Dividend
The number being divided. Here, the dividend is 156.
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Long Division Explained
Learn long division using the divide, multiply, subtract, and bring-down process, then build confidence with guided interactive practice.
Long division is a method used to divide larger numbers by breaking the calculation into smaller, repeatable steps. You work through the dividend one digit at a time instead of trying to solve everything at once.
What Is Long Division?
Long division organizes a division problem so each part can be solved in order. At every stage, you decide how many times the divisor fits into the current number, record that quotient digit, and continue until all digits have been used.
The Repeated Pattern
Divide, multiply, subtract, and bring down. Repeat these four steps until there are no digits left to bring down.
Parts of a Division Problem
In the statement 156 ÷ 12 = 13, each number has a specific name.
Divisor
The number you divide by. Here, the divisor is 12.
Quotient
The result of the division. Here, the quotient is 13.
Remainder
The amount left over when the divisor does not divide evenly into the dividend.
Divide, Multiply, Subtract, and Bring Down
These four steps repeat as you work through each digit of the dividend.
Divide
Determine how many times the divisor fits into the current number.
Multiply
Multiply the quotient digit by the divisor and write the product below.
Subtract
Subtract the product from the number directly above it.
Bring Down
Bring down the next digit and repeat the same process.
Remember the Order
Always follow the same sequence: divide, multiply, subtract, bring down, and then repeat.
Long Division With Remainders
A remainder is the amount left after the final subtraction. The remainder must always be smaller than the divisor.
Example of a Remainder
Suppose a division problem ends with a quotient of 13 and an amount of 2 left over. The answer can be written as:
13 R2
Important Remainder Rule
A remainder cannot be equal to or greater than the divisor. If it is, the divisor can fit at least one more time.
How to Check a Long Division Answer
You can check a long division answer by multiplying the quotient by the divisor. If the problem has a remainder, add the remainder afterward.
The Checking Formula
Step 1:
Multiply the quotient by the divisor.
Step 2:
Add the remainder, if there is one.
Step 3:
Compare the result with the original
dividend.
Divisor × Quotient + Remainder = Dividend
Common Long Division Mistakes
Writing a Quotient Digit in the Wrong Place
Place each quotient digit directly above the dividend digit currently being used.
Forgetting to Multiply
After dividing, multiply the quotient digit by the divisor before subtracting.
Making a Subtraction Error
Check each subtraction carefully because one mistake can affect every later step.
Forgetting to Bring Down a Digit
Bring down one digit at a time after completing each subtraction.
Leaving a Remainder That Is Too Large
The remainder must always be smaller than the divisor.
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