The **Division** is one of the **Basic arithmetic** in the **Mathematics**. You will find these very often during your school years, so you should be able to use them. To do this, we will help you not only with the **Explanations** in this text and different **Examples**, but also with **Exercises**.

## Properties of the Division

The **Division** is defined in mathematics as the counterpart of the **Multiplication** denotes. There are for the individual terms of a **Division** certain names. This is the name of the number **divided** becomes, **Dividend**. The number through which the **Dividend** is divided, one calls **Divisor**. Finally, the result of a **Division** as **Quotient**.

### Note

### Note

The symbol for the **Division** is the $\large \; \; :$

The **Technical terms** for a division are: **Dividend** **: divisor = quotient**

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## Examples of division

Here we give a few **Examples** for the **Division of numbers**. In the beginning smaller numbers up to 10, in the last examples the numbers go beyond 10.

Let us imagine the task.

We have exactly **6 apples** bought from the supermarket. These we want to find out with our two friends **divide**, so that each of us **three** has the same number of apples. So we calculate the **6 apples through 3**. So we look how often the 3 fits into the 6. It is exactly 2 times. So everyone gets exactly 2 apples. We proceed in the same way with the other tasks. But it can also happen that you have a **Remainder** receive. We then write this as follows:

$7 \; : \; 2 \; = \; 3 \; remainder \; 1$

Here the $2$ fits into the $7$ exactly $3$ times, but there is still a $1$ left over, so the $remainder \; 1$.

### Example

### Example

More **Examples** **the** **Division** are:

$5 \; : \; 3 \; = \; 1\; remainder \; 2 $

$15 \; : \; 2 \; = \; 7\; remainder \; 1$

## Written division

There are at the **Division** also the possibility to divide in writing. Here the two numbers which are to be divided are written next to each other as always, but one calculates step by step among each other. This is a very good method, especially with large numbers, to quickly arrive at the correct **Solution** to come.

Let’s have a look at the **written division** on an example:

In the figure we see that first the two numbers are written down one after the other. The next step is to consider how many times the divisor fits into the **first** **number** fits. Since this one is a $1$, it doesn’t fit in a time. Thus, we consider how often the divisor in the first **both numbers** fits.

We find out that the number $4$ fits exactly 2 times into the number 11, so there is a **Rest** from $3$ gives. This one we enter one line lower, here marked in $\textcolor$ and write the **next number** next to it, so here the $\textcolor$. Now let’s look again at how often the **Divisor** fits into the number. The result is exactly $8$ times. Thus, the solution for dividing $112 \; : \; 4$ exactly $28$. There remains no **remainder**. This is the procedure for **written** **Division**.

*To deepen this topic look also again in the Exercises!*