Division, along with addition, subtraction, and multiplication, is one of the four standard arithmetic operations that today's students are required to master.
Long division enables mathematicians to use their knowledge of basic division facts to break a problem down into simple steps and find its solution, which for any division problem is known as the quotient.
In all division problems, the number that is being used to divide is called the divisor, while the number that is being divided is called the dividend. In long division problems, the dividend is at least 3 digits long.
Long division itself uses a multi-step process that students often remember by using the acronym DMSB, which stands for Divide, Multiply, Subtract, and Bring-down.
For example, if a problem has 210 as the dividend, and 5 as the divisor, the number 210 is divided by the digit 5.
If the first digit of the dividend is not divisible by the divisor, as in this case where 2 is not divisible by 5, the first two digits of the dividend are divided by the divisor (21 ÷ 5).
The second step of long division, multiply, is used to ascertain that 5 x 4 is 20. The 4 becomes the first digit of the quotient.
The next step of long division is the subtraction step. Because 5 x 4 has a product of 20, and because the actual number being divided was 21, subtraction can be used to find the remainder, which is 1 (21-20 = 1).
The final step in solving 210 ÷ 5 is the 'bring-down' step of long division. In this step the next digit of the dividend is 'brought down' and put to the right of the remainder.
In this example, that digit is a 0, so it is 'brought down' and put to the right of the 1 to make a 10.
To complete the long division problem, the DMSB steps are repeated, and the 10 is divided by 5. Because 5 x 2 = 10, there is no remainder and because no more digits remain in the dividend, the 2 is placed to the right of the 4 in the quotient, which is 42.
The answer to the long division problem 210 ÷ 5 is 42.
There are a variety of ways to set-up long division problems, and although there are alternative approaches, the DMSB method is one of the most common for solving long division on paper.