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LONG DIVISION vs SHORT DIVISION

As one of the division facts, division is the inverse of multiplication. We have learnt this in my previous article on Division Facts.

The division problem 20 ➗ 5 asks the question ‘what number multiplied by 5 gives 20?’ or indeed, ‘what number multiplied by 5 gives 20? We know that 4 x 5 = 20,

so 20 ➗ 5 = 4.

This looks quite simple and straightforward. However, solving division problems becomes more challenging with larger numbers. There are therefore two main methods used in working out division problems: They are the short division and the long division methods. The short division works well in dividing by 12 or less because we usually learn times table up to 12 x 12.

In short division, the numbers in a division problem can have the bus shelter (bus stop) arrangement or in the form of a fraction. Shall we try the following example :

156 ➗ 12 ; This can be written with the bus shelter as 12 Г156 and to calculate this we take each digit of the dividend (number in shelter) starting from the left and asking how many times the divisor (number outside shelter) can divide it.

From the example above, how many times does 12 go into (divide) 1? It is 0 times. So we write 0 directly on top of 1. The number 1 is now a remainder so it is carried over to the next column, turning 5 to 15.

The next question is how many times does 12 go into 15? It is 1 remainder 3. We then write 1 exactly on top of the bus shelter, in line with 15 and the remainder 3, carried over to the 6, making it 36.

How many times does 12 go into 36? It is 3 times. So 156 ➗ 12 = 13. The zero written on top of 1 and before the 1 as quotient is insignificant.

The other short method is in the form of a fraction and the division involves simplifying (cancellation). So 156 ➗ 12 will be 156/12 and this will be cancelled out or divided with a common factor. 4 is a common factor for both numbers: 4 will divide 12 into 3; and 156 into 39. Now the fraction becomes 39/3; 3 is also a common factor that can divide 3 ( into 1 ) and 39 ( into 13). So the fraction is simplified to 3/1 which is equal to 13.

The next method which is the traditional algorithm for division is long division. When larger numbers are involved in division problems, their remainders get larger and become much difficult to calculate in your head.

This is where long division comes in to help set it all out neatly and let's you do a subtraction to work out the remainder. We will be using 3 models of doing long division: The shelter / bus stop model; the Chunking model; and the Rectangular array or Box / Area model.

In long division, there are steps we need to follow: First we divide; then multiply; the third step is to subtract; and the fourth step is to bring over. Remainder is always less than the divisor. An example of long division using the bus stop (shelter )method may look like this.

The shelter / bus stop model:

The Chunking model

This method adds up the chunks or groups of the divisor.

The Rectangular Array or Area / Box method

With this method the number of boxes are based on the number of digits the quotient will have. The whole dividend is written in the first box whiles the divisor is written outside the array and on the left side; just like the bus stop model.

Below are links to long division and short division worksheets for you to practise.

https://www.mathsisfun.com/worksheets/long-division.php

https://www.mathsisfun.com/worksheets/print.php?w=54520

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