulas and Properties

Basic Division Formula

Dividend ÷ Divisor = Quotient

When there is a remainder: Dividend = (Divisor × Quotient) + Remainder

Division Properties

Division by 1: Any number divided by 1 equals itself (a ÷ 1 = a)
Division by itself: Any number divided by itself equals 1 (a ÷ a = 1, where a ≠ 0)
Division by zero: Division by zero is undefined
Zero divided by any number: 0 ÷ a = 0 (where a ≠ 0)
Commutative property: Division is NOT commutative (a ÷ b ≠ b ÷ a)
Associative property: Division is NOT associative ((a ÷ b) ÷ c ≠ a ÷ (b ÷ c))

Converting Between Forms

Remainder to Fraction:

Quotient R Remainder = Quotient + (Remainder / Divisor)

Example: 14 R2 = 14 + (2/7) = 14 2/7

Fraction to Decimal:

Perform long division on the fraction: Numerator ÷ Denominator

Example: 2/7 = 2 ÷ 7 = 0.285714...

Checking Your Answer

To verify a division result, use the inverse operation (multiplication):

(Divisor × Quotient) + Remainder = Dividend

Example: (7 × 14) + 2 = 98 + 2 = 100 ✓