# Basic arithmetic: this is how division works

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

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.

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

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!