In arithmetic

Arithmetic

Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...

, short division is a procedure

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

 which breaks down a division

Division (mathematics)

right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...

 problem into a series of easy steps. As in all division problems, one number, called the dividend

Division (mathematics)

right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...

, is divided by another, called the divisor

Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...

, producing a result called the quotient

Quotient

In mathematics, a quotient is the result of division. For example, when dividing 6 by 3, the quotient is 2, while 6 is called the dividend, and 3 the divisor. The quotient further is expressed as the number of times the divisor divides into the dividend e.g. The quotient of 6 and 2 is also 3.A...

. Short division is an abbreviated form of long division

Long division

In arithmetic, long division is a standard procedure suitable for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a...

. Because it relies on mental arithmetic, it is suitable for use only if the divisor is a small number — typically less than 10.

Short division enables computations involving arbitrarily large dividends to be performed by following a series of simple steps.

Notation

Short division does not use the / (slash) or ÷ (obelus) signs, instead displaying the dividend, divisor, and (once it is found) quotient in a tableau. An example is shown below, representing the division of 500 by 4 (with a result of 125).

Example

The procedure involves several steps. As an example, consider the problem of 950 divided by 4:

1. The dividend and divisor are written in the short division tableau:
   
   
   Now instead of dividing the whole dividend (950) by the divisor (4), we will take as many digits of the dividend as necessary (starting from the left) to form a number that contains the divisor at least once, but less than ten times. In this case, that partial dividend is 9.
   
   
2. The first number to be divided by the divisor (4) is the partial dividend (9). We write the integer
   Integer
   The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
   
    part of the result (2) above the division bar over the leftmost digit of the dividend, and we write the remainder (1) as a small digit (or digits) to the above and to the right of the partial dividend (9).
   
   
   
3. Next we repeat step 2, using the small digits just written along with the next digit of the dividend to form a new partial dividend (15). Dividing the new partial dividend by the divisor (4), we write the results as before: the quotient above the next digit of the dividend, and the remainder to the right. (Here 15 divided by 4 is 3, with a remainder of 3.)
   
   
   
4. We repeat step 2 until there are no digits remaining in the dividend. (In this example, the next step is to find that 30 divided by 4 is 7, with a remainder of 2.) The number written above the bar (237) is the quotient, and the result of the last subtraction is the remainder for the entire problem (2).
   
   
   
5. The answer to the above example is expressed as 237 with remainder 2. Alternatively, one can continue the above procedure to produce a decimal answer. We continue the process by adding a decimal and zeroes as necessary to the right of the dividend, treating each zero as another digit of the dividend. Thus the next step in such a calculation would give the following:
   
   

See also

• Chunking (division)
  Chunking (division)
  In mathematics education at primary school level, chunking is an elementary approach for solving simple division questions, by repeated subtraction....
  
  
• Long division
  Long division
  In arithmetic, long division is a standard procedure suitable for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a...
  
  
• Fourier division
  Fourier division
  Fourier division or cross division is a pencil-and-paper method of division which helps to simplify the process when the divisor has more than two digits. It was invented by Joseph Fourier.-Method:...
  
  
• Elementary arithmetic
  Elementary arithmetic
  Elementary arithmetic is the simplified portion of arithmetic which is considered necessary and appropriate during primary education. It includes the operations of addition, subtraction, multiplication, and division. It is taught in elementary school....
  
  
• Division (digital)
  Division (digital)
  Several algorithms exist to perform division in digital designs. These algorithms fall into two main categories: slow division and fast division. Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring, non-performing restoring,...
  
  
• Arbitrary-precision arithmetic
  Arbitrary-precision arithmetic
  In computer science, arbitrary-precision arithmetic indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most ALU hardware, which typically...
  
  
• Polynomial long division
  Polynomial long division
  In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division...
  
  
• Synthetic division
  Synthetic division
  Synthetic division is a method of performing polynomial long division, with less writing and fewer calculations. It is mostly taught for division by binomials of the formx - a,\ but the method generalizes to division by any monic polynomial...
  
  

External links

• Alternative Division Algorithms: Double Division, Partial Quotients & Column Division, Partial Quotients Movie

• Lesson in Short Division: TheMathPage.com