How long division

I took a sneak peek at them completing a long division question in the arithmetic paper and watched them methodically work their way through it to achieve the correct answer. It was a case of long division made easy at last for this primary pupil, all thanks to the long division method explained below!

See the long division examples below, dividing 45, by First we show the short division method and then the long division method. With short division, children still need to work out the remainders. Many will need to do this via written subtraction anyway, and even if they can calculate them mentally, we all know how many mistakes are made by overconfident children when working at speed — especially when they refuse to write their workings-out!

Fear not! This is my tried and tested KS2 long division method when teaching Year 5 or Year 6. Warning: multiplication tables will be required! Recap short division, ensuring children can talk through the process. For example, you could ask:. Once children are confident with short division, they can move onto long division.

Of course, there are occasionally those that know their multiplication and division facts and can whizz through these — I know a few children who would quickly list multiples of 97 by adding and subtracting 3 each time, but until we have a class full of children that can do that without prompting, this method will be worth it! The first time I did this, it was one of those lessons which on the face of it looked intensely boring, but my Year 6 children got so carried away with their partitioning for long division that they even asked to stay into their lunchtime to finish the questions!

I ask the children to list nine multiples every time — asking them why you would only need nine multiples for any long division question is a good way of obtaining their understanding of the division process. Obviously, as they gain confidence in the method, they only need list as many as necessary. Firstly, I show them a completed modelled example:.

Then, I complete the division myself next to the modelled long division example to show them how I achieved it, always talking through each step as I go. Remember to work slowly through from the first digital of the dividend. I encourage the children to write the four symbols down on their page to remind themselves of the steps. They should have a solid understanding of these steps as, apart from the last one, they are the same as the short division process:.

This method is far more coherently explained in the context of a specific long division question. We are now working with the first three digits combined which has ensured that all the place values are correctly aligned.

This needs to be included in our next step. There is no remainder, so we know that the divisor must fit into the original number exactly. So our final answer is 12, divided by 24 is They can do this by multiplying their answer by the divisor to see if the original number is produced.

In arithmetic, long division is a standard division algorithm for dividing large numbers, breaking down a division problem into a series of easier steps.

It requires the construction of a tableau. Now, let us follow the steps given below to see how long division takes place. Given below are a few important points that would help you while working with long division:. Long division problems also include problems related to long division polynomials and long division with decimals.

When there are no common factors between the numerator and the denominator, or if you can't find the factors, you can use the long division process to simplify the expression. For more details about long division polynomials, visit the Dividing Polynomials page. Long division with decimals can be easily done just as the normal long division.

For more details about long division with decimals, visit the Dividing Decimals page. Example 1: Ron planted 75 trees equally in 3 rows. How many trees did he plant in each row? To find the number of trees in each row, we have to divide 75 by 3 because there is an equal number of trees in each of the three rows.

Calculate the amount given to each man. We have to calculate the amount given to each man. To do so, we have to divide by 25 using the long division method. The following steps explain the process of long division:.

Given below are the 5 main steps of long division. Put , the dividend, on the inside of the bracket. The dividend is the number you're dividing. Put 32, the divisor, on the outside of the bracket. The divisor is the number you're dividing by. Divide the first number of the dividend, 4 by the divisor, You can ignore the remainder for now.

Put the 0 on top of the division bracket. This is the beginning of the quotient answer. Next, multiply 0 by the divisor 32 and insert the result 0 below the first number of the dividend inside the bracket. Draw a line under the 0 and subtract 0 from 4. Bring down the next number of the dividend and insert it after the 4 so you have Divide 48 by the divisor, The answer is 1.