, long division
is a method for division
of two real numbers
. It requires only the means to write the numbers down, and it simple to perform even for large dividends because the algorithm
separates a complex division problem into smaller problems. However, the procedure requires various numbers to be divided by the divisor
: this is simple with single-digit divisors, but becomes harder with larger ones.
Another form of long division is used for dividing polynomials - this process can be simplified using synthetic division.
This is long division notation for 500 ÷ 4 = 125:
The method involves several steps:
1. Write the dividend and divisor in this form:
In this example, 500 is the dividend and 4 is the divisor.
2. Consider the leftmost digit of the dividend (5). Find the largest multiple of the divisor that is less than the leftmost digit: in other words, mentally perform "5 divided by 4". If this digit is too small, consider the first two digits.
In this case, the largest multiple of 4 that is less than 5 is 4. Write this number under the leftmost digit of the dividend. Write the multiple divided by the divisor (4 divided by 4 = 1) above the line over the leftmost digit of the dividend.
3. Subtract the digit under the dividend from the digit used in the dividend. Write the result (remainder) (5 - 4 = 1)
under the bottom digit, then drop the zero (the second digit) to the right of it.
4. Repeat steps 2 and 3, except use the number you just created to divide by, and write above and under the second digit.
5. Repeat step 4 until there are no digits remaining in the dividend. The number written above the bar is the quotient, and the last remainder calculated is the remainder for the entire problem.