What is 180 divided by 11

Written dividing

Written dividing is today's topic. This method will help you divide large numbers on paper. You will first learn this for the case with no remainder. Then I'll show you how you can use the same method to divide with a remainder. As a more advanced topic, you will also find below how to divide point numbers. As a basis for written dividing with and without remainder, you should master the multiplication tables. So should you subtract writing can. We also show you all these basics in detail in ourMath tutoring. Let's get started!

Written dividing or dividing

Written division is one of the four basic arithmetic operations. To divide or “divide”, you divide a large number (the dividend) by a divisor (also called a divisor) and get the result (the quotient).

28                   :                   4                   =                   7 

Dividend divisor quotient

This type of division makes sense, especially for division tasks where the dividend goes far beyond the multiplication table, and it helps you to find a solution quickly. In addition, you should be able to solve small division problems so that you can divide easily in writing.

Background information on why written dividing is important, as well as further details, can be found, for example, on the page ofUniversity of Landau. But also in ours Homework assistance you will find a lot of information and exercises for written dividing.

Divide with remainder - Divide in writing

In order to understand how to divide in writing, I would like to briefly remind you of dividing with the rest.

Let's start with a simple division, for example 10: 5. You know for sure that the result is 2 because the 5 fits into the 10 exactly twice.
But because it also fits exactly twice into the 10, there is nothing left here. It looks different at 11: 5, for example. This division does not work, but since you already know that the 5 fits into the 10 twice, we can say that it also fits into the 11 twice.

So if a division doesn't work out, you can still enter the result as a division with remainder.

So: 11: 5 = 2 remainder 1

Half-written division

You can often divide large numbers without having to divide in writing, but with simple observations and simplifications. Let's take 192: 6 as an example.

First, you're looking for a number smaller than 192, which is a simple multiple of 6. Since you have 3 • 6 = 18 in your head, the 180 is well suited, because the 6 fits in here 30 times! That leaves 192 - 180 = 12. Here the 6 fits in twice and since 30 + 2 = 32, you have your result!

So it applies: 192 : 6 = 32

Written division declaration

Written dividing is based on dividing the (large) dividend step by step by the divider until you have the desired result (see Schipper / Dröge / Ebeling (2000)). The easiest way to do this is using the following scheme. I'll show you an example.

An example: sharing with large numbers

Now we recommend that you familiarize yourself with our topic of written multiplication. First, write down the division problem and leave enough space below the dividend and to the right of the equal sign. The sharing is now a repetition of the following four steps.

We take as an example: 5752 : 3

  1. Divide the first digit of the dividend by the divider (see orange arrow). Since the division 5: 3 does not work, we carry out a division with the remainder. It is 5: 3 = 1 remainder 2. We note the 1 to the right of the equal sign.
  2. Now multiply 1 by 3 (green arrow) and write the result 3 below the 5 by which we first divided.
  3. Now subtract the first digit of the dividend with the result of the multiplication.
  4. In the fourth step, you finally move the next digit of the dividend down to the right of the result of the subtraction (blue).

The number 27 is now your new starting point. Starting from here you repeat the above 4 steps up to the last digit of the dividend.

The first iteration should look like this:

At this point you have to be a little careful! Since the 2 is smaller than the 3, it fits zero times into the 3. So you write a zero next to the 9. The remaining steps now look like this:

So we have our result:The following applies: 5727: 3 = 1909!

On the website of theUniversity of Kassel you can find more excellent explanations and videos for written dividing.

A little special case

It can happen that the first digit of the dividend is smaller than the divisor. Take 123: 3 as an example. Here the 1 is smaller than the 3. Then you simply add the next digit, so start with 12: 3!

Danger!If the first digit of the dividend is too small, you add the next digit and then divide this number by the divisor.

Here is another complete example for the special case:

In the following you will see again the four steps of the written division for the special case that the first factor of the division is smaller than the divisor.

1. You divide the first digit of the dividend by the divisor. If it's too small, add the next digit of the dividend. Then write the result to the right of the equal sign

2. Multiply the result by the divisor and write the product under the number that you divided in the first step.

3. Subtract the numbers from steps 1) and 2)

4. Finally, move the next digit of the dividend down next to the result of the subtraction.

Now repeat all steps up to the last digit of the dividend!

For the written division, you divide the individual digits of the dividend one after the other by the divisor. You carry out the 4 steps "divide, multiply, subtract and move" one after the other. Then you repeat these four steps up to the last digit of the dividend. This method also helps you to divide by the remainder in writing or to divide the written decimal numbers.

Divide in writing with the remainder

The above scheme of the written division also gives you the desired remainder if the division does not work. It is the same as the last digit below, which has always been zero up to now:

Written division with a comma - not periodically

The nice thing about the above method for written division is that you can also easily do the written division with decimal numbers.

There are two rules to be observed here

  1. If you come to the point of the dividend, you also put the point in the result.
  2. You do the math until you get the remainder 0. If you are not finished with the last digit of the dividend, you add a zero.

Example: Division with a comma - not periodic

We take a look at the example of 12.6: 8:

Divide in writing with a comma - periodically

Since you only stop dividing with a comma when you have reached zero, you may get into a loop. In this case the result is periodic. As soon as you recognize the loop, you can enter the period in the result (cf. Bartnitzky, H / Brügelmann, H (2009)). We take the example 687: 11

Since the number 5 (see orange arrow) appears again as a result in the subtraction, the partial results will be repeated. So in the result you get the period 45 after the decimal point. Also remember to put the decimal point as soon as you have reached the decimal point of the dividend.

Table 1: Written dividing - an overview

In writing, dividing tasks with solutions

Now you are equipped with valuable knowledge for written sharing and can now apply the theory straight away in practice. We have created the written division worksheet for you so that you can practice what you have learned directly. Of course, we also provide you with the solutions to the division tasks with detailed explanations and solutions.

Dividing in writing means that you divide the individual digits of the dividend one after the other by the divider. You carry out the above four steps “divide, multiply, subtract and move” one after the other. Then you repeat these four steps up to the last digit of the dividend. This method also helps you to divide by the remainder in writing or to divide the decimal numbers in writing. Try our dividing exercises right now!You are also cordially invited to refresh your knowledge in the area of ​​written addition.

literature

Schipper, W. / Dröge, R. / Ebeling, A. (2000): Handbook for Math Lessons4th school year. Hanover:

Bartnitzky, H / Brügelmann, H (2009): Primary school course book,Frankfurt a.M .: Primary School Association.

FAQs for dividing

Why is dividing so important in writing?

The written division helps you to divide large numbers on the one hand, on the other hand this type of division can help you to divide with remainder or with commas. You will also encounter the polynomial division later, which is based on the written division.

What is necessary to prepare for the written division?

To divide in writing, you need a good knowledge of the multiplication table and how to divide smaller numbers with remainder. It is also an advantage if you are confident in subtracting. Our early childhood education is also an ideal preparation.

How does division work when the divider has more than one digit?

In the same way, you just have to make sure that the divisor is smaller than the digits of the dividend, as with ordinary written division. If not, you have to add more digits.

How can I check if the written division is correct?

There is a simple test for written division. All you have to do is multiply your result by the factor. If the dividend comes out here, you've calculated correctly!

Why do I need written dividing?

You can certainly use a calculator instead of dividing in this way. But in mathematics it is also important to learn entire procedures and to be able to calculate with as few errors as possible. It is also elementary for practicing mental arithmetic and for the multiplication tables. Also see it sporty and try to get faster in it!